{-# OPTIONS_GHC -Wunused-imports #-}

{-# LANGUAGE NondecreasingIndentation #-}

-- | Unification algorithm for specializing datatype indices, as described in
--     \"Unifiers as Equivalences: Proof-Relevant Unification of Dependently
--     Typed Data\" by Jesper Cockx, Dominique Devriese, and Frank Piessens
--     (ICFP 2016).
--
--   This is the unification algorithm used for checking the left-hand side
--   of clauses (see @Agda.TypeChecking.Rules.LHS@), coverage checking (see
--   @Agda.TypeChecking.Coverage@) and indirectly also for interactive case
--   splitting (see @Agda.Interaction.MakeCase@).
--
--   A unification problem (of type @UnifyState@) consists of:
--
--   1. A telescope @varTel@ of free variables, some or all of which are
--      flexible (as indicated by @flexVars@).
--
--   2. A telescope @eqTel@ containing the types of the equations.
--
--   3. Left- and right-hand sides for each equation:
--      @varTel ⊢ eqLHS : eqTel@ and @varTel ⊢ eqRHS : eqTel@.
--
--   The unification algorithm can end in three different ways:
--   (type @UnificationResult@):
--
--   - A *positive success* @Unifies (tel, sigma, ps)@ with @tel ⊢ sigma : varTel@,
--     @tel ⊢ eqLHS [ varTel ↦ sigma ] ≡ eqRHS [ varTel ↦ sigma ] : eqTel@,
--     and @tel ⊢ ps : eqTel@. In this case, @sigma;ps@ is an *equivalence*
--     between the telescopes @tel@ and @varTel(eqLHS ≡ eqRHS)@.
--
--   - A *negative success* @NoUnify err@ means that a conflicting equation
--     was found (e.g an equation between two distinct constructors or a cycle).
--
--   - A *failure* @UnifyStuck err@ means that the unifier got stuck.
--
--   The unification algorithm itself consists of two parts:
--
--   1. A *unification strategy* takes a unification problem and produces a
--      list of suggested unification rules (of type @UnifyStep@). Strategies
--      can be constructed by composing simpler strategies (see for example the
--      definition of @completeStrategyAt@).
--
--   2. The *unification engine* @unifyStep@ takes a unification rule and tries
--      to apply it to the given state, writing the result to the UnifyOutput
--      on a success.
--
--   The unification steps (of type @UnifyStep@) are the following:
--
--   - *Deletion* removes a reflexive equation @u =?= v : a@ if the left- and
--     right-hand side @u@ and @v@ are (definitionally) equal. This rule results
--     in a failure if --without-K is enabled (see \"Pattern Matching Without K\"
--     by Jesper Cockx, Dominique Devriese, and Frank Piessens (ICFP 2014).
--
--   - *Solution* solves an equation if one side is (eta-equivalent to) a
--     flexible variable. In case both sides are flexible variables, the
--     unification strategy makes a choice according to the @chooseFlex@
--     function in @Agda.TypeChecking.Rules.LHS.Problem@.
--
--   - *Injectivity* decomposes an equation of the form
--     @c us =?= c vs : D pars is@ where @c : Δc → D pars js@ is a constructor
--     of the inductive datatype @D@ into a sequence of equations
--     @us =?= vs : delta@. In case @D@ is an indexed datatype,
--     *higher-dimensional unification* is applied (see below).
--
--   - *Conflict* detects absurd equations of the form
--     @c₁ us =?= c₂ vs : D pars is@ where @c₁@ and @c₂@ are two distinct
--     constructors of the datatype @D@.
--
--   - *Cycle* detects absurd equations of the form @x =?= v : D pars is@ where
--     @x@ is a variable of the datatype @D@ that occurs strongly rigid in @v@.
--
--   - *EtaExpandVar* eta-expands a single flexible variable @x : R@ where @R@
--     is a (eta-expandable) record type, replacing it by one variable for each
--     field of @R@.
--
--   - *EtaExpandEquation* eta-expands an equation @u =?= v : R@ where @R@ is a
--     (eta-expandable) record type, replacing it by one equation for each field
--     of @R@. The left- and right-hand sides of these equations are the
--     projections of @u@ and @v@.
--
--   - *LitConflict* detects absurd equations of the form @l₁ =?= l₂ : A@ where
--     @l₁@ and @l₂@ are distinct literal terms.
--
--   - *StripSizeSuc* simplifies an equation of the form
--     @sizeSuc x =?= sizeSuc y : Size@ to @x =?= y : Size@.
--
--   - *SkipIrrelevantEquation@ removes an equation between irrelevant terms.
--
--   - *TypeConInjectivity* decomposes an equation of the form
--     @D us =?= D vs : Set i@ where @D@ is a datatype. This rule is only used
--     if --injective-type-constructors is enabled.
--
--   Higher-dimensional unification (new, does not yet appear in any paper):
--   If an equation of the form @c us =?= c vs : D pars is@ is encountered where
--   @c : Δc → D pars js@ is a constructor of an indexed datatype
--   @D pars : Φ → Set ℓ@, it is in general unsound to just simplify this
--   equation to @us =?= vs : Δc@. For this reason, the injectivity rule in the
--   paper restricts the indices @is@ to be distinct variables that are bound in
--   the telescope @eqTel@. But we can be more general by introducing new
--   variables @ks@ to the telescope @eqTel@ and equating these to @is@:
--   @
--       Δ₁(x : D pars is)Δ₂
--        ≃
--       Δ₁(ks : Φ)(x : D pars ks)(ps : is ≡Φ ks)Δ₂
--   @
--   Since @ks@ are distinct variables, it's now possible to apply injectivity
--   to the equation @x@, resulting in the following new equation telescope:
--   @
--     Δ₁(ys : Δc)(ps : is ≡Φ js[Δc ↦ ys])Δ₂
--   @
--   Now we can solve the equations @ps@ by recursively calling the unification
--   algorithm with flexible variables @Δ₁(ys : Δc)@. This is called
--   *higher-dimensional unification* since we are unifying equality proofs
--   rather than terms. If the higher-dimensional unification succeeds, the
--   resulting telescope serves as the new equation telescope for the original
--   unification problem.

module Agda.TypeChecking.Rules.LHS.Unify
  ( UnificationResult
  , UnificationResult'(..)
  , NoLeftInv(..)
  , unifyIndices'
  , unifyIndices ) where

import Prelude hiding (null)

import Control.Monad.State  ( gets, modify, evalStateT )
import Control.Monad.Writer ( WriterT(..), MonadWriter(..) )
import Control.Monad.Except ( runExceptT )

import Data.Semigroup hiding (Arg)
import qualified Data.List as List
import qualified Data.IntSet as IntSet
import qualified Data.IntMap as IntMap
import Data.IntMap (IntMap)

import qualified Agda.Benchmarking as Bench

import Agda.Interaction.Options (optInjectiveTypeConstructors)

import Agda.Syntax.Common
import Agda.Syntax.Internal

import Agda.TypeChecking.Monad
import qualified Agda.TypeChecking.Monad.Benchmark as Bench
import Agda.TypeChecking.Conversion.Pure (pureEqualTermB, pureEqualTypeB)
import Agda.TypeChecking.Constraints ()
import Agda.TypeChecking.Datatypes
import Agda.TypeChecking.Irrelevance
import Agda.TypeChecking.Reduce
import qualified Agda.TypeChecking.Patterns.Match as Match
import Agda.TypeChecking.Pretty
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Telescope
import Agda.TypeChecking.Free
import Agda.TypeChecking.Free.Precompute
import Agda.TypeChecking.Free.Reduce
import Agda.TypeChecking.Records

import Agda.TypeChecking.Rules.LHS.Problem
import Agda.TypeChecking.Rules.LHS.Unify.Types
import Agda.TypeChecking.Rules.LHS.Unify.LeftInverse

import Agda.Utils.Either
import Agda.Utils.Function
import Agda.Utils.Functor
import Agda.Utils.List
import Agda.Utils.ListT
import Agda.Utils.Maybe
import Agda.Utils.Monad
import Agda.Utils.Null
import Agda.Utils.PartialOrd
import Agda.Utils.Singleton
import Agda.Utils.Size

import Agda.Utils.Impossible


-- | Result of 'unifyIndices'.
type UnificationResult = UnificationResult'
  ( Telescope                  -- @tel@
  , PatternSubstitution        -- @sigma@ s.t. @tel ⊢ sigma : varTel@
  , [NamedArg DeBruijnPattern] -- @ps@    s.t. @tel ⊢ ps    : eqTel @
  )

type FullUnificationResult = UnificationResult'
  ( Telescope                  -- @tel@
  , PatternSubstitution        -- @sigma@ s.t. @tel ⊢ sigma : varTel@
  , [NamedArg DeBruijnPattern] -- @ps@    s.t. @tel ⊢ ps    : eqTel @
  , Either NoLeftInv (Substitution, Substitution) -- (τ,leftInv)
  )

data UnificationResult' a
  = Unifies  a                        -- ^ Unification succeeded.
  | NoUnify  NegativeUnification      -- ^ Terms are not unifiable.
  | UnifyBlocked Blocker              -- ^ Unification got blocked on a metavariable
  | UnifyStuck   [UnificationFailure] -- ^ Some other error happened, unification got stuck.
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-- | Unify indices.
--
--   In @unifyIndices gamma flex a us vs@,
--
--   * @us@ and @vs@ are the argument lists to unify, eliminating type @a@.
--
--   * @gamma@ is the telescope of free variables in @us@ and @vs@.
--
--   * @flex@ is the set of flexible (instantiable) variabes in @us@ and @vs@.
--
--   The result is the most general unifier of @us@ and @vs@.
unifyIndices
  :: Maybe NoLeftInv -- ^ Do we have a reason for not computing a left inverse?
  -> Telescope       -- ^ @gamma@
  -> FlexibleVars    -- ^ @flex@
  -> Type            -- ^ @a@
  -> Args            -- ^ @us@
  -> Args            -- ^ @vs@
  -> TCM UnificationResult
unifyIndices :: Maybe NoLeftInv
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  :: Maybe NoLeftInv -- ^ Do we have a reason for not computing a left inverse?
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  -> FlexibleVars  -- ^ @flex@
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  -> Args          -- ^ @us@
  -> Args          -- ^ @vs@
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forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Telescope -> m Doc
prettyTCM Telescope
tel
          , (TCMT IO Doc
"flex =" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+>) (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Nat -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Functor m => Nat -> m Doc -> m Doc
nest Nat
2 (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Telescope -> TCMT IO Doc -> TCMT IO Doc
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext Telescope
tel (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ String -> TCMT IO Doc
forall (m :: * -> *). Applicative m => String -> m Doc
text (String -> TCMT IO Doc) -> String -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ [Nat] -> String
forall a. Show a => a -> String
show ([Nat] -> String) -> [Nat] -> String
forall a b. (a -> b) -> a -> b
$ (FlexibleVar Nat -> Nat) -> FlexibleVars -> [Nat]
forall a b. (a -> b) -> [a] -> [b]
map FlexibleVar Nat -> Nat
forall a. FlexibleVar a -> a
flexVar FlexibleVars
flex
          , (TCMT IO Doc
"a    =" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+>) (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Nat -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Functor m => Nat -> m Doc -> m Doc
nest Nat
2 (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Telescope -> TCMT IO Doc -> TCMT IO Doc
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext Telescope
tel (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Functor m => m Doc -> m Doc
parens (Type -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Type -> m Doc
prettyTCM Type
a)
          , (TCMT IO Doc
"us   =" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+>) (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Nat -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Functor m => Nat -> m Doc -> m Doc
nest Nat
2 (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Telescope -> TCMT IO Doc -> TCMT IO Doc
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext Telescope
tel (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ [TCMT IO Doc] -> TCMT IO Doc
forall (m :: * -> *) (t :: * -> *).
(Applicative m, Foldable t) =>
t (m Doc) -> m Doc
prettyList ([TCMT IO Doc] -> TCMT IO Doc) -> [TCMT IO Doc] -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ (Arg Term -> TCMT IO Doc) -> [Arg Term] -> [TCMT IO Doc]
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Arg Term -> m Doc
prettyTCM [Arg Term]
us
          , (TCMT IO Doc
"vs   =" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+>) (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Nat -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Functor m => Nat -> m Doc -> m Doc
nest Nat
2 (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ Telescope -> TCMT IO Doc -> TCMT IO Doc
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext Telescope
tel (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ [TCMT IO Doc] -> TCMT IO Doc
forall (m :: * -> *) (t :: * -> *).
(Applicative m, Foldable t) =>
t (m Doc) -> m Doc
prettyList ([TCMT IO Doc] -> TCMT IO Doc) -> [TCMT IO Doc] -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ (Arg Term -> TCMT IO Doc) -> [Arg Term] -> [TCMT IO Doc]
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Arg Term -> m Doc
prettyTCM [Arg Term]
vs
          ]
    initialState    <- Telescope
-> FlexibleVars
-> Type
-> [Arg Term]
-> [Arg Term]
-> TCMT IO UnifyState
forall (m :: * -> *).
PureTCM m =>
Telescope
-> FlexibleVars -> Type -> [Arg Term] -> [Arg Term] -> m UnifyState
initUnifyState Telescope
tel FlexibleVars
flex Type
a [Arg Term]
us [Arg Term]
vs
    reportSDoc "tc.lhs.unify" 20 $ "initial unifyState:" <+> prettyTCM initialState
    (result,log) <- runUnifyLogT $ unify initialState rightToLeftStrategy
    forM result $ \ UnifyState
s -> do -- Unifies case
        let output :: UnifyOutput
output = [UnifyOutput] -> UnifyOutput
forall a. Monoid a => [a] -> a
mconcat [UnifyOutput
output | (UnificationStep UnifyState
_ UnifyStep
_ UnifyOutput
output,UnifyState
_) <- UnifyLog
log ]
        let ps :: [NamedArg (Pattern' DBPatVar)]
ps = Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
applySubst (UnifyOutput -> PatternSubstitution
unifyProof UnifyOutput
output) ([NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a b. (a -> b) -> a -> b
$ Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a t. DeBruijn a => Tele (Dom t) -> [NamedArg a]
teleNamedArgs (UnifyState -> Telescope
eqTel UnifyState
initialState)
        tauInv <- do
          strict     <- (TCEnv -> Bool) -> TCMT IO Bool
forall (m :: * -> *) a. MonadTCEnv m => (TCEnv -> a) -> m a
asksTC TCEnv -> Bool
envSplitOnStrict
          cubicalCompatible <- cubicalCompatibleOption
          withoutK <- withoutKOption
          case linv of
            Just NoLeftInv
reason -> Either NoLeftInv (Substitution, Substitution)
-> TCMT IO (Either NoLeftInv (Substitution, Substitution))
forall a. a -> TCMT IO a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (NoLeftInv -> Either NoLeftInv (Substitution, Substitution)
forall a b. a -> Either a b
Left NoLeftInv
reason)
            Maybe NoLeftInv
Nothing
              | Bool
strict            -> Either NoLeftInv (Substitution, Substitution)
-> TCMT IO (Either NoLeftInv (Substitution, Substitution))
forall a. a -> TCMT IO a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (NoLeftInv -> Either NoLeftInv (Substitution, Substitution)
forall a b. a -> Either a b
Left NoLeftInv
SplitOnStrict)
              | Bool
cubicalCompatible -> UnifyState
-> UnifyLog
-> TCMT IO (Either NoLeftInv (Substitution, Substitution))
forall (tcm :: * -> *).
(PureTCM tcm, MonadError TCErr tcm) =>
UnifyState
-> UnifyLog -> tcm (Either NoLeftInv (Substitution, Substitution))
buildLeftInverse UnifyState
initialState UnifyLog
log
              | Bool
withoutK          -> Either NoLeftInv (Substitution, Substitution)
-> TCMT IO (Either NoLeftInv (Substitution, Substitution))
forall a. a -> TCMT IO a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (NoLeftInv -> Either NoLeftInv (Substitution, Substitution)
forall a b. a -> Either a b
Left NoLeftInv
NoCubical)
              | Bool
otherwise         -> Either NoLeftInv (Substitution, Substitution)
-> TCMT IO (Either NoLeftInv (Substitution, Substitution))
forall a. a -> TCMT IO a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (NoLeftInv -> Either NoLeftInv (Substitution, Substitution)
forall a b. a -> Either a b
Left NoLeftInv
WithKEnabled)
        reportSDoc "tc.lhs.unify" 20 $ "ps:" <+> pretty ps
        return $ (varTel s, unifySubst output, ps, tauInv)



