{-# OPTIONS_GHC -Wunused-imports #-}

{-# LANGUAGE NondecreasingIndentation #-}

module Agda.TypeChecking.Rules.LHS.Unify.LeftInverse where

import Prelude hiding ((!!), null)

import Control.Monad
import Control.Monad.State
import Control.Monad.Except

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

import Agda.TypeChecking.Monad
import Agda.TypeChecking.Primitive hiding (Nat)
import Agda.TypeChecking.Names
import Agda.TypeChecking.Reduce
import Agda.TypeChecking.Pretty
import Agda.TypeChecking.Substitute
import Agda.TypeChecking.Telescope
import Agda.TypeChecking.Records

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

import Agda.Utils.List
import Agda.Utils.Maybe
import Agda.Utils.Monad
import Agda.Utils.Null
import Agda.Utils.Size

import Agda.Utils.Impossible

instance PrettyTCM NoLeftInv where
  prettyTCM :: forall (m :: * -> *). MonadPretty m => NoLeftInv -> m Doc
prettyTCM (UnsupportedYet UnifyStep
s) = [m Doc] -> m Doc
forall (m :: * -> *) (t :: * -> *).
(Applicative m, Foldable t) =>
t (m Doc) -> m Doc
fsep ([m Doc] -> m Doc) -> [m Doc] -> m Doc
forall a b. (a -> b) -> a -> b
$ String -> [m Doc]
forall (m :: * -> *). Applicative m => String -> [m Doc]
pwords String
"It relies on" [m Doc] -> [m Doc] -> [m Doc]
forall a. [a] -> [a] -> [a]
++ [UnifyStep -> m Doc
forall (m :: * -> *). MonadPretty m => UnifyStep -> m Doc
explainStep UnifyStep
s m Doc -> m Doc -> m Doc
forall a. Semigroup a => a -> a -> a
<> m Doc
","] [m Doc] -> [m Doc] -> [m Doc]
forall a. [a] -> [a] -> [a]
++ String -> [m Doc]
forall (m :: * -> *). Applicative m => String -> [m Doc]
pwords String
"which is not yet supported"
  prettyTCM NoLeftInv
UnsupportedCxt     = String -> m Doc
forall (m :: * -> *). Applicative m => String -> m Doc
fwords String
"it relies on higher-dimensional unification, which is not yet supported"
  prettyTCM (Illegal UnifyStep
s)        = [m Doc] -> m Doc
forall (m :: * -> *) (t :: * -> *).
(Applicative m, Foldable t) =>
t (m Doc) -> m Doc
fsep ([m Doc] -> m Doc) -> [m Doc] -> m Doc
forall a b. (a -> b) -> a -> b
$ String -> [m Doc]
forall (m :: * -> *). Applicative m => String -> [m Doc]
pwords String
"It relies on" [m Doc] -> [m Doc] -> [m Doc]
forall a. [a] -> [a] -> [a]
++ [UnifyStep -> m Doc
forall (m :: * -> *). MonadPretty m => UnifyStep -> m Doc
explainStep UnifyStep
s m Doc -> m Doc -> m Doc
forall a. Semigroup a => a -> a -> a
<> m Doc
","] [m Doc] -> [m Doc] -> [m Doc]
forall a. [a] -> [a] -> [a]
++ String -> [m Doc]
forall (m :: * -> *). Applicative m => String -> [m Doc]
pwords String
"which is incompatible with" [m Doc] -> [m Doc] -> [m Doc]
forall a. [a] -> [a] -> [a]
++ [String -> m Doc
forall (m :: * -> *). Applicative m => String -> m Doc
text String
"Cubical Agda"]
  prettyTCM NoLeftInv
NoCubical          = String -> m Doc
forall (m :: * -> *). Applicative m => String -> m Doc
fwords String
"Cubical Agda is disabled"
  prettyTCM NoLeftInv
WithKEnabled       = String -> m Doc
forall (m :: * -> *). Applicative m => String -> m Doc
fwords String
"The K rule is enabled"
  prettyTCM NoLeftInv
SplitOnStrict      = String -> m Doc
forall (m :: * -> *). Applicative m => String -> m Doc
fwords String
"It splits on a type in SSet"
  prettyTCM NoLeftInv
SplitOnFlat        = String -> m Doc
forall (m :: * -> *). Applicative m => String -> m Doc
fwords String
"It splits on a @♭ argument"