type UnifyStrategy = UnifyState -> ListT TCM UnifyStep


--UNUSED Liang-Ting Chen 2019-07-16
--leftToRightStrategy :: UnifyStrategy
--leftToRightStrategy s =
--    msum (for [0..n-1] $ \k -> completeStrategyAt k s)
--  where n = size $ eqTel s

rightToLeftStrategy :: UnifyStrategy
rightToLeftStrategy :: UnifyStrategy
rightToLeftStrategy UnifyState
s =
    [ListT TCM UnifyStep] -> ListT TCM UnifyStep
forall (t :: * -> *) (m :: * -> *) a.
(Foldable t, MonadPlus m) =>
t (m a) -> m a
msum ([Nat] -> (Nat -> ListT TCM UnifyStep) -> [ListT TCM UnifyStep]
forall (m :: * -> *) a b. Functor m => m a -> (a -> b) -> m b
for (Nat -> [Nat]
forall a. Integral a => a -> [a]
downFrom Nat
n) ((Nat -> ListT TCM UnifyStep) -> [ListT TCM UnifyStep])
-> (Nat -> ListT TCM UnifyStep) -> [ListT TCM UnifyStep]
forall a b. (a -> b) -> a -> b
$ \Nat
k -> Nat -> UnifyStrategy
completeStrategyAt Nat
k UnifyState
s)
  where n :: Nat
n = Telescope -> Nat
forall a. Sized a => a -> Nat
size (Telescope -> Nat) -> Telescope -> Nat
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
s

completeStrategyAt :: Int -> UnifyStrategy
completeStrategyAt :: Nat -> UnifyStrategy
completeStrategyAt Nat
k UnifyState
s = [ListT TCM UnifyStep] -> ListT TCM UnifyStep
forall (t :: * -> *) (m :: * -> *) a.
(Foldable t, MonadPlus m) =>
t (m a) -> m a
msum ([ListT TCM UnifyStep] -> ListT TCM UnifyStep)
-> [ListT TCM UnifyStep] -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ ((Nat -> UnifyStrategy) -> ListT TCM UnifyStep)
-> [Nat -> UnifyStrategy] -> [ListT TCM UnifyStep]
forall a b. (a -> b) -> [a] -> [b]
map (\Nat -> UnifyStrategy
strat -> Nat -> UnifyStrategy
strat Nat
k UnifyState
s) ([Nat -> UnifyStrategy] -> [ListT TCM UnifyStep])
-> [Nat -> UnifyStrategy] -> [ListT TCM UnifyStep]
forall a b. (a -> b) -> a -> b
$
-- ASR (2021-02-07). The below eta-expansions are required by GHC >=
-- 9.0.1 (see Issue #4955).
    [ (\Nat
n -> Nat -> UnifyStrategy
skipIrrelevantStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
basicUnifyStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
literalStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
dataStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
etaExpandVarStrategy  Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
etaExpandEquationStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
injectiveTypeConStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
injectivePragmaStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
simplifySizesStrategy Nat
n)
    , (\Nat
n -> Nat -> UnifyStrategy
checkEqualityStrategy Nat
n)
    ]

-- | @isHom n x@ returns x lowered by n if the variables 0..n-1 don't occur in x.
--
-- This is naturally sensitive to normalization.
isHom :: (Free a, Subst a) => Int -> a -> Maybe a
isHom :: forall a. (Free a, Subst a) => Nat -> a -> Maybe a
isHom Nat
n a
x = do
  Bool -> Maybe ()
forall b (m :: * -> *). (IsBool b, MonadPlus m) => b -> m ()
guard (Bool -> Maybe ()) -> Bool -> Maybe ()
forall a b. (a -> b) -> a -> b
$ All -> Bool
getAll (All -> Bool) -> All -> Bool
forall a b. (a -> b) -> a -> b
$ SingleVar All -> IgnoreSorts -> a -> All
forall a c t.
(IsVarSet a c, Free t) =>
SingleVar c -> IgnoreSorts -> t -> c
runFree (Bool -> All
All (Bool -> All) -> (Nat -> Bool) -> SingleVar All
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Nat -> Nat -> Bool
forall a. Ord a => a -> a -> Bool
>= Nat
n)) IgnoreSorts
IgnoreNot a
x
  a -> Maybe a
forall a. a -> Maybe a
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> Maybe a) -> a -> Maybe a
forall a b. (a -> b) -> a -> b
$ Nat -> a -> a
forall a. Subst a => Nat -> a -> a
raise (-Nat
n) a
x

findFlexible :: Int -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible :: Nat -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible Nat
i FlexibleVars
flex = (FlexibleVar Nat -> Bool)
-> FlexibleVars -> Maybe (FlexibleVar Nat)
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Maybe a
List.find ((Nat
i Nat -> Nat -> Bool
forall a. Eq a => a -> a -> Bool
==) (Nat -> Bool)
-> (FlexibleVar Nat -> Nat) -> FlexibleVar Nat -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FlexibleVar Nat -> Nat
forall a. FlexibleVar a -> a
flexVar) FlexibleVars
flex

basicUnifyStrategy :: Int -> UnifyStrategy
basicUnifyStrategy :: Nat -> UnifyStrategy
basicUnifyStrategy Nat
k UnifyState
s = do
  Equal dom@Dom{unDom = a} u v <- Equality -> ListT TCM Equality
forall (m :: * -> *).
(HasBuiltins m, HasOptions m) =>
Equality -> m Equality
eqUnLevel (Nat -> UnifyState -> Equality
getEquality Nat
k UnifyState
s)
    -- Andreas, 2019-02-23: reduce equality for the sake of isHom?
  ha <- fromMaybeMP $ isHom n a
  (mi, mj) <- addContext (varTel s) $ (,) <$> isEtaVar u ha <*> isEtaVar v ha
  reportSDoc "tc.lhs.unify" 30 $ "isEtaVar results: " <+> text (show [mi,mj])
  case (mi, mj) of
    (Just Nat
i, Just Nat
j)
     | Nat
i Nat -> Nat -> Bool
forall a. Eq a => a -> a -> Bool
== Nat
j -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero -- Taken care of by checkEqualityStrategy
    (Just Nat
i, Just Nat
j)
     | Just FlexibleVar Nat
fi <- Nat -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible Nat
i FlexibleVars
flex
     , Just FlexibleVar Nat
fj <- Nat -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible Nat
j FlexibleVars
flex -> do
       let choice :: FlexChoice
choice = FlexibleVar Nat -> FlexibleVar Nat -> FlexChoice
forall a. ChooseFlex a => a -> a -> FlexChoice
chooseFlex FlexibleVar Nat
fi FlexibleVar Nat
fj
           firstTryLeft :: ListT TCM UnifyStep
firstTryLeft  = [ListT TCM UnifyStep] -> ListT TCM UnifyStep
forall (t :: * -> *) (m :: * -> *) a.
(Foldable t, MonadPlus m) =>
t (m a) -> m a
msum [ UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Nat
-> Dom Type -> FlexibleVar Nat -> Term -> Either () () -> UnifyStep
Solution Nat
k Dom Type
dom{unDom = ha} FlexibleVar Nat
fi Term
v Either () ()
forall {b}. Either () b
left)
                                , UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Nat
-> Dom Type -> FlexibleVar Nat -> Term -> Either () () -> UnifyStep
Solution Nat
k Dom Type
dom{unDom = ha} FlexibleVar Nat
fj Term
u Either () ()
forall {a}. Either a ()
right)]
           firstTryRight :: ListT TCM UnifyStep
firstTryRight = [ListT TCM UnifyStep] -> ListT TCM UnifyStep
forall (t :: * -> *) (m :: * -> *) a.
(Foldable t, MonadPlus m) =>
t (m a) -> m a
msum [ UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Nat
-> Dom Type -> FlexibleVar Nat -> Term -> Either () () -> UnifyStep
Solution Nat
k Dom Type
dom{unDom = ha} FlexibleVar Nat
fj Term
u Either () ()
forall {a}. Either a ()
right)
                                , UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (Nat
-> Dom Type -> FlexibleVar Nat -> Term -> Either () () -> UnifyStep
Solution Nat
k Dom Type
dom{unDom = ha} FlexibleVar Nat
fi Term
v Either () ()
forall {b}. Either () b
left)]
       String -> Nat -> TCMT IO Doc -> ListT TCM ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
40 (TCMT IO Doc -> ListT TCM ()) -> TCMT IO Doc -> ListT TCM ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"fi = " TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> String -> TCMT IO Doc
forall (m :: * -> *). Applicative m => String -> m Doc
text (FlexibleVar Nat -> String
forall a. Show a => a -> String
show FlexibleVar Nat
fi)
       String -> Nat -> TCMT IO Doc -> ListT TCM ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
40 (TCMT IO Doc -> ListT TCM ()) -> TCMT IO Doc -> ListT TCM ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"fj = " TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> String -> TCMT IO Doc
forall (m :: * -> *). Applicative m => String -> m Doc
text (FlexibleVar Nat -> String
forall a. Show a => a -> String
show FlexibleVar Nat
fj)
       String -> Nat -> TCMT IO Doc -> ListT TCM ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
40 (TCMT IO Doc -> ListT TCM ()) -> TCMT IO Doc -> ListT TCM ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"chooseFlex: " TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> String -> TCMT IO Doc
forall (m :: * -> *). Applicative m => String -> m Doc
text (FlexChoice -> String
forall a. Show a => a -> String
show FlexChoice
choice)
       case FlexChoice
choice of
         FlexChoice
ChooseLeft   -> ListT TCM UnifyStep
firstTryLeft
         FlexChoice
ChooseRight  -> ListT TCM UnifyStep
firstTryRight
         FlexChoice
ExpandBoth   -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero -- This should be taken care of by etaExpandEquationStrategy
         FlexChoice
ChooseEither -> ListT TCM UnifyStep
firstTryRight
    (Just Nat
i, Maybe Nat
_)
     | Just FlexibleVar Nat
fi <- Nat -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible Nat
i FlexibleVars
flex -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat
-> Dom Type -> FlexibleVar Nat -> Term -> Either () () -> UnifyStep
Solution Nat
k Dom Type
dom{unDom = ha} FlexibleVar Nat
fi Term
v Either () ()
forall {b}. Either () b
left
    (Maybe Nat
_, Just Nat
j)
     | Just FlexibleVar Nat
fj <- Nat -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible Nat
j FlexibleVars
flex -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat
-> Dom Type -> FlexibleVar Nat -> Term -> Either () () -> UnifyStep
Solution Nat
k Dom Type
dom{unDom = ha} FlexibleVar Nat
fj Term
u Either () ()
forall {a}. Either a ()
right
    (Maybe Nat, Maybe Nat)
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
  where
    flex :: FlexibleVars
flex = UnifyState -> FlexibleVars
flexVars UnifyState
s
    n :: Nat
n = UnifyState -> Nat
eqCount UnifyState
s
    left :: Either () b
left = () -> Either () b
forall a b. a -> Either a b
Left (); right :: Either a ()
right = () -> Either a ()
forall a b. b -> Either a b
Right ()

dataStrategy :: Int -> UnifyStrategy
dataStrategy :: Nat -> UnifyStrategy
dataStrategy Nat
k UnifyState
s = do
  Equal Dom{unDom = a} u v <- Equality -> ListT TCM Equality
forall (m :: * -> *). HasBuiltins m => Equality -> m Equality
eqConstructorForm (Equality -> ListT TCM Equality)
-> ListT TCM Equality -> ListT TCM Equality
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< Equality -> ListT TCM Equality
forall (m :: * -> *).
(HasBuiltins m, HasOptions m) =>
Equality -> m Equality
eqUnLevel (Equality -> ListT TCM Equality)
-> ListT TCM Equality -> ListT TCM Equality
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< Nat -> UnifyState -> ListT TCM Equality
forall (m :: * -> *).
(MonadReduce m, MonadAddContext m) =>
Nat -> UnifyState -> m Equality
getReducedEqualityUnraised Nat
k UnifyState
s
  sortOk <- reduce (getSort a) <&> \case
    Type{} -> Bool
True
    Inf{}  -> Bool
True
    SSet{} -> Bool
True
    Sort
_      -> Bool
False
  case unEl a of
    Def QName
d Elims
es | Bool
sortOk -> do
      npars <- ListT TCM (Maybe Nat) -> ListT TCM Nat
forall (m :: * -> *) a. MonadPlus m => m (Maybe a) -> m a
catMaybesMP (ListT TCM (Maybe Nat) -> ListT TCM Nat)
-> ListT TCM (Maybe Nat) -> ListT TCM Nat
forall a b. (a -> b) -> a -> b
$ QName -> ListT TCM (Maybe Nat)
forall (m :: * -> *). HasConstInfo m => QName -> m (Maybe Nat)
getNumberOfParameters QName
d
      let (pars,ixs) = splitAt npars $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
      reportSDoc "tc.lhs.unify" 40 $ addContext (varTel s `abstract` eqTel s) $
        "Found equation at datatype " <+> prettyTCM d
         <+> " with parameters " <+> prettyTCM (raise (size (eqTel s) - k) pars)
      case (u, v) of
        (Con ConHead
c ConInfo
_ Elims
_   , Con ConHead
c' ConInfo
_ Elims
_  ) | ConHead
c ConHead -> ConHead -> Bool
forall a. Eq a => a -> a -> Bool
== ConHead
c' -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat
-> Type
-> QName
-> [Arg Term]
-> [Arg Term]
-> ConHead
-> UnifyStep
Injectivity Nat
k Type
a QName
d [Arg Term]
pars [Arg Term]
ixs ConHead
c
        (Con ConHead
c ConInfo
_ Elims
_   , Con ConHead
c' ConInfo
_ Elims
_  ) -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Type -> QName -> [Arg Term] -> Term -> Term -> UnifyStep
Conflict Nat
k Type
a QName
d [Arg Term]
pars Term
u Term
v
        (Var Nat
i []  , Term
v         ) -> Nat -> Term -> ListT TCM UnifyStep -> ListT TCM UnifyStep
forall {m :: * -> *} {a} {b}.
(ForceNotFree a, Reduce a, MonadReduce m, Free a, MonadPlus m) =>
Nat -> a -> m b -> m b
ifOccursStronglyRigid Nat
i Term
v (ListT TCM UnifyStep -> ListT TCM UnifyStep)
-> ListT TCM UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Type -> QName -> [Arg Term] -> Nat -> Term -> UnifyStep
Cycle Nat
k Type
a QName
d [Arg Term]
pars Nat
i Term
v
        (Term
u         , Var Nat
j []  ) -> Nat -> Term -> ListT TCM UnifyStep -> ListT TCM UnifyStep
forall {m :: * -> *} {a} {b}.
(ForceNotFree a, Reduce a, MonadReduce m, Free a, MonadPlus m) =>
Nat -> a -> m b -> m b
ifOccursStronglyRigid Nat
j Term
u (ListT TCM UnifyStep -> ListT TCM UnifyStep)
-> ListT TCM UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Type -> QName -> [Arg Term] -> Nat -> Term -> UnifyStep
Cycle Nat
k Type
a QName
d [Arg Term]
pars Nat
j Term
u
        (Term, Term)
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
    Term
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
  where
    ifOccursStronglyRigid :: Nat -> a -> m b -> m b
ifOccursStronglyRigid Nat
i a
u m b
ret = do
        -- Call forceNotFree to reduce u as far as possible
        -- around any occurrences of i
        (_ , u) <- IntSet -> a -> m (IntMap IsFree, a)
forall a (m :: * -> *).
(ForceNotFree a, Reduce a, MonadReduce m) =>
IntSet -> a -> m (IntMap IsFree, a)
forceNotFree (Nat -> IntSet
forall el coll. Singleton el coll => el -> coll
singleton Nat
i) a
u
        case flexRigOccurrenceIn i u of
          Just FlexRig
StronglyRigid -> m b
ret
          Maybe FlexRig
_ -> m b
forall a. m a
forall (m :: * -> *) a. MonadPlus m => m a
mzero

checkEqualityStrategy :: Int -> UnifyStrategy
checkEqualityStrategy :: Nat -> UnifyStrategy
checkEqualityStrategy Nat
k UnifyState
s = do
  let Equal Dom{unDom :: forall t e. Dom' t e -> e
unDom = Type
a} Term
u Term
v = Nat -> UnifyState -> Equality
getEquality Nat
k UnifyState
s
      n :: Nat
n = UnifyState -> Nat
eqCount UnifyState
s
  ha <- Maybe Type -> ListT TCM Type
forall (m :: * -> *) a. MonadPlus m => Maybe a -> m a
fromMaybeMP (Maybe Type -> ListT TCM Type) -> Maybe Type -> ListT TCM Type
forall a b. (a -> b) -> a -> b
$ Nat -> Type -> Maybe Type
forall a. (Free a, Subst a) => Nat -> a -> Maybe a
isHom Nat
n Type
a
  return $ Deletion k ha u v

literalStrategy :: Int -> UnifyStrategy
literalStrategy :: Nat -> UnifyStrategy
literalStrategy Nat
k UnifyState
s = do
  let n :: Nat
n = UnifyState -> Nat
eqCount UnifyState
s
  Equal Dom{unDom = a} u v <- Equality -> ListT TCM Equality
forall (m :: * -> *).
(HasBuiltins m, HasOptions m) =>
Equality -> m Equality
eqUnLevel (Equality -> ListT TCM Equality) -> Equality -> ListT TCM Equality
forall a b. (a -> b) -> a -> b
$ Nat -> UnifyState -> Equality
getEquality Nat
k UnifyState
s
  ha <- fromMaybeMP $ isHom n a
  (u, v) <- reduce (u, v)
  case (u , v) of
    (Lit Literal
l1 , Lit Literal
l2)
     | Literal
l1 Literal -> Literal -> Bool
forall a. Eq a => a -> a -> Bool
== Literal
l2  -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Type -> Term -> Term -> UnifyStep
Deletion Nat
k Type
ha Term
u Term
v
     | Bool
otherwise -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Type -> Literal -> Literal -> UnifyStep
LitConflict Nat
k Type
ha Literal
l1 Literal
l2
    (Term, Term)
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero

etaExpandVarStrategy :: Int -> UnifyStrategy
etaExpandVarStrategy :: Nat -> UnifyStrategy
etaExpandVarStrategy Nat
k UnifyState
s = do
  Equal Dom{unDom = a} u v <- Equality -> ListT TCM Equality
forall (m :: * -> *).
(HasBuiltins m, HasOptions m) =>
Equality -> m Equality
eqUnLevel (Equality -> ListT TCM Equality)
-> ListT TCM Equality -> ListT TCM Equality
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< Nat -> UnifyState -> ListT TCM Equality
forall (m :: * -> *).
(MonadReduce m, MonadAddContext m) =>
Nat -> UnifyState -> m Equality
getReducedEquality Nat
k UnifyState
s
  shouldEtaExpand u v a s `mplus` shouldEtaExpand v u a s
  where
    -- TODO: use IsEtaVar to check if the term is a variable
    shouldEtaExpand :: Term -> Term -> Type -> UnifyStrategy
    shouldEtaExpand :: Term -> Term -> Type -> UnifyStrategy
shouldEtaExpand (Var Nat
i Elims
es) Term
v Type
a UnifyState
s = do
      fi       <- Maybe (FlexibleVar Nat) -> ListT TCM (FlexibleVar Nat)
forall (m :: * -> *) a. MonadPlus m => Maybe a -> m a
fromMaybeMP (Maybe (FlexibleVar Nat) -> ListT TCM (FlexibleVar Nat))
-> Maybe (FlexibleVar Nat) -> ListT TCM (FlexibleVar Nat)
forall a b. (a -> b) -> a -> b
$ Nat -> FlexibleVars -> Maybe (FlexibleVar Nat)
findFlexible Nat
i (UnifyState -> FlexibleVars
flexVars UnifyState
s)
      reportSDoc "tc.lhs.unify" 50 $
        "Found flexible variable " <+> text (show i)
      -- Issue 2888: Do this if there are only projections or if it's a singleton
      -- record or if it's unified against a record constructor term. Basically
      -- we need to avoid EtaExpandEquation if EtaExpandVar is possible, or the
      -- forcing translation is unhappy.
      let k  = UnifyState -> Nat
varCount UnifyState
s Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
- Nat
1 Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
- Nat
i -- position of var i in telescope
          b0 = Dom Type -> Type
forall t e. Dom' t e -> e
unDom (Dom Type -> Type) -> Dom Type -> Type
forall a b. (a -> b) -> a -> b
$ Nat -> UnifyState -> Dom Type
getVarTypeUnraised Nat
k UnifyState
s
      b         <- addContext (telFromList $ take k $ telToList $ varTel s) $ reduce b0
      (d, pars) <- catMaybesMP $ isEtaRecordType b
      ps        <- fromMaybeMP $ allProjElims es
      guard =<< orM
        [ pure $ not $ null ps
        , isRecCon v  -- is the other term a record constructor?
        , (Right True ==) <$> runBlocked (isSingletonRecord d pars)
        ]
      reportSDoc "tc.lhs.unify" 50 $
        "with projections " <+> prettyTCM (map snd ps)
      reportSDoc "tc.lhs.unify" 50 $
        "at record type " <+> prettyTCM d
      return $ EtaExpandVar fi d pars
    shouldEtaExpand Term
_ Term
_ Type
_ UnifyState
_ = ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero

    isRecCon :: Term -> f Bool
isRecCon (Con ConHead
c ConInfo
_ Elims
_) = Maybe (QName, RecordData) -> Bool
forall a. Maybe a -> Bool
isJust (Maybe (QName, RecordData) -> Bool)
-> f (Maybe (QName, RecordData)) -> f Bool
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName -> f (Maybe (QName, RecordData))
forall (m :: * -> *).
HasConstInfo m =>
QName -> m (Maybe (QName, RecordData))
isRecordConstructor (ConHead -> QName
conName ConHead
c)
    isRecCon Term
_           = Bool -> f Bool
forall a. a -> f a
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
False

etaExpandEquationStrategy :: Int -> UnifyStrategy
etaExpandEquationStrategy :: Nat -> UnifyStrategy
etaExpandEquationStrategy Nat
k UnifyState
s = do
  -- Andreas, 2019-02-23, re #3578, is the following reduce redundant?
  Equal Dom{unDom = a} u v <- Nat -> UnifyState -> ListT TCM Equality
forall (m :: * -> *).
(MonadReduce m, MonadAddContext m) =>
Nat -> UnifyState -> m Equality
getReducedEqualityUnraised Nat
k UnifyState
s
  (d, pars) <- catMaybesMP $ addContext tel $ isEtaRecordType a
  guard =<< orM
    [ (Right True ==) <$> runBlocked (isSingletonRecord d pars)
    , shouldProject u
    , shouldProject v
    ]
  return $ EtaExpandEquation k d pars
  where
    shouldProject :: PureTCM m => Term -> m Bool
    shouldProject :: forall (m :: * -> *). PureTCM m => Term -> m Bool
shouldProject = \case
      Def QName
f Elims
es   -> QName -> m Bool
forall (m :: * -> *).
(HasConstInfo m, HasBuiltins m) =>
QName -> m Bool
usesCopatterns QName
f
      Con ConHead
c ConInfo
_ Elims
_  -> Maybe (QName, RecordData) -> Bool
forall a. Maybe a -> Bool
isJust (Maybe (QName, RecordData) -> Bool)
-> m (Maybe (QName, RecordData)) -> m Bool
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName -> m (Maybe (QName, RecordData))
forall (m :: * -> *).
HasConstInfo m =>
QName -> m (Maybe (QName, RecordData))
isRecordConstructor (ConHead -> QName
conName ConHead
c)

      Var Nat
_ Elims
_    -> Bool -> m Bool
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
False
      Lam ArgInfo
_ Abs Term
_    -> m Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
      Lit Literal
_      -> m Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
      Pi Dom Type
_ Abs Type
_     -> m Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
      Sort Sort
_     -> m Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
      Level Level
_    -> m Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
      MetaV MetaId
_ Elims
_  -> Bool -> m Bool
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
False
      DontCare Term
_ -> Bool -> m Bool
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
False
      Dummy String
s Elims
_  -> String -> m Bool
forall (m :: * -> *) a.
(HasCallStack, MonadDebug m) =>
String -> m a
__IMPOSSIBLE_VERBOSE__ String
s

    tel :: Telescope
tel = UnifyState -> Telescope
varTel UnifyState
s Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` ListTel -> Telescope
telFromList (Nat -> ListTel -> ListTel
forall a. Nat -> [a] -> [a]
take Nat
k (ListTel -> ListTel) -> ListTel -> ListTel
forall a b. (a -> b) -> a -> b
$ Telescope -> ListTel
forall t. Tele (Dom t) -> [Dom (String, t)]
telToList (Telescope -> ListTel) -> Telescope -> ListTel
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
s)

simplifySizesStrategy :: Int -> UnifyStrategy
simplifySizesStrategy :: Nat -> UnifyStrategy
simplifySizesStrategy Nat
k UnifyState
s = do
  isSizeName <- ListT TCM (QName -> Bool)
forall (m :: * -> *).
(HasOptions m, HasBuiltins m) =>
m (QName -> Bool)
isSizeNameTest
  Equal Dom{unDom = a} u v <- getReducedEquality k s
  case unEl a of
    Def QName
d Elims
_ -> do
      Bool -> ListT TCM ()
forall b (m :: * -> *). (IsBool b, MonadPlus m) => b -> m ()
guard (Bool -> ListT TCM ()) -> Bool -> ListT TCM ()
forall a b. (a -> b) -> a -> b
$ QName -> Bool
isSizeName QName
d
      su <- Term -> ListT TCM SizeView
forall (m :: * -> *).
(HasBuiltins m, MonadTCEnv m, ReadTCState m) =>
Term -> m SizeView
sizeView Term
u
      sv <- sizeView v
      case (su, sv) of
        (SizeSuc Term
u, SizeSuc Term
v) -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Term -> Term -> UnifyStep
StripSizeSuc Nat
k Term
u Term
v
        (SizeSuc Term
u, SizeView
SizeInf  ) -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Term -> Term -> UnifyStep
StripSizeSuc Nat
k Term
u Term
v
        (SizeView
SizeInf  , SizeSuc Term
v) -> UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> Term -> Term -> UnifyStep
StripSizeSuc Nat
k Term
u Term
v
        (SizeView, SizeView)
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
    Term
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero

injectiveTypeConStrategy :: Int -> UnifyStrategy
injectiveTypeConStrategy :: Nat -> UnifyStrategy
injectiveTypeConStrategy Nat
k UnifyState
s = do
  injTyCon <- PragmaOptions -> Bool
optInjectiveTypeConstructors (PragmaOptions -> Bool)
-> ListT TCM PragmaOptions -> ListT TCM Bool
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> ListT TCM PragmaOptions
forall (m :: * -> *). HasOptions m => m PragmaOptions
pragmaOptions
  guard injTyCon
  eq <- eqUnLevel =<< getReducedEquality k s
  case eq of
    Equal Dom Type
a u :: Term
u@(Def QName
d Elims
es) v :: Term
v@(Def QName
d' Elims
es') | QName
d QName -> QName -> Bool
forall a. Eq a => a -> a -> Bool
== QName
d' -> do
      -- d must be a data, record or axiom
      def <- QName -> ListT TCM Definition
forall (m :: * -> *). HasConstInfo m => QName -> m Definition
getConstInfo QName
d
      guard $ case theDef def of
                Datatype{} -> Bool
True
                Record{}   -> Bool
True
                Axiom{}    -> Bool
True
                DataOrRecSig{} -> Bool
True
                AbstractDefn{} -> Bool
False -- True triggers issue #2250
                Function{}   -> Bool
False
                Primitive{}  -> Bool
False
                PrimitiveSort{} -> Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
                GeneralizableVar{} -> Bool
forall a. HasCallStack => a
__IMPOSSIBLE__
                Constructor{} -> Bool
forall a. HasCallStack => a
__IMPOSSIBLE__  -- Never a type!
      let us = [Arg Term] -> Maybe [Arg Term] -> [Arg Term]
forall a. a -> Maybe a -> a
fromMaybe [Arg Term]
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe [Arg Term] -> [Arg Term]) -> Maybe [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Elims -> Maybe [Arg Term]
forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es
          vs = [Arg Term] -> Maybe [Arg Term] -> [Arg Term]
forall a. a -> Maybe a -> a
fromMaybe [Arg Term]
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe [Arg Term] -> [Arg Term]) -> Maybe [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Elims -> Maybe [Arg Term]
forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es'
      return $ TypeConInjectivity k d us vs
    Equality
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero

injectivePragmaStrategy :: Int -> UnifyStrategy
injectivePragmaStrategy :: Nat -> UnifyStrategy
injectivePragmaStrategy Nat
k UnifyState
s = do
  eq <- Equality -> ListT TCM Equality
forall (m :: * -> *).
(HasBuiltins m, HasOptions m) =>
Equality -> m Equality
eqUnLevel (Equality -> ListT TCM Equality)
-> ListT TCM Equality -> ListT TCM Equality
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< Nat -> UnifyState -> ListT TCM Equality
forall (m :: * -> *).
(MonadReduce m, MonadAddContext m) =>
Nat -> UnifyState -> m Equality
getReducedEquality Nat
k UnifyState
s
  case eq of
    Equal Dom Type
a u :: Term
u@(Def QName
d Elims
es) v :: Term
v@(Def QName
d' Elims
es') | QName
d QName -> QName -> Bool
forall a. Eq a => a -> a -> Bool
== QName
d' -> do
      -- d must have an injective pragma
      def <- QName -> ListT TCM Definition
forall (m :: * -> *). HasConstInfo m => QName -> m Definition
getConstInfo QName
d
      guard $ defInjective def
      let us = [Arg Term] -> Maybe [Arg Term] -> [Arg Term]
forall a. a -> Maybe a -> a
fromMaybe [Arg Term]
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe [Arg Term] -> [Arg Term]) -> Maybe [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Elims -> Maybe [Arg Term]
forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es
          vs = [Arg Term] -> Maybe [Arg Term] -> [Arg Term]
forall a. a -> Maybe a -> a
fromMaybe [Arg Term]
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe [Arg Term] -> [Arg Term]) -> Maybe [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Elims -> Maybe [Arg Term]
forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es'
      return $ TypeConInjectivity k d us vs
    Equality
_ -> ListT TCM UnifyStep
forall a. ListT TCM a
forall (m :: * -> *) a. MonadPlus m => m a
mzero

skipIrrelevantStrategy :: Int -> UnifyStrategy
skipIrrelevantStrategy :: Nat -> UnifyStrategy
skipIrrelevantStrategy Nat
k UnifyState
s = do
  let Equal Dom Type
a Term
_ Term
_ = Nat -> UnifyState -> Equality
getEquality Nat
k UnifyState
s                                 -- reduce not necessary
  Telescope -> ListT TCM () -> ListT TCM ()
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext (UnifyState -> Telescope
varTel UnifyState
s Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` UnifyState -> Telescope
eqTel UnifyState
s) (ListT TCM () -> ListT TCM ()) -> ListT TCM () -> ListT TCM ()
forall a b. (a -> b) -> a -> b
$
    Bool -> ListT TCM ()
forall b (m :: * -> *). (IsBool b, MonadPlus m) => b -> m ()
guard (Bool -> ListT TCM ())
-> (Either Blocker Bool -> Bool)
-> Either Blocker Bool
-> ListT TCM ()
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Either Blocker Bool -> Either Blocker Bool -> Bool
forall a. Eq a => a -> a -> Bool
== Bool -> Either Blocker Bool
forall a b. b -> Either a b
Right Bool
True) (Either Blocker Bool -> ListT TCM ())
-> ListT TCM (Either Blocker Bool) -> ListT TCM ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< BlockT (ListT TCM) Bool -> ListT TCM (Either Blocker Bool)
forall (m :: * -> *) a.
Monad m =>
BlockT m a -> m (Either Blocker a)
runBlocked (Dom Type -> BlockT (ListT TCM) Bool
forall a (m :: * -> *).
(LensRelevance a, LensSort a, PrettyTCM a, PureTCM m,
 MonadBlock m) =>
a -> m Bool
isIrrelevantOrPropM Dom Type
a)  -- reduction takes place here
  -- TODO: do something in case the above is blocked (i.e. `Left b`)
  UnifyStep -> ListT TCM UnifyStep
forall a. a -> ListT TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnifyStep -> ListT TCM UnifyStep)
-> UnifyStep -> ListT TCM UnifyStep
forall a b. (a -> b) -> a -> b
$ Nat -> UnifyStep
SkipIrrelevantEquation Nat
k


----------------------------------------------------
-- Actually doing the unification
----------------------------------------------------

unifyStep
  :: UnifyState -> UnifyStep -> UnifyStepT TCM (UnificationResult' UnifyState)
unifyStep :: UnifyState
-> UnifyStep -> UnifyStepT TCM (UnificationResult' UnifyState)
unifyStep UnifyState
s Deletion{ deleteAt :: UnifyStep -> Nat
deleteAt = Nat
k , deleteType :: UnifyStep -> Type
deleteType = Type
a , deleteLeft :: UnifyStep -> Term
deleteLeft = Term
u , deleteRight :: UnifyStep -> Term
deleteRight = Term
v } = do
    -- Check definitional equality of u and v
    isReflexive <- Telescope
-> WriterT UnifyOutput TCM (Either Blocker Bool)
-> WriterT UnifyOutput TCM (Either Blocker Bool)
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext (UnifyState -> Telescope
varTel UnifyState
s) (WriterT UnifyOutput TCM (Either Blocker Bool)
 -> WriterT UnifyOutput TCM (Either Blocker Bool))
-> WriterT UnifyOutput TCM (Either Blocker Bool)
-> WriterT UnifyOutput TCM (Either Blocker Bool)
forall a b. (a -> b) -> a -> b
$ Type
-> Term -> Term -> WriterT UnifyOutput TCM (Either Blocker Bool)
forall (m :: * -> *).
PureTCM m =>
Type -> Term -> Term -> m (Either Blocker Bool)
pureEqualTermB Type
a Term
u Term
v
    withoutK <- withoutKOption
    splitOnStrict <- asksTC envSplitOnStrict
    case isReflexive of
      Left Blocker
block   -> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ Blocker -> UnificationResult' UnifyState
forall a. Blocker -> UnificationResult' a
UnifyBlocked Blocker
block
      Right Bool
False  -> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck []
      Right Bool
True | Bool
withoutK Bool -> Bool -> Bool
&& Bool -> Bool
not Bool
splitOnStrict
                   -> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck [Telescope -> Type -> Term -> UnificationFailure
UnifyReflexiveEq (UnifyState -> Telescope
varTel UnifyState
s) Type
a Term
u]
      Right Bool
True   -> do
        let (UnifyState
s', PatternSubstitution
sigma) = Nat -> Term -> UnifyState -> (UnifyState, PatternSubstitution)
solveEq Nat
k Term
u UnifyState
s
        PatternSubstitution -> WriterT UnifyOutput TCM ()
forall (m :: * -> *).
MonadWriter UnifyOutput m =>
PatternSubstitution -> m ()
tellUnifyProof PatternSubstitution
sigma
        UnifyState -> UnificationResult' UnifyState
forall a. a -> UnificationResult' a
Unifies (UnifyState -> UnificationResult' UnifyState)
-> WriterT UnifyOutput TCM UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Telescope -> WriterT UnifyOutput TCM Telescope)
-> UnifyState -> WriterT UnifyOutput TCM UnifyState
Lens' UnifyState Telescope
lensEqTel Telescope -> WriterT UnifyOutput TCM Telescope
forall a (m :: * -> *). (Reduce a, MonadReduce m) => a -> m a
reduce UnifyState
s'

unifyStep UnifyState
s step :: UnifyStep
step@Solution{} = RetryNormalised
-> UnifyState
-> UnifyStep
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall (m :: * -> *).
(PureTCM m, MonadWriter UnifyOutput m) =>
RetryNormalised
-> UnifyState -> UnifyStep -> m (UnificationResult' UnifyState)
solutionStep RetryNormalised
RetryNormalised UnifyState
s UnifyStep
step

unifyStep UnifyState
s (Injectivity Nat
k Type
a QName
d [Arg Term]
pars [Arg Term]
ixs ConHead
c) = do
  WriterT UnifyOutput TCM Bool
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM (QName -> WriterT UnifyOutput TCM Bool
forall (m :: * -> *). HasConstInfo m => QName -> m Bool
consOfHIT (QName -> WriterT UnifyOutput TCM Bool)
-> QName -> WriterT UnifyOutput TCM Bool
forall a b. (a -> b) -> a -> b
$ ConHead -> QName
conName ConHead
c) (UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck []) (UnifyStepT TCM (UnificationResult' UnifyState)
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ do
  withoutK <- WriterT UnifyOutput TCM Bool
forall (m :: * -> *). HasOptions m => m Bool
withoutKOption

  -- Split equation telescope into parts before and after current equation
  let (eqListTel1, _ : eqListTel2) = splitAt k $ telToList $ eqTel s
      (eqTel1, eqTel2) = (telFromList eqListTel1, telFromList eqListTel2)

  -- Get constructor telescope and target indices
  cdef  <- getConInfo c
  let ctype  = Definition -> Type
defType Definition
cdef Type -> [Arg Term] -> Type
`piApply` [Arg Term]
pars
  addContext (varTel s `abstract` eqTel1) $ reportSDoc "tc.lhs.unify" 40 $
    "Constructor type: " <+> prettyTCM ctype
  TelV ctel ctarget <- addContext (varTel s `abstract` eqTel1) $ telView ctype
  let cixs = case Type -> Term
forall t a. Type'' t a -> a
unEl Type
ctarget of
               Def QName
d' Elims
es | QName
d QName -> QName -> Bool
forall a. Eq a => a -> a -> Bool
== QName
d' ->
                 let args :: [Arg Term]
args = [Arg Term] -> Maybe [Arg Term] -> [Arg Term]
forall a. a -> Maybe a -> a
fromMaybe [Arg Term]
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe [Arg Term] -> [Arg Term]) -> Maybe [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Elims -> Maybe [Arg Term]
forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es
                 in  Nat -> [Arg Term] -> [Arg Term]
forall a. Nat -> [a] -> [a]
drop ([Arg Term] -> Nat
forall a. [a] -> Nat
forall (t :: * -> *) a. Foldable t => t a -> Nat
length [Arg Term]
pars) [Arg Term]
args
               Term
_ -> [Arg Term]
forall a. HasCallStack => a
__IMPOSSIBLE__

  -- Get index telescope of the datatype
  dtype    <- (`piApply` pars) . defType <$> getConstInfo d
  addContext (varTel s `abstract` eqTel1) $ reportSDoc "tc.lhs.unify" 40 $
    "Datatype type: " <+> prettyTCM dtype

  -- This is where the magic of higher-dimensional unification happens
  -- We need to generalize the indices `ixs` to the target indices of the
  -- constructor `cixs`. This is done by calling the unification algorithm
  -- recursively (this doesn't get stuck in a loop because a type should
  -- never be indexed over itself). Note the similarity with the
  -- computeNeighbourhood function in Agda.TypeChecking.Coverage.
  let hduTel = Telescope
eqTel1 Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` Telescope
ctel
      notforced = Nat -> IsForced -> [IsForced]
forall a. Nat -> a -> [a]
replicate (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
hduTel) IsForced
NotForced

  -- The left inverse computed here is not actually used when computing
  -- a left inverse for the overall match, so as a slight optimisation
  -- we just don't bother computing it. __IMPOSSIBLE__ because that
  -- field in the result is never evaluated.
  res <- lift $ addContext (varTel s) $ unifyIndices' (Just __IMPOSSIBLE__)
           hduTel
           (allFlexVars notforced hduTel)
           (raise (size ctel) dtype)
           (raise (size ctel) ixs)
           cixs
  case res of
    -- Higher-dimensional unification can never end in a conflict,
    -- because `cong c1 ...` and `cong c2 ...` don't even have the
    -- same type for distinct constructors c1 and c2.
    NoUnify NegativeUnification
_ -> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. HasCallStack => a
__IMPOSSIBLE__

    -- Higher-dimensional unification is blocked: propagate
    UnifyBlocked Blocker
block -> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ Blocker -> UnificationResult' UnifyState
forall a. Blocker -> UnificationResult' a
UnifyBlocked Blocker
block

    -- Higher-dimensional unification has failed. If not --without-K,
    -- we can simply ignore the higher-dimensional equations and
    -- simplify the equation as in the non-indexed case.
    UnifyStuck [UnificationFailure]
_ | Bool -> Bool
not Bool
withoutK -> do
      -- using the same variable names as in the case where hdu succeeds.
      let eqTel1' :: Telescope
eqTel1' = Telescope
eqTel1 Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` Telescope
ctel
          rho1 :: PatternSubstitution
rho1    = Nat -> PatternSubstitution
forall a. Nat -> Substitution' a
raiseS (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
ctel)
          ceq :: Pattern' DBPatVar
ceq     = ConHead
-> ConPatternInfo
-> [NamedArg (Pattern' DBPatVar)]
-> Pattern' DBPatVar
forall x.
ConHead -> ConPatternInfo -> [NamedArg (Pattern' x)] -> Pattern' x
ConP ConHead
c ConPatternInfo
noConPatternInfo ([NamedArg (Pattern' DBPatVar)] -> Pattern' DBPatVar)
-> [NamedArg (Pattern' DBPatVar)] -> Pattern' DBPatVar
forall a b. (a -> b) -> a -> b
$ Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a t. DeBruijn a => Tele (Dom t) -> [NamedArg a]
teleNamedArgs Telescope
ctel
          rho3 :: PatternSubstitution
rho3    = Pattern' DBPatVar -> PatternSubstitution -> PatternSubstitution
forall a. DeBruijn a => a -> Substitution' a -> Substitution' a
consS Pattern' DBPatVar
ceq PatternSubstitution
rho1
          eqTel2' :: Telescope
eqTel2' = PatternSubstitution -> Telescope -> Telescope
forall a. TermSubst a => PatternSubstitution -> a -> a
applyPatSubst PatternSubstitution
rho3 Telescope
eqTel2
          eqTel' :: Telescope
eqTel'  = Telescope
eqTel1' Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` Telescope
eqTel2'
          rho :: PatternSubstitution
rho     = Nat -> PatternSubstitution -> PatternSubstitution
forall a. Nat -> Substitution' a -> Substitution' a
liftS (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
eqTel2) PatternSubstitution
rho3

      PatternSubstitution -> WriterT UnifyOutput TCM ()
forall (m :: * -> *).
MonadWriter UnifyOutput m =>
PatternSubstitution -> m ()
tellUnifyProof PatternSubstitution
rho

      eqTel' <- Telescope
-> WriterT UnifyOutput TCM Telescope
-> WriterT UnifyOutput TCM Telescope
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext (UnifyState -> Telescope
varTel UnifyState
s) (WriterT UnifyOutput TCM Telescope
 -> WriterT UnifyOutput TCM Telescope)
-> WriterT UnifyOutput TCM Telescope
-> WriterT UnifyOutput TCM Telescope
forall a b. (a -> b) -> a -> b
$ Telescope -> WriterT UnifyOutput TCM Telescope
forall a (m :: * -> *). (Reduce a, MonadReduce m) => a -> m a
reduce Telescope
eqTel'