data NoLeftInv
  = UnsupportedYet {NoLeftInv -> UnifyStep
badStep :: UnifyStep}
  | Illegal        {badStep :: UnifyStep}
  | NoCubical
  | WithKEnabled
  | SplitOnStrict  -- ^ splitting on a Strict Set.
  | SplitOnFlat    -- ^ splitting on a @♭ argument
  | UnsupportedCxt
  deriving Int -> NoLeftInv -> ShowS
[NoLeftInv] -> ShowS
NoLeftInv -> String
(Int -> NoLeftInv -> ShowS)
-> (NoLeftInv -> String)
-> ([NoLeftInv] -> ShowS)
-> Show NoLeftInv
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> NoLeftInv -> ShowS
showsPrec :: Int -> NoLeftInv -> ShowS
$cshow :: NoLeftInv -> String
show :: NoLeftInv -> String
$cshowList :: [NoLeftInv] -> ShowS
showList :: [NoLeftInv] -> ShowS
Show

buildLeftInverse :: (PureTCM tcm, MonadError TCErr tcm) => UnifyState -> UnifyLog -> tcm (Either NoLeftInv (Substitution, Substitution))
buildLeftInverse :: forall (tcm :: * -> *).
(PureTCM tcm, MonadError TCErr tcm) =>
UnifyState
-> UnifyLog -> tcm (Either NoLeftInv (Substitution, Substitution))
buildLeftInverse UnifyState
s0 UnifyLog
log = do
  String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv.badstep" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ do
    cubical <- TCMT IO (Maybe Cubical)
forall (m :: * -> *). HasOptions m => m (Maybe Cubical)
cubicalOption
    "cubical:" <+> text (show cubical)
  String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv.badstep" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ do
    pathp <- BuiltinId -> TCMT IO (Maybe Term)
forall (m :: * -> *) a.
(HasBuiltins m, IsBuiltin a) =>
a -> m (Maybe Term)
getTerm' BuiltinId
builtinPathP
    "pathp:" <+> text (show $ isJust pathp)
  let cond :: tcm Bool
cond = [tcm Bool] -> tcm Bool
forall (f :: * -> *) (m :: * -> *).
(Foldable f, Monad m) =>
f (m Bool) -> m Bool
andM
       -- TODO: handle open contexts: they happen during "higher dimensional" unification,
       --       in injectivity cases.
       [
         Context -> Bool
forall a. Null a => a -> Bool
null (Context -> Bool) -> tcm Context -> tcm Bool
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> tcm Context
forall (m :: * -> *). MonadTCEnv m => m Context
getContext
       ]
  tcm Bool
-> tcm (Either NoLeftInv (Substitution, Substitution))
-> tcm (Either NoLeftInv (Substitution, Substitution))
-> tcm (Either NoLeftInv (Substitution, Substitution))
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifNotM tcm Bool
cond (Either NoLeftInv (Substitution, Substitution)
-> tcm (Either NoLeftInv (Substitution, Substitution))
forall a. a -> tcm a
forall (m :: * -> *) a. Monad m => a -> m a
return (Either NoLeftInv (Substitution, Substitution)
 -> tcm (Either NoLeftInv (Substitution, Substitution)))
-> Either NoLeftInv (Substitution, Substitution)
-> tcm (Either NoLeftInv (Substitution, Substitution))
forall a b. (a -> b) -> a -> b
$ NoLeftInv -> Either NoLeftInv (Substitution, Substitution)
forall a b. a -> Either a b
Left NoLeftInv
UnsupportedCxt) (tcm (Either NoLeftInv (Substitution, Substitution))
 -> tcm (Either NoLeftInv (Substitution, Substitution)))
-> tcm (Either NoLeftInv (Substitution, Substitution))
-> tcm (Either NoLeftInv (Substitution, Substitution))
forall a b. (a -> b) -> a -> b
$ do
  equivs <- UnifyLog
-> ((UnifyLogEntry, UnifyState)
    -> tcm (Either NoLeftInv (Retract, Term)))
-> tcm [Either NoLeftInv (Retract, Term)]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
t a -> (a -> m b) -> m (t b)
forM UnifyLog
log (((UnifyLogEntry, UnifyState)
  -> tcm (Either NoLeftInv (Retract, Term)))
 -> tcm [Either NoLeftInv (Retract, Term)])
-> ((UnifyLogEntry, UnifyState)
    -> tcm (Either NoLeftInv (Retract, Term)))
-> tcm [Either NoLeftInv (Retract, Term)]
forall a b. (a -> b) -> a -> b
$ (UnifyLogEntry
 -> UnifyState -> tcm (Either NoLeftInv (Retract, Term)))
-> (UnifyLogEntry, UnifyState)
-> tcm (Either NoLeftInv (Retract, Term))
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry UnifyLogEntry
-> UnifyState -> tcm (Either NoLeftInv (Retract, Term))
forall (tcm :: * -> *).
(PureTCM tcm, MonadError TCErr tcm) =>
UnifyLogEntry
-> UnifyState -> tcm (Either NoLeftInv (Retract, Term))
buildEquiv
  case sequence equivs of
    Left NoLeftInv
no -> do
      String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv.badstep" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"No Left Inverse:" 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 (NoLeftInv -> UnifyStep
badStep NoLeftInv
no)
      Either NoLeftInv (Substitution, Substitution)
-> tcm (Either NoLeftInv (Substitution, Substitution))
forall a. a -> tcm a
forall (m :: * -> *) a. Monad m => a -> m a
return (NoLeftInv -> Either NoLeftInv (Substitution, Substitution)