      -- Compute new lhs and rhs by matching the old ones against rho
      (lhs', rhs') <- addContext (varTel s) $ do
        let ps = Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
applySubst PatternSubstitution
Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
rho ([NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a b. (a -> b) -> a -> b
$ Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a t. DeBruijn a => Tele (Dom t) -> [NamedArg a]
teleNamedArgs (Telescope -> [NamedArg (Pattern' DBPatVar)])
-> Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
s
        (lhsMatch, _) <- Match.matchPatterns ps $ eqLHS s
        (rhsMatch, _) <- Match.matchPatterns ps $ eqRHS s
        case (lhsMatch, rhsMatch) of
          (Match.Yes Simplification
_ IntMap (Arg Term)
lhs', Match.Yes Simplification
_ IntMap (Arg Term)
rhs') -> ([Arg Term], [Arg Term])
-> WriterT UnifyOutput TCM ([Arg Term], [Arg Term])
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return
            ([Arg Term] -> [Arg Term]
forall a. [a] -> [a]
reverse ([Arg Term] -> [Arg Term]) -> [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Empty -> Nat -> IntMap (Arg Term) -> [Arg Term]
forall a. Empty -> Nat -> IntMap (Arg a) -> [Arg a]
Match.matchedArgs Empty
forall a. HasCallStack => a
__IMPOSSIBLE__ (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
eqTel') IntMap (Arg Term)
lhs',
             [Arg Term] -> [Arg Term]
forall a. [a] -> [a]
reverse ([Arg Term] -> [Arg Term]) -> [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Empty -> Nat -> IntMap (Arg Term) -> [Arg Term]
forall a. Empty -> Nat -> IntMap (Arg a) -> [Arg a]
Match.matchedArgs Empty
forall a. HasCallStack => a
__IMPOSSIBLE__ (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
eqTel') IntMap (Arg Term)
rhs')
          (Match Term, Match Term)
_ -> WriterT UnifyOutput TCM ([Arg Term], [Arg Term])
forall a. HasCallStack => a
__IMPOSSIBLE__

      return $ Unifies $ s { eqTel = eqTel' , eqLHS = lhs' , eqRHS = rhs' }


    UnifyStuck [UnificationFailure]
_ -> let n :: Nat
n           = UnifyState -> Nat
eqCount UnifyState
s
                        Equal Dom{unDom :: forall t e. Dom' t e -> e
unDom = Type
a} Term
u Term
v = Nat -> UnifyState -> Equality
getEquality Nat
k UnifyState
s
                    in UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck [Telescope
-> Type -> Term -> Term -> [Arg Term] -> UnificationFailure
UnifyIndicesNotVars
                         (UnifyState -> Telescope
varTel UnifyState
s Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` UnifyState -> Telescope
eqTel UnifyState
s) Type
a
                         (Nat -> Term -> Term
forall a. Subst a => Nat -> a -> a
raise Nat
n Term
u) (Nat -> Term -> Term
forall a. Subst a => Nat -> a -> a
raise Nat
n Term
v) (Nat -> [Arg Term] -> [Arg Term]
forall a. Subst a => Nat -> a -> a
raise (Nat
nNat -> Nat -> Nat
forall a. Num a => a -> a -> a
-Nat
k) [Arg Term]
ixs)]

    Unifies (Telescope
eqTel1', PatternSubstitution
rho0, [NamedArg (Pattern' DBPatVar)]
_, Either NoLeftInv (Substitution, Substitution)
_) -> do
      -- Split ps0 into parts for eqTel1 and ctel
      let (PatternSubstitution
rho1, PatternSubstitution
rho2) = Nat
-> PatternSubstitution
-> (PatternSubstitution, PatternSubstitution)
forall a.
Nat -> Substitution' a -> (Substitution' a, Substitution' a)
splitS (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
ctel) PatternSubstitution
rho0

      -- Compute new equation telescope context and substitution
      let ceq :: Pattern' DBPatVar
ceq     = ConHead
-> ConPatternInfo
-> [NamedArg (Pattern' DBPatVar)]
-> Pattern' DBPatVar
forall x.
ConHead -> ConPatternInfo -> [NamedArg (Pattern' x)] -> Pattern' x
ConP ConHead
c ConPatternInfo
noConPatternInfo ([NamedArg (Pattern' DBPatVar)] -> Pattern' DBPatVar)
-> [NamedArg (Pattern' DBPatVar)] -> Pattern' DBPatVar
forall a b. (a -> b) -> a -> b
$ Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
applySubst PatternSubstitution
Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
rho2 ([NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a b. (a -> b) -> a -> b
$ Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a t. DeBruijn a => Tele (Dom t) -> [NamedArg a]
teleNamedArgs Telescope
ctel
          rho3 :: PatternSubstitution
rho3    = Pattern' DBPatVar -> PatternSubstitution -> PatternSubstitution
forall a. DeBruijn a => a -> Substitution' a -> Substitution' a
consS Pattern' DBPatVar
ceq PatternSubstitution
rho1
          eqTel2' :: Telescope
eqTel2' = PatternSubstitution -> Telescope -> Telescope
forall a. TermSubst a => PatternSubstitution -> a -> a
applyPatSubst PatternSubstitution
rho3 Telescope
eqTel2
          eqTel' :: Telescope
eqTel'  = Telescope
eqTel1' Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
`abstract` Telescope
eqTel2'
          rho :: PatternSubstitution
rho     = Nat -> PatternSubstitution -> PatternSubstitution
forall a. Nat -> Substitution' a -> Substitution' a
liftS (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
eqTel2) PatternSubstitution
rho3

      PatternSubstitution -> WriterT UnifyOutput TCM ()
forall (m :: * -> *).
MonadWriter UnifyOutput m =>
PatternSubstitution -> m ()
tellUnifyProof PatternSubstitution
rho

      eqTel' <- Telescope
-> WriterT UnifyOutput TCM Telescope
-> WriterT UnifyOutput TCM Telescope
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext (UnifyState -> Telescope
varTel UnifyState
s) (WriterT UnifyOutput TCM Telescope
 -> WriterT UnifyOutput TCM Telescope)
-> WriterT UnifyOutput TCM Telescope
-> WriterT UnifyOutput TCM Telescope
forall a b. (a -> b) -> a -> b
$ Telescope -> WriterT UnifyOutput TCM Telescope
forall a (m :: * -> *). (Reduce a, MonadReduce m) => a -> m a
reduce Telescope
eqTel'

      -- Compute new lhs and rhs by matching the old ones against rho
      (lhs', rhs') <- addContext (varTel s) $ do
        let ps = Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
applySubst PatternSubstitution
Substitution' (SubstArg [NamedArg (Pattern' DBPatVar)])
rho ([NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)])
-> [NamedArg (Pattern' DBPatVar)] -> [NamedArg (Pattern' DBPatVar)]
forall a b. (a -> b) -> a -> b
$ Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a t. DeBruijn a => Tele (Dom t) -> [NamedArg a]
teleNamedArgs (Telescope -> [NamedArg (Pattern' DBPatVar)])
-> Telescope -> [NamedArg (Pattern' DBPatVar)]
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
s
        (lhsMatch, _) <- Match.matchPatterns ps $ eqLHS s
        (rhsMatch, _) <- Match.matchPatterns ps $ eqRHS s
        case (lhsMatch, rhsMatch) of
          (Match.Yes Simplification
_ IntMap (Arg Term)
lhs', Match.Yes Simplification
_ IntMap (Arg Term)
rhs') -> ([Arg Term], [Arg Term])
-> WriterT UnifyOutput TCM ([Arg Term], [Arg Term])
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return
            ([Arg Term] -> [Arg Term]
forall a. [a] -> [a]
reverse ([Arg Term] -> [Arg Term]) -> [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Empty -> Nat -> IntMap (Arg Term) -> [Arg Term]
forall a. Empty -> Nat -> IntMap (Arg a) -> [Arg a]
Match.matchedArgs Empty
forall a. HasCallStack => a
__IMPOSSIBLE__ (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
eqTel') IntMap (Arg Term)
lhs',
             [Arg Term] -> [Arg Term]
forall a. [a] -> [a]
reverse ([Arg Term] -> [Arg Term]) -> [Arg Term] -> [Arg Term]
forall a b. (a -> b) -> a -> b
$ Empty -> Nat -> IntMap (Arg Term) -> [Arg Term]
forall a. Empty -> Nat -> IntMap (Arg a) -> [Arg a]
Match.matchedArgs Empty
forall a. HasCallStack => a
__IMPOSSIBLE__ (Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
eqTel') IntMap (Arg Term)
rhs')
          (Match Term, Match Term)
_ -> WriterT UnifyOutput TCM ([Arg Term], [Arg Term])
forall a. HasCallStack => a
__IMPOSSIBLE__

      return $ Unifies $ s { eqTel = eqTel' , eqLHS = lhs' , eqRHS = rhs' }

unifyStep UnifyState
s Conflict
  { conflictLeft :: UnifyStep -> Term
conflictLeft  = Term
u
  , conflictRight :: UnifyStep -> Term
conflictRight = Term
v
  } =
  case Term
u of
    Con ConHead
h ConInfo
_ Elims
_ -> do
      WriterT UnifyOutput TCM Bool
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM (QName -> WriterT UnifyOutput TCM Bool
forall (m :: * -> *). HasConstInfo m => QName -> m Bool
consOfHIT (QName -> WriterT UnifyOutput TCM Bool)
-> QName -> WriterT UnifyOutput TCM Bool
forall a b. (a -> b) -> a -> b
$ ConHead -> QName
conName ConHead
h) (UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck []) (UnifyStepT TCM (UnificationResult' UnifyState)
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ do
        UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ NegativeUnification -> UnificationResult' UnifyState
forall a. NegativeUnification -> UnificationResult' a
NoUnify (NegativeUnification -> UnificationResult' UnifyState)
-> NegativeUnification -> UnificationResult' UnifyState
forall a b. (a -> b) -> a -> b
$ Telescope -> Term -> Term -> NegativeUnification
UnifyConflict (UnifyState -> Telescope
varTel UnifyState
s) Term
u Term
v
    Term
_ -> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. HasCallStack => a
__IMPOSSIBLE__
unifyStep UnifyState
s Cycle
  { cycleVar :: UnifyStep -> Nat
cycleVar        = Nat
i
  , cycleOccursIn :: UnifyStep -> Term
cycleOccursIn   = Term
u
  } =
  case Term
u of
    Con ConHead
h ConInfo
_ Elims
_ -> do
      WriterT UnifyOutput TCM Bool
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM (QName -> WriterT UnifyOutput TCM Bool
forall (m :: * -> *). HasConstInfo m => QName -> m Bool
consOfHIT (QName -> WriterT UnifyOutput TCM Bool)
-> QName -> WriterT UnifyOutput TCM Bool
forall a b. (a -> b) -> a -> b
$ ConHead -> QName
conName ConHead
h) (UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck []) (UnifyStepT TCM (UnificationResult' UnifyState)
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ do
        UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ NegativeUnification -> UnificationResult' UnifyState
forall a. NegativeUnification -> UnificationResult' a
NoUnify (NegativeUnification -> UnificationResult' UnifyState)
-> NegativeUnification -> UnificationResult' UnifyState
forall a b. (a -> b) -> a -> b
$ Telescope -> Nat -> Term -> NegativeUnification
UnifyCycle (UnifyState -> Telescope
varTel UnifyState
s) Nat
i Term
u
    Term
_ -> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. HasCallStack => a
__IMPOSSIBLE__

unifyStep UnifyState
s EtaExpandVar{ expandVar :: UnifyStep -> FlexibleVar Nat
expandVar = FlexibleVar Nat
fi, expandVarRecordType :: UnifyStep -> QName
expandVarRecordType = QName
d , expandVarParameters :: UnifyStep -> [Arg Term]
expandVarParameters = [Arg Term]
pars } = do
  recd <- RecordData -> Maybe RecordData -> RecordData
forall a. a -> Maybe a -> a
fromMaybe RecordData
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe RecordData -> RecordData)
-> WriterT UnifyOutput TCM (Maybe RecordData)
-> WriterT UnifyOutput TCM RecordData
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName -> WriterT UnifyOutput TCM (Maybe RecordData)
forall (m :: * -> *).
HasConstInfo m =>
QName -> m (Maybe RecordData)
isRecord QName
d
  let delta = RecordData -> Telescope
_recTel RecordData
recd Telescope -> [Arg Term] -> Telescope
forall t. Apply t => t -> [Arg Term] -> t
`apply` [Arg Term]
pars
      c     = RecordData -> ConHead
_recConHead RecordData
recd
  let nfields         = Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
delta
      (varTel', rho)  = expandTelescopeVar (varTel s) (m-1-i) delta c
      projectFlexible = [ ArgInfo
-> IsForced
-> FlexibleVarKind
-> Maybe Nat
-> Nat
-> FlexibleVar Nat
forall a.
ArgInfo
-> IsForced -> FlexibleVarKind -> Maybe Nat -> a -> FlexibleVar a
FlexibleVar (FlexibleVar Nat -> ArgInfo
forall a. LensArgInfo a => a -> ArgInfo
getArgInfo FlexibleVar Nat
fi) (FlexibleVar Nat -> IsForced
forall a. FlexibleVar a -> IsForced
flexForced FlexibleVar Nat
fi) (Nat -> FlexibleVarKind
projFlexKind Nat
j) (FlexibleVar Nat -> Maybe Nat
forall a. FlexibleVar a -> Maybe Nat
flexPos FlexibleVar Nat
fi) (Nat
i Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
+ Nat
j) | Nat
j <- [Nat
0 .. Nat
nfields Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
- Nat
1] ]
  tellUnifySubst $ rho
  return $ Unifies $ UState
    { varTel   = varTel'
    , flexVars = projectFlexible ++ liftFlexibles nfields (flexVars s)
    , eqTel    = applyPatSubst rho $ eqTel s
    , eqLHS    = applyPatSubst rho $ eqLHS s
    , eqRHS    = applyPatSubst rho $ eqRHS s
    }
  where
    i :: Nat
i = FlexibleVar Nat -> Nat
forall a. FlexibleVar a -> a
flexVar FlexibleVar Nat
fi
    m :: Nat
m = UnifyState -> Nat
varCount UnifyState
s

    projFlexKind :: Int -> FlexibleVarKind
    projFlexKind :: Nat -> FlexibleVarKind
projFlexKind Nat
j = case FlexibleVar Nat -> FlexibleVarKind
forall a. FlexibleVar a -> FlexibleVarKind
flexKind FlexibleVar Nat
fi of
      RecordFlex [FlexibleVarKind]
ks -> FlexibleVarKind -> [FlexibleVarKind] -> Nat -> FlexibleVarKind
forall a. a -> [a] -> Nat -> a
indexWithDefault FlexibleVarKind
ImplicitFlex [FlexibleVarKind]
ks Nat
j
      FlexibleVarKind
ImplicitFlex  -> FlexibleVarKind
ImplicitFlex
      FlexibleVarKind
DotFlex       -> FlexibleVarKind
DotFlex
      FlexibleVarKind
OtherFlex     -> FlexibleVarKind
OtherFlex

    liftFlexible :: Int -> Int -> Maybe Int
    liftFlexible :: Nat -> Nat -> Maybe Nat
liftFlexible Nat
n Nat
j = if Nat
j Nat -> Nat -> Bool
forall a. Eq a => a -> a -> Bool
== Nat
i then Maybe Nat
forall a. Maybe a
Nothing else Nat -> Maybe Nat
forall a. a -> Maybe a
Just (if Nat
j Nat -> Nat -> Bool
forall a. Ord a => a -> a -> Bool
> Nat
i then Nat
j Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
+ (Nat
nNat -> Nat -> Nat
forall a. Num a => a -> a -> a
-Nat
1) else Nat
j)

    liftFlexibles :: Int -> FlexibleVars -> FlexibleVars
    liftFlexibles :: Nat -> FlexibleVars -> FlexibleVars
liftFlexibles Nat
n FlexibleVars
fs = (FlexibleVar Nat -> Maybe (FlexibleVar Nat))
-> FlexibleVars -> FlexibleVars
forall a b. (a -> Maybe b) -> [a] -> [b]
mapMaybe ((Nat -> Maybe Nat) -> FlexibleVar Nat -> Maybe (FlexibleVar Nat)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> FlexibleVar a -> f (FlexibleVar b)
traverse ((Nat -> Maybe Nat) -> FlexibleVar Nat -> Maybe (FlexibleVar Nat))
-> (Nat -> Maybe Nat) -> FlexibleVar Nat -> Maybe (FlexibleVar Nat)
forall a b. (a -> b) -> a -> b
$ Nat -> Nat -> Maybe Nat
liftFlexible Nat
n) FlexibleVars
fs

unifyStep UnifyState
s EtaExpandEquation{ expandAt :: UnifyStep -> Nat
expandAt = Nat
k, expandRecordType :: UnifyStep -> QName
expandRecordType = QName
d, expandParameters :: UnifyStep -> [Arg Term]
expandParameters = [Arg Term]
pars } = do
  recd  <- RecordData -> Maybe RecordData -> RecordData
forall a. a -> Maybe a -> a
fromMaybe RecordData
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe RecordData -> RecordData)
-> WriterT UnifyOutput TCM (Maybe RecordData)
-> WriterT UnifyOutput TCM RecordData
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName -> WriterT UnifyOutput TCM (Maybe RecordData)
forall (m :: * -> *).
HasConstInfo m =>
QName -> m (Maybe RecordData)
isRecord QName
d
  let delta = RecordData -> Telescope
_recTel RecordData
recd Telescope -> [Arg Term] -> Telescope
forall t. Apply t => t -> [Arg Term] -> t
`apply` [Arg Term]
pars
      c     = RecordData -> ConHead
_recConHead RecordData
recd
  lhs   <- expandKth $ eqLHS s
  rhs   <- expandKth $ eqRHS s
  let (tel, sigma) = expandTelescopeVar (eqTel s) k delta c
  tellUnifyProof sigma
  Unifies <$> do
   lensEqTel reduce $ s
    { eqTel    = tel
    , eqLHS    = lhs
    , eqRHS    = rhs
    }
  where
    expandKth :: [Arg Term] -> WriterT UnifyOutput TCM [Arg Term]
expandKth [Arg Term]
us = do
      let ([Arg Term]
us1,Arg Term
v:[Arg Term]
us2) = ([Arg Term], [Arg Term])
-> Maybe ([Arg Term], [Arg Term]) -> ([Arg Term], [Arg Term])
forall a. a -> Maybe a -> a
fromMaybe ([Arg Term], [Arg Term])
forall a. HasCallStack => a
__IMPOSSIBLE__ (Maybe ([Arg Term], [Arg Term]) -> ([Arg Term], [Arg Term]))
-> Maybe ([Arg Term], [Arg Term]) -> ([Arg Term], [Arg Term])
forall a b. (a -> b) -> a -> b
$ Nat -> [Arg Term] -> Maybe ([Arg Term], [Arg Term])
forall n a. Integral n => n -> [a] -> Maybe ([a], [a])
splitExactlyAt Nat
k [Arg Term]
us
      vs <- (Telescope, [Arg Term]) -> [Arg Term]
forall a b. (a, b) -> b
snd ((Telescope, [Arg Term]) -> [Arg Term])
-> WriterT UnifyOutput TCM (Telescope, [Arg Term])
-> WriterT UnifyOutput TCM [Arg Term]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName
-> [Arg Term]
-> Term
-> WriterT UnifyOutput TCM (Telescope, [Arg Term])
forall (m :: * -> *).
(HasConstInfo m, MonadDebug m, ReadTCState m) =>
QName -> [Arg Term] -> Term -> m (Telescope, [Arg Term])
etaExpandRecord QName
d [Arg Term]
pars (Arg Term -> Term
forall e. Arg e -> e
unArg Arg Term
v)
      vs <- reduce vs
      return $ us1 ++ vs ++ us2

unifyStep UnifyState
s LitConflict
  { litType :: UnifyStep -> Type
litType          = Type
a
  , litConflictLeft :: UnifyStep -> Literal
litConflictLeft  = Literal
l
  , litConflictRight :: UnifyStep -> Literal
litConflictRight = Literal
l'
  } = UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ NegativeUnification -> UnificationResult' UnifyState
forall a. NegativeUnification -> UnificationResult' a
NoUnify (NegativeUnification -> UnificationResult' UnifyState)
-> NegativeUnification -> UnificationResult' UnifyState
forall a b. (a -> b) -> a -> b
$ Telescope -> Term -> Term -> NegativeUnification
UnifyConflict (UnifyState -> Telescope
varTel UnifyState
s) (Literal -> Term
Lit Literal
l) (Literal -> Term
Lit Literal
l')

unifyStep UnifyState
s (StripSizeSuc Nat
k Term
u Term
v) = do
  sizeTy <- WriterT UnifyOutput TCM Type
forall (m :: * -> *).
(HasBuiltins m, MonadTCEnv m, ReadTCState m) =>
m Type
sizeType
  sizeSu <- sizeSuc 1 (var 0)
  let n          = UnifyState -> Nat
eqCount UnifyState
s
      sub        = Nat -> Substitution -> Substitution
forall a. Nat -> Substitution' a -> Substitution' a
liftS (Nat
nNat -> Nat -> Nat
forall a. Num a => a -> a -> a
-Nat
kNat -> Nat -> Nat
forall a. Num a => a -> a -> a
-Nat
1) (Substitution -> Substitution) -> Substitution -> Substitution
forall a b. (a -> b) -> a -> b
$ Term -> Substitution -> Substitution
forall a. DeBruijn a => a -> Substitution' a -> Substitution' a
consS Term
sizeSu (Substitution -> Substitution) -> Substitution -> Substitution
forall a b. (a -> b) -> a -> b
$ Nat -> Substitution
forall a. Nat -> Substitution' a
raiseS Nat
1
      eqFlatTel  = Telescope -> [Dom Type]
forall a. TermSubst a => Tele (Dom a) -> [Dom a]
flattenTel (Telescope -> [Dom Type]) -> Telescope -> [Dom Type]
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
s
      eqFlatTel' = Substitution' (SubstArg [Dom Type]) -> [Dom Type] -> [Dom Type]
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
applySubst Substitution
Substitution' (SubstArg [Dom Type])
sub ([Dom Type] -> [Dom Type]) -> [Dom Type] -> [Dom Type]
forall a b. (a -> b) -> a -> b
$ Nat -> (Dom Type -> Dom Type) -> [Dom Type] -> [Dom Type]
forall a. Nat -> (a -> a) -> [a] -> [a]
updateAt Nat
k ((Type -> Type) -> Dom Type -> Dom Type
forall a b. (a -> b) -> Dom' Term a -> Dom' Term b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((Type -> Type) -> Dom Type -> Dom Type)
-> (Type -> Type) -> Dom Type -> Dom Type
forall a b. (a -> b) -> a -> b
$ Type -> Type -> Type
forall a b. a -> b -> a
const Type
sizeTy) ([Dom Type] -> [Dom Type]) -> [Dom Type] -> [Dom Type]
forall a b. (a -> b) -> a -> b
$ [Dom Type]
eqFlatTel
      eqTel'     = [String] -> [Dom Type] -> Telescope
unflattenTel (Telescope -> [String]
teleNames (Telescope -> [String]) -> Telescope -> [String]
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
s) [Dom Type]
eqFlatTel'
  -- TODO: tellUnifyProof sub
  -- but sizeSu is not a constructor, so sub is not a PatternSubstitution!
  return $ Unifies $ s
    { eqTel = eqTel'
    , eqLHS = updateAt k (const $ defaultArg u) $ eqLHS s
    , eqRHS = updateAt k (const $ defaultArg v) $ eqRHS s
    }

unifyStep UnifyState
s (SkipIrrelevantEquation Nat
k) = do
  let lhs :: [Arg Term]
lhs = UnifyState -> [Arg Term]
eqLHS UnifyState
s
      (UnifyState
s', PatternSubstitution
sigma) = Nat -> Term -> UnifyState -> (UnifyState, PatternSubstitution)
solveEq Nat
k (Term -> Term
DontCare (Term -> Term) -> Term -> Term
forall a b. (a -> b) -> a -> b
$ Arg Term -> Term
forall e. Arg e -> e
unArg (Arg Term -> Term) -> Arg Term -> Term
forall a b. (a -> b) -> a -> b
$ Arg Term -> [Arg Term] -> Nat -> Arg Term
forall a. a -> [a] -> Nat -> a
indexWithDefault Arg Term
forall a. HasCallStack => a
__IMPOSSIBLE__ [Arg Term]
lhs Nat
k) UnifyState
s
  PatternSubstitution -> WriterT UnifyOutput TCM ()
forall (m :: * -> *).
MonadWriter UnifyOutput m =>
PatternSubstitution -> m ()
tellUnifyProof PatternSubstitution
sigma
  UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyOutput TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyStepT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyStepT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ UnifyState -> UnificationResult' UnifyState
forall a. a -> UnificationResult' a
Unifies UnifyState
s'

unifyStep UnifyState
s (TypeConInjectivity Nat
k QName
d [Arg Term]
us [Arg Term]
vs) = do
  dtype <- Definition -> Type
defType (Definition -> Type)
-> WriterT UnifyOutput TCM Definition
-> WriterT UnifyOutput TCM Type
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName -> WriterT UnifyOutput TCM Definition
forall (m :: * -> *). HasConstInfo m => QName -> m Definition
getConstInfo QName
d
  TelV dtel _ <- telView dtype
  let deq = QName -> Elims -> Term
Def QName
d (Elims -> Term) -> Elims -> Term
forall a b. (a -> b) -> a -> b
$ (Arg Term -> Elim) -> [Arg Term] -> Elims
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> Elim
forall a. Arg a -> Elim' a
Apply ([Arg Term] -> Elims) -> [Arg Term] -> Elims
forall a b. (a -> b) -> a -> b
$ Telescope -> [Arg Term]
forall a t. DeBruijn a => Tele (Dom t) -> [Arg a]
teleArgs Telescope
dtel
  -- TODO: tellUnifyProof ???
  -- but d is not a constructor...
  Unifies <$> do
   lensEqTel reduce $ s
    { eqTel = dtel `abstract` applyUnder k (eqTel s) (raise k deq)
    , eqLHS = us ++ dropAt k (eqLHS s)
    , eqRHS = vs ++ dropAt k (eqRHS s)
    }

data RetryNormalised = RetryNormalised | DontRetryNormalised
  deriving (RetryNormalised -> RetryNormalised -> Bool
(RetryNormalised -> RetryNormalised -> Bool)
-> (RetryNormalised -> RetryNormalised -> Bool)
-> Eq RetryNormalised
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: RetryNormalised -> RetryNormalised -> Bool
== :: RetryNormalised -> RetryNormalised -> Bool
$c/= :: RetryNormalised -> RetryNormalised -> Bool
/= :: RetryNormalised -> RetryNormalised -> Bool
Eq, Nat -> RetryNormalised -> ShowS
[RetryNormalised] -> ShowS
RetryNormalised -> String
(Nat -> RetryNormalised -> ShowS)
-> (RetryNormalised -> String)
-> ([RetryNormalised] -> ShowS)
-> Show RetryNormalised
forall a.
(Nat -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Nat -> RetryNormalised -> ShowS
showsPrec :: Nat -> RetryNormalised -> ShowS
$cshow :: RetryNormalised -> String
show :: RetryNormalised -> String
$cshowList :: [RetryNormalised] -> ShowS
showList :: [RetryNormalised] -> ShowS
Show)

solutionStep
  :: (PureTCM m, MonadWriter UnifyOutput m)
  => RetryNormalised
  -> UnifyState
  -> UnifyStep
  -> m (UnificationResult' UnifyState)
solutionStep :: forall (m :: * -> *).
(PureTCM m, MonadWriter UnifyOutput m) =>
RetryNormalised
-> UnifyState -> UnifyStep -> m (UnificationResult' UnifyState)
solutionStep RetryNormalised
retry UnifyState
s
  step :: UnifyStep
step@Solution{ solutionAt :: UnifyStep -> Nat
solutionAt   = Nat
k
               , solutionType :: UnifyStep -> Dom Type
solutionType = dom :: Dom Type
dom@Dom{ unDom :: forall t e. Dom' t e -> e
unDom = Type
a }
               , solutionVar :: UnifyStep -> FlexibleVar Nat
solutionVar  = fi :: FlexibleVar Nat
fi@FlexibleVar{ flexVar :: forall a. FlexibleVar a -> a
flexVar = Nat
i }
               , solutionTerm :: UnifyStep -> Term
solutionTerm = Term
u } = do
  let m :: Nat
m = UnifyState -> Nat
varCount UnifyState
s

  -- Now we have to be careful about forced variables in `u`. If they appear
  -- in pattern positions we need to bind them there rather in their forced positions. We can safely
  -- ignore non-pattern positions and forced pattern positions, because in that case there will be
  -- other equations where the variable can be bound.
  -- NOTE: If we're doing make-case we ignore forced variables. This is safe since we take the
  -- result of unification and build user clauses that will be checked again with forcing turned on.
  inMakeCase <- Lens' TCEnv Bool -> m Bool
forall (m :: * -> *) a. MonadTCEnv m => Lens' TCEnv a -> m a
viewTC (Bool -> f Bool) -> TCEnv -> f TCEnv
Lens' TCEnv Bool
eMakeCase
  let forcedVars | Bool
inMakeCase = IntMap Modality
forall a. IntMap a
IntMap.empty
                 | Bool
otherwise  = [(Nat, Modality)] -> IntMap Modality
forall a. [(Nat, a)] -> IntMap a
IntMap.fromList [ (FlexibleVar Nat -> Nat
forall a. FlexibleVar a -> a
flexVar FlexibleVar Nat
fi, FlexibleVar Nat -> Modality
forall a. LensModality a => a -> Modality
getModality FlexibleVar Nat
fi) | FlexibleVar Nat
fi <- UnifyState -> FlexibleVars
flexVars UnifyState
s,
                                                                                 FlexibleVar Nat -> IsForced
forall a. FlexibleVar a -> IsForced
flexForced FlexibleVar Nat
fi IsForced -> IsForced -> Bool
forall a. Eq a => a -> a -> Bool
== IsForced
Forced ]
  (p, bound) <- patternBindingForcedVars forcedVars u