forall a b. a -> Either a b
Left NoLeftInv
no)
    Right [(Retract, Term)]
xs -> do
    -- Γ,φ,us =_Δ vs ⊢ τ0 : Γ', φ
    -- Γ,φ,us =_Δ vs, i : I ⊢ leftInv0 : Γ,φ,us =_Δ vs
    -- leftInv0 : [wkS |φ,us =_Δ vs| ρ,φ,refls][τ0] = IdS : Γ,φ,us =_Δ vs
    (tau0,leftInv0) <- case [(Retract, Term)]
xs of
      [] -> (Substitution, Substitution) -> tcm (Substitution, Substitution)
forall a. a -> tcm a
forall (m :: * -> *) a. Monad m => a -> m a
return (Substitution
forall a. Substitution' a
idS,Int -> Substitution
forall a. Int -> Substitution' a
raiseS Int
1)
      [(Retract, Term)]
xs -> do
        let
            loop :: [(Retract, Term)] -> m Retract
loop [] = m Retract
forall a. HasCallStack => a
__IMPOSSIBLE__
            loop [(Retract, Term)
x] = Retract -> m Retract
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (Retract -> m Retract) -> Retract -> m Retract
forall a b. (a -> b) -> a -> b
$ (Retract, Term) -> Retract
forall a b. (a, b) -> a
fst (Retract, Term)
x
            loop ((Retract, Term)
x:[(Retract, Term)]
xs) = do
              r <- [(Retract, Term)] -> m Retract
loop [(Retract, Term)]
xs
              uncurry composeRetract x r
        (_,_,tau,leftInv) <- [(Retract, Term)] -> tcm Retract
forall {m :: * -> *}.
(PureTCM m, MonadError TCErr m) =>
[(Retract, Term)] -> m Retract
loop [(Retract, Term)]
xs
        return (tau,leftInv)
    -- Γ,φ,us =_Δ vs ⊢ τ0 : Γ', φ
    -- leftInv0 : [wkS |φ,us =_Δ vs| ρ,1,refls][τ] = idS : Γ,φ,us =_Δ vs
    let tau = Substitution
tau0 Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Int -> Substitution
forall a. Int -> Substitution' a
raiseS Int
1
    unview <- intervalUnview'
    let replaceAt Int
n a
x [a]
xs = [a]
xs0 [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
xs1
                where ([a]
xs0,a
_:[a]
xs1) = Int -> [a] -> ([a], [a])
forall a. Int -> [a] -> ([a], [a])
splitAt Int
n [a]
xs
    let max Term
r Term
s = IntervalView -> Term
unview (IntervalView -> Term) -> IntervalView -> Term
forall a b. (a -> b) -> a -> b
$ Arg Term -> Arg Term -> IntervalView
IMax (Term -> Arg Term
forall e. e -> Arg e
argN Term
r) (Term -> Arg Term
forall e. e -> Arg e
argN Term
s)
        neg Term
r = IntervalView -> Term
unview (IntervalView -> Term) -> IntervalView -> Term
forall a b. (a -> b) -> a -> b
$ Arg Term -> IntervalView
INeg (Term -> Arg Term
forall e. e -> Arg e
argN Term
r)
    let phieq = Term -> Term
neg (Int -> Term
var Int
0) Term -> Term -> Term
`max` Int -> Term
var (Telescope -> Int
forall a. Sized a => a -> Int
size (UnifyState -> Telescope
eqTel UnifyState
s0) Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1)
                       -- I + us =_Δ vs -- inplaceS
    let leftInv = Impossible -> [Term] -> Substitution
forall a. DeBruijn a => Impossible -> [a] -> Substitution' a
termsS Impossible
forall a. HasCallStack => a
__IMPOSSIBLE__ ([Term] -> Substitution) -> [Term] -> Substitution
forall a b. (a -> b) -> a -> b
$ Int -> Term -> [Term] -> [Term]
forall {a}. Int -> a -> [a] -> [a]
replaceAt (Telescope -> Int
forall a. Sized a => a -> Int
size (UnifyState -> Telescope
varTel UnifyState
s0)) Term
phieq ([Term] -> [Term]) -> [Term] -> [Term]
forall a b. (a -> b) -> a -> b
$ (Int -> Term) -> [Int] -> [Term]
forall a b. (a -> b) -> [a] -> [b]
map (Substitution -> Int -> Term
forall a. EndoSubst a => Substitution' a -> Int -> a
lookupS Substitution
leftInv0) ([Int] -> [Term]) -> [Int] -> [Term]
forall a b. (a -> b) -> a -> b
$ Int -> [Int]
forall a. Integral a => a -> [a]
downFrom (Telescope -> Int
forall a. Sized a => a -> Int
size (UnifyState -> Telescope
varTel UnifyState
s0) Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Telescope -> Int
forall a. Sized a => a -> Int
size (UnifyState -> Telescope
eqTel UnifyState
s0))
    let working_tel = Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
abstract (UnifyState -> Telescope
varTel UnifyState
s0) (Dom Type -> Abs Telescope -> Telescope
forall a. a -> Abs (Tele a) -> Tele a
ExtendTel Dom Type
HasCallStack => Dom Type
__DUMMY_DOM__ (Abs Telescope -> Telescope) -> Abs Telescope -> Telescope
forall a b. (a -> b) -> a -> b
$ String -> Telescope -> Abs Telescope
forall a. String -> a -> Abs a
Abs String
"phi0" (Telescope -> Abs Telescope) -> Telescope -> Abs Telescope
forall a b. (a -> b) -> a -> b
$ (UnifyState -> Telescope
eqTel UnifyState
s0))
    reportSDoc "tc.lhs.unify.inv" 20 $ "=== before mod"
    do
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau0    :" <+> prettyTCM tau0
        addContext working_tel $ addContext ("r" :: String, __DUMMY_DOM__)
                               $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv0:  " <+> prettyTCM leftInv0