  -- To maintain the invariant that each variable in varTel is bound exactly once in the pattern
  -- substitution we need to turn the bound variables in `p` into dot patterns in the rest of the
  -- substitution.
  let dotSub = (PatternSubstitution -> PatternSubstitution -> PatternSubstitution)
-> PatternSubstitution
-> [PatternSubstitution]
-> PatternSubstitution
forall a b. (a -> b -> b) -> b -> [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr PatternSubstitution -> PatternSubstitution -> PatternSubstitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
composeS PatternSubstitution
forall a. Substitution' a
idS [ Nat -> Pattern' DBPatVar -> PatternSubstitution
forall a. EndoSubst a => Nat -> a -> Substitution' a
inplaceS Nat
i (Term -> Pattern' DBPatVar
forall a. Term -> Pattern' a
dotP (Nat -> Elims -> Term
Var Nat
i [])) | Nat
i <- IntMap Modality -> [Nat]
forall a. IntMap a -> [Nat]
IntMap.keys IntMap Modality
bound ]

  -- We moved the binding site of some forced variables, so we need to update their modalities in
  -- the telescope. The new modality is the combination of the modality of the variable we are
  -- instantiating and the modality of the binding site in the pattern (returned by
  -- patternBindingForcedVars).
  let updModality Modality
md IntMap Modality
vars Telescope
tel
        | IntMap Modality -> Bool
forall a. IntMap a -> Bool
IntMap.null IntMap Modality
vars = Telescope
tel
        | Bool
otherwise        = ListTel -> Telescope
telFromList (ListTel -> Telescope) -> ListTel -> Telescope
forall a b. (a -> b) -> a -> b
$ (Nat -> Dom (String, Type) -> Dom (String, Type))
-> [Nat] -> ListTel -> ListTel
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Nat -> Dom (String, Type) -> Dom (String, Type)
upd (Nat -> [Nat]
forall a. Integral a => a -> [a]
downFrom (Nat -> [Nat]) -> Nat -> [Nat]
forall a b. (a -> b) -> a -> b
$ Telescope -> Nat
forall a. Sized a => a -> Nat
size Telescope
tel) (Telescope -> ListTel
forall t. Tele (Dom t) -> [Dom (String, t)]
telToList Telescope
tel)
        where
          upd :: Nat -> Dom (String, Type) -> Dom (String, Type)
upd Nat
i Dom (String, Type)
a | Just Modality
md' <- Nat -> IntMap Modality -> Maybe Modality
forall a. Nat -> IntMap a -> Maybe a
IntMap.lookup Nat
i IntMap Modality
vars = Modality -> Dom (String, Type) -> Dom (String, Type)
forall a. LensModality a => Modality -> a -> a
setModality (Modality -> Modality -> Modality
composeModality Modality
md Modality
md') Dom (String, Type)
a
                  | Bool
otherwise                        = Dom (String, Type)
a
  s <- return $ s { varTel = updModality (getModality fi) bound (varTel s) }

  reportSDoc "tc.lhs.unify.force" 45 $ vcat
    [ "forcedVars =" <+> pretty (IntMap.keys forcedVars)
    , "u          =" <+> prettyTCM u
    , "p          =" <+> prettyTCM p
    , "bound      =" <+> pretty (IntMap.keys bound)
    , "dotSub     =" <+> pretty dotSub ]

  -- Check that the type of the variable is equal to the type of the equation
  -- (not just a subtype), otherwise we cannot instantiate (see Issue 2407).
  let dom'@Dom{ unDom = a' } = getVarType (m-1-i) s
  equalTypes <- addContext (varTel s) $ do
    reportSDoc "tc.lhs.unify" 45 $ "Equation type: " <+> prettyTCM a
    reportSDoc "tc.lhs.unify" 45 $ "Variable type: " <+> prettyTCM a'
    pureEqualTypeB a a'

  -- The conditions on the relevances are as follows (see #2640):
  -- - If the type of the equation is relevant, then the solution must be
  --   usable in a relevant position.
  -- - If the type of the equation is (shape-)irrelevant, then the solution
  --   must be usable in a μ-relevant position where μ is the relevance
  --   of the variable being solved.
  --
  -- Jesper, Andreas, 2018-10-17: the quantity of the equation is morally
  -- always @Quantity0@, since the indices of the data type are runtime erased.
  -- Thus, we need not change the quantity of the solution.
  envmod <- currentModality
  let eqrel  = Dom Type -> Relevance
forall a. LensRelevance a => a -> Relevance
getRelevance Dom Type
dom
      eqmod  = Dom Type -> Modality
forall a. LensModality a => a -> Modality
getModality Dom Type
dom
      varmod = Dom Type -> Modality
forall a. LensModality a => a -> Modality
getModality Dom Type
dom'
      mod    = Bool -> (Modality -> Modality) -> Modality -> Modality
forall b a. IsBool b => b -> (a -> a) -> a -> a
applyUnless (Relevance
shapeIrrelevant Relevance -> Relevance -> Bool
`moreRelevant` Relevance
eqrel) (Relevance -> Modality -> Modality
forall a. LensRelevance a => Relevance -> a -> a
setRelevance Relevance
eqrel)
             (Modality -> Modality) -> Modality -> Modality
forall a b. (a -> b) -> a -> b
$ Bool -> (Modality -> Modality) -> Modality -> Modality
forall b a. IsBool b => b -> (a -> a) -> a -> a
applyUnless (Modality -> Bool
forall a. LensQuantity a => a -> Bool
usableQuantity Modality
envmod) (Quantity -> Modality -> Modality
forall a. LensQuantity a => Quantity -> a -> a
setQuantity Quantity
zeroQuantity)
             (Modality -> Modality) -> Modality -> Modality
forall a b. (a -> b) -> a -> b
$ Modality
varmod
  reportSDoc "tc.lhs.unify" 65 $ text $ "Equation modality: " ++ show (getModality dom)
  reportSDoc "tc.lhs.unify" 65 $ text $ "Variable modality: " ++ show varmod
  reportSDoc "tc.lhs.unify" 65 $ text $ "Solution must be usable in a " ++ show mod ++ " position."
  -- Andreas, 2018-10-18
  -- Currently, the modality check has problems with meta-variables created in the type signature,
  -- and thus, in quantity 0, that get into terms using the unifier, and there are checked to be
  -- non-erased, i.e., have quantity ω.
  -- Ulf, 2019-12-13. We still do it though.
  -- Andrea, 2020-10-15: It looks at meta instantiations now.
  eusable <- addContext (varTel s) $ runExceptT $ usableMod mod u
  caseEitherM (return eusable) (return . UnifyBlocked) $ \ Bool
usable -> do

  String -> Nat -> TCMT IO Doc -> m ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
45 (TCMT IO Doc -> m ()) -> TCMT IO Doc -> m ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"Modality ok: " TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Bool -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Bool -> m Doc
prettyTCM Bool
usable
  Bool -> m () -> m ()
forall b (m :: * -> *). (IsBool b, Monad m) => b -> m () -> m ()
unless Bool
usable (m () -> m ()) -> m () -> m ()
forall a b. (a -> b) -> a -> b
$ String -> Nat -> TCMT IO Doc -> m ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
65 (TCMT IO Doc -> m ()) -> TCMT IO Doc -> m ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"Rejected solution: " TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Term -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Term -> m Doc
prettyTCM Term
u

  -- We need a Flat equality to solve a Flat variable.
  -- This also ought to take care of the need for a usableCohesion check.
  if Bool -> Bool
not (Modality -> Cohesion
forall a. LensCohesion a => a -> Cohesion
getCohesion Modality
eqmod Cohesion -> Cohesion -> Bool
`moreCohesion` Modality -> Cohesion
forall a. LensCohesion a => a -> Cohesion
getCohesion Modality
varmod) then UnificationResult' UnifyState -> m (UnificationResult' UnifyState)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> m (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> m (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck [] else do

  case Either Blocker Bool
equalTypes of
    Left Blocker
block  -> UnificationResult' UnifyState -> m (UnificationResult' UnifyState)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> m (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> m (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ Blocker -> UnificationResult' UnifyState
forall a. Blocker -> UnificationResult' a
UnifyBlocked Blocker
block
    Right Bool
False -> UnificationResult' UnifyState -> m (UnificationResult' UnifyState)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> m (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> m (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck []
    Right Bool
True | Bool
usable ->
      case Nat
-> Pattern' DBPatVar
-> UnifyState
-> Maybe (UnifyState, PatternSubstitution)
solveVar (Nat
m Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
- Nat
1 Nat -> Nat -> Nat
forall a. Num a => a -> a -> a
- Nat
i) Pattern' DBPatVar
p UnifyState
s of
        Maybe (UnifyState, PatternSubstitution)
Nothing | RetryNormalised
retry RetryNormalised -> RetryNormalised -> Bool
forall a. Eq a => a -> a -> Bool
== RetryNormalised
RetryNormalised -> do
          u <- Term -> m Term
forall a (m :: * -> *). (Normalise a, MonadReduce m) => a -> m a
normalise Term
u
          s <- lensVarTel normalise s
          solutionStep DontRetryNormalised s step{ solutionTerm = u }
        Maybe (UnifyState, PatternSubstitution)
Nothing ->
          UnificationResult' UnifyState -> m (UnificationResult' UnifyState)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> m (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> m (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck [Telescope -> Type -> Nat -> Term -> UnificationFailure
UnifyRecursiveEq (UnifyState -> Telescope
varTel UnifyState
s) Type
a Nat
i Term
u]
        Just (UnifyState
s', PatternSubstitution
sub) -> do
          let rho :: PatternSubstitution
rho = PatternSubstitution
sub PatternSubstitution -> PatternSubstitution -> PatternSubstitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` PatternSubstitution
dotSub
          PatternSubstitution -> m ()
forall (m :: * -> *).
MonadWriter UnifyOutput m =>
PatternSubstitution -> m ()
tellUnifySubst PatternSubstitution
rho
          let (UnifyState
s'', PatternSubstitution
sigma) = Nat -> Term -> UnifyState -> (UnifyState, PatternSubstitution)
solveEq Nat
k (PatternSubstitution -> Term -> Term
forall a. TermSubst a => PatternSubstitution -> a -> a
applyPatSubst PatternSubstitution
rho Term
u) UnifyState
s'
          PatternSubstitution -> m ()
forall (m :: * -> *).
MonadWriter UnifyOutput m =>
PatternSubstitution -> m ()
tellUnifyProof PatternSubstitution
sigma
          UnificationResult' UnifyState -> m (UnificationResult' UnifyState)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> m (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> m (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ UnifyState -> UnificationResult' UnifyState
forall a. a -> UnificationResult' a
Unifies UnifyState
s''
          -- Andreas, 2019-02-23, issue #3578: do not eagerly reduce
          -- Unifies <$> liftTCM (reduce s'')
    Right Bool
True -> UnificationResult' UnifyState -> m (UnificationResult' UnifyState)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> m (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> m (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck [Telescope -> Type -> Nat -> Term -> Modality -> UnificationFailure
UnifyUnusableModality (UnifyState -> Telescope
varTel UnifyState
s) Type
a Nat
i Term
u Modality
mod]
solutionStep RetryNormalised
_ UnifyState
_ UnifyStep
_ = m (UnificationResult' UnifyState)
forall a. HasCallStack => a
__IMPOSSIBLE__

unify :: UnifyState -> UnifyStrategy -> UnifyLogT TCM (UnificationResult' UnifyState)
unify :: UnifyState
-> UnifyStrategy -> UnifyLogT TCM (UnificationResult' UnifyState)
unify UnifyState
s UnifyStrategy
strategy = if UnifyState -> Bool
isUnifyStateSolved UnifyState
s
                   then UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ UnifyState -> UnificationResult' UnifyState
forall a. a -> UnificationResult' a
Unifies UnifyState
s
                   else ListT TCM UnifyStep
-> UnifyLogT TCM (UnificationResult' UnifyState)
tryUnifyStepsAndContinue (UnifyStrategy
strategy UnifyState
s)
  where
    tryUnifyStepsAndContinue
      :: ListT TCM UnifyStep -> UnifyLogT TCM (UnificationResult' UnifyState)
    tryUnifyStepsAndContinue :: ListT TCM UnifyStep
-> UnifyLogT TCM (UnificationResult' UnifyState)
tryUnifyStepsAndContinue ListT TCM UnifyStep
steps = do
      x <- (UnifyStep
 -> UnifyLogT TCM (UnificationResult' UnifyState)
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnifyLogT TCM (UnificationResult' UnifyState)
-> ListT (WriterT UnifyLog' TCM) UnifyStep
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b -> m b) -> m b -> ListT m a -> m b
foldListT UnifyStep
-> UnifyLogT TCM (UnificationResult' UnifyState)
-> UnifyLogT TCM (UnificationResult' UnifyState)
tryUnifyStep UnifyLogT TCM (UnificationResult' UnifyState)
forall (m :: * -> *) a. Monad m => m (UnificationResult' a)
failure ((forall a1. TCM a1 -> WriterT UnifyLog' TCM a1)
-> ListT TCM UnifyStep -> ListT (WriterT UnifyLog' TCM) UnifyStep
forall (m :: * -> *) (m' :: * -> *) a.
(Monad m, Monad m') =>
(forall a1. m a1 -> m' a1) -> ListT m a -> ListT m' a
liftListT TCM a1 -> WriterT UnifyLog' TCM a1
forall a1. TCM a1 -> WriterT UnifyLog' TCM a1
forall (m :: * -> *) a. Monad m => m a -> WriterT UnifyLog' m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift ListT TCM UnifyStep
steps)
      case x of
        Unifies UnifyState
s'     -> UnifyState
-> UnifyStrategy -> UnifyLogT TCM (UnificationResult' UnifyState)
unify UnifyState
s' UnifyStrategy
strategy
        NoUnify NegativeUnification
err    -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ NegativeUnification -> UnificationResult' UnifyState
forall a. NegativeUnification -> UnificationResult' a
NoUnify NegativeUnification
err
        UnifyBlocked Blocker
b -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ Blocker -> UnificationResult' UnifyState
forall a. Blocker -> UnificationResult' a
UnifyBlocked Blocker
b
        UnifyStuck [UnificationFailure]
err -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck [UnificationFailure]
err