    reportSDoc "tc.lhs.unify.inv" 20 $ "=== after mod"
    do
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau    :" <+> prettyTCM tau
        addContext working_tel $ addContext ("r" :: String, __DUMMY_DOM__)
                               $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv:   " <+> prettyTCM leftInv

    return $ Right (tau,leftInv)

type Retract = (Telescope, Substitution, Substitution, Substitution)
     -- Γ (the problem, including equalities),
     -- Δ ⊢ ρ : Γ
     -- Γ ⊢ τ : Δ
     -- Γ, i : I ⊢ leftInv : Γ, such that (λi. leftInv) : ρ[τ] = id_Γ

--- Γ ⊢ us : Δ   Γ ⊢ termsS e us : Δ
termsS ::  DeBruijn a => Impossible -> [a] -> Substitution' a
termsS :: forall a. DeBruijn a => Impossible -> [a] -> Substitution' a
termsS Impossible
e [a]
xs = [a] -> [a]
forall a. [a] -> [a]
reverse [a]
xs [a] -> Substitution' a -> Substitution' a
forall a. DeBruijn a => [a] -> Substitution' a -> Substitution' a
++# Impossible -> Substitution' a
forall a. Impossible -> Substitution' a
EmptyS Impossible
e

composeRetract :: (PureTCM tcm, MonadError TCErr tcm, MonadDebug tcm,HasBuiltins tcm, MonadAddContext tcm) => Retract -> Term -> Retract -> tcm Retract
composeRetract :: forall (tcm :: * -> *).
(PureTCM tcm, MonadError TCErr tcm, MonadDebug tcm,
 HasBuiltins tcm, MonadAddContext tcm) =>
Retract -> Term -> Retract -> tcm Retract
composeRetract (Telescope
prob0,Substitution
rho0,Substitution
tau0,Substitution
leftInv0) Term
phi0 (Telescope
prob1,Substitution
rho1,Substitution
tau1,Substitution
leftInv1) = do
  String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"=== composing"
  String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"Γ0   :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Telescope -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Telescope -> m Doc
prettyTCM Telescope
prob0
  Telescope -> tcm () -> 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 Telescope
prob0 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"tau0  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
tau0
  String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"Γ1   :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Telescope -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Telescope -> m Doc
prettyTCM Telescope
prob1
  Telescope -> tcm () -> 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 Telescope
prob1 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"tau1  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
tau1