    tryUnifyStep :: UnifyStep
                 -> UnifyLogT TCM (UnificationResult' UnifyState)
                 -> UnifyLogT TCM (UnificationResult' UnifyState)
    tryUnifyStep :: UnifyStep
-> UnifyLogT TCM (UnificationResult' UnifyState)
-> UnifyLogT TCM (UnificationResult' UnifyState)
tryUnifyStep UnifyStep
step UnifyLogT TCM (UnificationResult' UnifyState)
fallback = do
      Telescope -> WriterT UnifyLog' TCM () -> WriterT UnifyLog' TCM ()
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
Telescope -> m a -> m a
addContext (UnifyState -> Telescope
varTel UnifyState
s) (WriterT UnifyLog' TCM () -> WriterT UnifyLog' TCM ())
-> WriterT UnifyLog' TCM () -> WriterT UnifyLog' TCM ()
forall a b. (a -> b) -> a -> b
$
        String -> Nat -> TCMT IO Doc -> WriterT UnifyLog' TCM ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
20 (TCMT IO Doc -> WriterT UnifyLog' TCM ())
-> TCMT IO Doc -> WriterT UnifyLog' TCM ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"trying unifyStep" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> UnifyStep -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => UnifyStep -> m Doc
prettyTCM UnifyStep
step
      (x, output) <- TCM (UnificationResult' UnifyState, UnifyOutput)
-> WriterT
     UnifyLog' TCM (UnificationResult' UnifyState, UnifyOutput)
forall (m :: * -> *) a. Monad m => m a -> WriterT UnifyLog' m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (TCM (UnificationResult' UnifyState, UnifyOutput)
 -> WriterT
      UnifyLog' TCM (UnificationResult' UnifyState, UnifyOutput))
-> TCM (UnificationResult' UnifyState, UnifyOutput)
-> WriterT
     UnifyLog' TCM (UnificationResult' UnifyState, UnifyOutput)
forall a b. (a -> b) -> a -> b
$ UnifyStepT TCM (UnificationResult' UnifyState)
-> TCM (UnificationResult' UnifyState, UnifyOutput)
forall w (m :: * -> *) a. WriterT w m a -> m (a, w)
runWriterT (UnifyStepT TCM (UnificationResult' UnifyState)
 -> TCM (UnificationResult' UnifyState, UnifyOutput))
-> UnifyStepT TCM (UnificationResult' UnifyState)
-> TCM (UnificationResult' UnifyState, UnifyOutput)
forall a b. (a -> b) -> a -> b
$ UnifyState
-> UnifyStep -> UnifyStepT TCM (UnificationResult' UnifyState)
unifyStep UnifyState
s UnifyStep
step
      case x of
        Unifies UnifyState
s'   -> do
          String -> Nat -> TCMT IO Doc -> WriterT UnifyLog' TCM ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
20 (TCMT IO Doc -> WriterT UnifyLog' TCM ())
-> TCMT IO Doc -> WriterT UnifyLog' TCM ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"unifyStep successful."
          String -> Nat -> TCMT IO Doc -> WriterT UnifyLog' TCM ()
forall (m :: * -> *).
MonadDebug m =>
String -> Nat -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify" Nat
20 (TCMT IO Doc -> WriterT UnifyLog' TCM ())
-> TCMT IO Doc -> WriterT UnifyLog' TCM ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"new unifyState:" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> UnifyState -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => UnifyState -> m Doc
prettyTCM UnifyState
s'
          -- tell output
          (UnifyLogEntry, UnifyState) -> WriterT UnifyLog' TCM ()
forall (m :: * -> *).
MonadWriter UnifyLog' m =>
(UnifyLogEntry, UnifyState) -> m ()
writeUnifyLog ((UnifyLogEntry, UnifyState) -> WriterT UnifyLog' TCM ())
-> (UnifyLogEntry, UnifyState) -> WriterT UnifyLog' TCM ()
forall a b. (a -> b) -> a -> b
$ (UnifyState -> UnifyStep -> UnifyOutput -> UnifyLogEntry
UnificationStep UnifyState
s UnifyStep
step UnifyOutput
output,UnifyState
s')
          UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return UnificationResult' UnifyState
x
        NoUnify{}       -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return UnificationResult' UnifyState
x
        UnifyBlocked Blocker
b1 -> do
          y <- UnifyLogT TCM (UnificationResult' UnifyState)
fallback
          case y of
            UnifyStuck [UnificationFailure]
_    -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ Blocker -> UnificationResult' UnifyState
forall a. Blocker -> UnificationResult' a
UnifyBlocked Blocker
b1
            UnifyBlocked Blocker
b2 -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ Blocker -> UnificationResult' UnifyState
forall a. Blocker -> UnificationResult' a
UnifyBlocked (Blocker -> UnificationResult' UnifyState)
-> Blocker -> UnificationResult' UnifyState
forall a b. (a -> b) -> a -> b
$ Blocker -> Blocker -> Blocker
unblockOnEither Blocker
b1 Blocker
b2
            UnificationResult' UnifyState
_               -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return UnificationResult' UnifyState
y
        UnifyStuck [UnificationFailure]
err1 -> do
          y <- UnifyLogT TCM (UnificationResult' UnifyState)
fallback
          case y of
            UnifyStuck [UnificationFailure]
err2 -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' UnifyState
 -> UnifyLogT TCM (UnificationResult' UnifyState))
-> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' UnifyState
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck ([UnificationFailure] -> UnificationResult' UnifyState)
-> [UnificationFailure] -> UnificationResult' UnifyState
forall a b. (a -> b) -> a -> b
$ [UnificationFailure]
err1 [UnificationFailure]
-> [UnificationFailure] -> [UnificationFailure]
forall a. [a] -> [a] -> [a]
++ [UnificationFailure]
err2
            UnificationResult' UnifyState
_               -> UnificationResult' UnifyState
-> UnifyLogT TCM (UnificationResult' UnifyState)
forall a. a -> WriterT UnifyLog' TCM a
forall (m :: * -> *) a. Monad m => a -> m a
return UnificationResult' UnifyState
y

    failure :: Monad m => m (UnificationResult' a)
    failure :: forall (m :: * -> *) a. Monad m => m (UnificationResult' a)
failure = UnificationResult' a -> m (UnificationResult' a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (UnificationResult' a -> m (UnificationResult' a))
-> UnificationResult' a -> m (UnificationResult' a)
forall a b. (a -> b) -> a -> b
$ [UnificationFailure] -> UnificationResult' a
forall a. [UnificationFailure] -> UnificationResult' a
UnifyStuck []

-- | Turn a term into a pattern while binding as many of the given forced variables as possible (in
--   non-forced positions).
patternBindingForcedVars :: PureTCM m => IntMap Modality -> Term -> m (DeBruijnPattern, IntMap Modality)
patternBindingForcedVars :: forall (m :: * -> *).
PureTCM m =>
IntMap Modality -> Term -> m (Pattern' DBPatVar, IntMap Modality)
patternBindingForcedVars IntMap Modality
forced Term
v = do
  let v' :: Term
v' = Term -> Term
forall a. PrecomputeFreeVars a => a -> a
precomputeFreeVars_ Term
v
  WriterT (IntMap Modality) m (Pattern' DBPatVar)
-> m (Pattern' DBPatVar, IntMap Modality)
forall w (m :: * -> *) a. WriterT w m a -> m (a, w)
runWriterT (StateT
  (IntMap Modality) (WriterT (IntMap Modality) m) (Pattern' DBPatVar)
-> IntMap Modality
-> WriterT (IntMap Modality) m (Pattern' DBPatVar)
forall (m :: * -> *) s a. Monad m => StateT s m a -> s -> m a
evalStateT (Modality
-> Term
-> StateT
     (IntMap Modality) (WriterT (IntMap Modality) m) (Pattern' DBPatVar)
forall {t :: (* -> *) -> * -> *} {t :: (* -> *) -> * -> *}
       {m :: * -> *} {a}.
(HasConstInfo (t (t m)), DeBruijn a,
 MonadWriter (IntMap Modality) (t (t m)),
 MonadState (IntMap Modality) (t (t m)), MonadTrans t, MonadTrans t,
 Monad (t m), MonadReduce m) =>
Modality -> Term -> t (t m) (Pattern' a)
go Modality
unitModality Term
v') IntMap Modality
forced)
  where
    noForced :: a -> m Bool
noForced a
v = (IntMap a -> Bool) -> m Bool
forall s (m :: * -> *) a. MonadState s m => (s -> a) -> m a
gets ((IntMap a -> Bool) -> m Bool) -> (IntMap a -> Bool) -> m Bool
forall a b. (a -> b) -> a -> b
$ IntSet -> IntSet -> Bool
IntSet.disjoint (a -> IntSet
forall a. PrecomputeFreeVars a => a -> IntSet
precomputedFreeVars a
v) (IntSet -> Bool) -> (IntMap a -> IntSet) -> IntMap a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. IntMap a -> IntSet
forall a. IntMap a -> IntSet
IntMap.keysSet

    bind :: a -> Nat -> m (Pattern' a)
bind a
md Nat
i = do
      (IntMap a -> Maybe a) -> m (Maybe a)
forall s (m :: * -> *) a. MonadState s m => (s -> a) -> m a
gets (Nat -> IntMap a -> Maybe a
forall a. Nat -> IntMap a -> Maybe a
IntMap.lookup Nat
i) m (Maybe a) -> (Maybe a -> m (Pattern' a)) -> m (Pattern' a)
forall a b. m a -> (a -> m b) -> m b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= \case
        Just a
md' | a -> PartialOrdering -> a -> Bool
forall a. PartialOrd a => a -> PartialOrdering -> a -> Bool
related a
md PartialOrdering
POLE a
md' -> do
          -- The new binding site must be more relevant (more relevant = smaller).
          -- "The forcing analysis guarantees that there exists such a position."
          -- Really? Andreas, 2021-08-18, issue #5506
          IntMap a -> m ()
forall w (m :: * -> *). MonadWriter w m => w -> m ()
tell   (IntMap a -> m ()) -> IntMap a -> m ()
forall a b. (a -> b) -> a -> b
$ Nat -> a -> IntMap a
forall a. Nat -> a -> IntMap a
IntMap.singleton Nat
i a
md
          (IntMap a -> IntMap a) -> m ()
forall s (m :: * -> *). MonadState s m => (s -> s) -> m ()
modify ((IntMap a -> IntMap a) -> m ()) -> (IntMap a -> IntMap a) -> m ()
forall a b. (a -> b) -> a -> b
$ Nat -> IntMap a -> IntMap a
forall a. Nat -> IntMap a -> IntMap a
IntMap.delete Nat
i
          Pattern' a -> m (Pattern' a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> m (Pattern' a)) -> Pattern' a -> m (Pattern' a)
forall a b. (a -> b) -> a -> b
$ a -> Pattern' a
forall a. a -> Pattern' a
varP (Nat -> a
forall a. DeBruijn a => Nat -> a
deBruijnVar Nat
i)
        Maybe a
_ -> Pattern' a -> m (Pattern' a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> m (Pattern' a)) -> Pattern' a -> m (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP (Nat -> Elims -> Term
Var Nat
i [])

    go :: Modality -> Term -> t (t m) (Pattern' a)
go Modality
md Term
v = t (t m) Bool
-> t (t m) (Pattern' a)
-> t (t m) (Pattern' a)
-> t (t m) (Pattern' a)
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM (Term -> t (t m) Bool
forall {a} {m :: * -> *} {a}.
(MonadState (IntMap a) m, PrecomputeFreeVars a) =>
a -> m Bool
noForced Term
v) (Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v) (t (t m) (Pattern' a) -> t (t m) (Pattern' a))
-> t (t m) (Pattern' a) -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ do
      v' <- t m Term -> t (t m) Term
forall (m :: * -> *) a. Monad m => m a -> t m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (t m Term -> t (t m) Term) -> t m Term -> t (t m) Term
forall a b. (a -> b) -> a -> b
$ m Term -> t m Term
forall (m :: * -> *) a. Monad m => m a -> t m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m Term -> t m Term) -> m Term -> t m Term
forall a b. (a -> b) -> a -> b
$ Term -> m Term
forall a (m :: * -> *). (Reduce a, MonadReduce m) => a -> m a
reduce Term
v
      case v' of
        Var Nat
i [] -> Modality -> Nat -> t (t m) (Pattern' a)
forall {m :: * -> *} {a} {a}.
(MonadState (IntMap a) m, PartialOrd a, MonadWriter (IntMap a) m,
 DeBruijn a) =>
a -> Nat -> m (Pattern' a)
bind Modality
md Nat
i  -- we know i is forced
        Con ConHead
c ConInfo
ci Elims
es
          | Just [Arg Term]
vs <- Elims -> Maybe [Arg Term]
forall a. [Elim' a] -> Maybe [Arg a]
allApplyElims Elims
es -> do
            fs <- Definition -> [IsForced]
defForced (Definition -> [IsForced])
-> t (t m) Definition -> t (t m) [IsForced]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> QName -> t (t m) Definition
forall (m :: * -> *). HasConstInfo m => QName -> m Definition
getConstInfo (ConHead -> QName
conName ConHead
c)
            let goArg IsForced
Forced    Arg Term
v = NamedArg (Pattern' a) -> t (t m) (NamedArg (Pattern' a))
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (NamedArg (Pattern' a) -> t (t m) (NamedArg (Pattern' a)))
-> NamedArg (Pattern' a) -> t (t m) (NamedArg (Pattern' a))
forall a b. (a -> b) -> a -> b
$ (Term -> Named NamedName (Pattern' a))
-> Arg Term -> NamedArg (Pattern' a)
forall a b. (a -> b) -> Arg a -> Arg b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Pattern' a -> Named NamedName (Pattern' a)
forall a name. a -> Named name a
unnamed (Pattern' a -> Named NamedName (Pattern' a))
-> (Term -> Pattern' a) -> Term -> Named NamedName (Pattern' a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Pattern' a
forall a. Term -> Pattern' a
dotP) Arg Term
v
                goArg IsForced
NotForced Arg Term
v = (Pattern' a -> Named NamedName (Pattern' a))
-> Arg (Pattern' a) -> NamedArg (Pattern' a)
forall a b. (a -> b) -> Arg a -> Arg b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Pattern' a -> Named NamedName (Pattern' a)
forall a name. a -> Named name a
unnamed (Arg (Pattern' a) -> NamedArg (Pattern' a))
-> t (t m) (Arg (Pattern' a)) -> t (t m) (NamedArg (Pattern' a))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Term -> t (t m) (Pattern' a))
-> Arg Term -> t (t m) (Arg (Pattern' a))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Arg a -> f (Arg b)
traverse (Modality -> Term -> t (t m) (Pattern' a)
go (Modality -> Term -> t (t m) (Pattern' a))
-> Modality -> Term -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Modality -> Modality -> Modality
composeModality Modality
md (Modality -> Modality) -> Modality -> Modality
forall a b. (a -> b) -> a -> b
$ Arg Term -> Modality
forall a. LensModality a => a -> Modality
getModality Arg Term
v) Arg Term
v
            (ps, bound) <- listen $ zipWithM goArg (fs ++ repeat NotForced) vs
            if IntMap.null bound
              then return $ dotP v  -- bound nothing
              else do
                let cpi = (ConInfo -> ConPatternInfo
toConPatternInfo ConInfo
ci) { conPLazy   = True } -- Not setting conPType. Is this a problem?
                return $ ConP c cpi $ map (setOrigin Inserted) ps
          | Bool
otherwise -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v   -- Higher constructor (es has IApply)

        -- Non-pattern positions
        Var Nat
_ (Elim
_:Elims
_) -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Lam{}       -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Pi{}        -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Def{}       -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        MetaV{}     -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Sort{}      -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Level{}     -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        DontCare{}  -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Dummy{}     -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
        Lit{}       -> Pattern' a -> t (t m) (Pattern' a)
forall a. a -> t (t m) a
forall (m :: * -> *) a. Monad m => a -> m a
return (Pattern' a -> t (t m) (Pattern' a))
-> Pattern' a -> t (t m) (Pattern' a)
forall a b. (a -> b) -> a -> b
$ Term -> Pattern' a
forall a. Term -> Pattern' a
dotP Term
v
          -- Andreas, 2023-08-20, issue #6767
          -- The last case is not __IMPOSSIBLE__ (regresssion in 2.6.2).
          -- It would be if we had reduced to `constructorForm`,
          -- however, turning a `LitNat` into constructors would only result in churn,
          -- since literals have no variables that could be bound.