  {-
  Γ0 = prob0
  S0 ⊢ ρ0 : Γ0
  Γ0 ⊢ τ0 : S0
  Γ0 ⊢ leftInv0 : ρ0[τ0] = idΓ0
  Γ0 ⊢ φ0
  Γ0,φ0 ⊢ leftInv0 = refl

  Γ1 = prob1
  S1 ⊢ ρ1 : Γ1
  Γ1 ⊢ τ1 : S1
  Γ1 ⊢ leftInv1 : ρ1[τ1] = idΓ1
  Γ1 ⊢ φ1 = φ0[τ0] (**)
  Γ1,φ1 ⊢ leftInv1 = refl
  S0 = Γ1

  (**) implies?
  Γ0,φ0 ⊢ leftInv1[τ0] = refl  (*)


  S1 ⊢ ρ := ρ0[ρ1] : Γ0
  Γ0 ⊢ τ := τ1[τ0] : S1
  -}

  let prob :: Telescope
prob = Telescope
prob0
  let rho :: Substitution
rho = Substitution
rho1 Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Substitution
rho0
  let tau :: Substitution
tau = Substitution
tau0 Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Substitution
tau1

  Telescope -> tcm () -> 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 Telescope
prob0 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"tau  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
tau

  {-
  Γ0 ⊢ leftInv : ρ[τ] = idΓ0
  Γ0 ⊢ leftInv : ρ0[ρ1[τ1]][τ0] = idΓ0
  Γ0 ⊢ step0 := ρ0[leftInv1[τ0]] : ρ0[ρ1[τ1]][τ0] = ρ0[τ0]

  Γ0,φ0 ⊢ step0 = refl     by (*)


  Γ0 ⊢ leftInv := step0 · leftInv0 : ρ0[ρ1[τ1]][τ0] = idΓ0

  Γ0 ⊢ leftInv := tr (\ i → ρ0[ρ1[τ1]][τ0] = leftInv0[i]) φ0 step0
  Γ0,φ0 ⊢ leftInv = refl  -- because it will become step0, which is refl when φ0

  Γ0, i : I ⊢ hcomp {Γ0} (\ j → \ { (i = 0) -> ρ0[ρ1[τ1]][τ0]
                                  ; (i = 1) -> leftInv0[j]
                                  ; (φ0 = 1) -> γ0
                                  })
                         (step0[i])




  -}
  let step0 :: Substitution
step0 = Int -> Substitution -> Substitution
forall a. Int -> Substitution' a -> Substitution' a
liftS Int
1 Substitution
tau0 Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Substitution
leftInv1 Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Substitution
rho0

  Telescope -> tcm () -> 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 Telescope
prob0 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ (String, Dom Type) -> tcm () -> tcm ()
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
(String, Dom Type) -> m a -> m a
addContext (String
"r" :: String, Dom Type
HasCallStack => Dom Type
__DUMMY_DOM__) (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"leftInv0  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
leftInv0
  Telescope -> tcm () -> 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 Telescope
prob1 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"rho0  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
rho0
  Telescope -> tcm () -> 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 Telescope
prob0 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"tau0  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
tau0
  Telescope -> tcm () -> 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 Telescope
prob0 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"rhos0[tau0]  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM (Substitution
tau0 Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Substitution
rho0)

  Telescope -> tcm () -> 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 Telescope
prob1 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ (String, Dom Type) -> tcm () -> tcm ()
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
(String, Dom Type) -> m a -> m a
addContext (String
"r" :: String, Dom Type
HasCallStack => Dom Type
__DUMMY_DOM__) (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"leftInv1  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
leftInv1
  Telescope -> tcm () -> 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 Telescope
prob0 (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ (String, Dom Type) -> tcm () -> tcm ()
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
(String, Dom Type) -> m a -> m a
addContext (String
"r" :: String, Dom Type
HasCallStack => Dom Type
__DUMMY_DOM__) (tcm () -> tcm ()) -> tcm () -> tcm ()
forall a b. (a -> b) -> a -> b
$ String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"step0  :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
step0

  interval <- tcm Type
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType
  max <- primIMax
  neg <- primINeg
  result <- sequenceA <$> do
    addContext prob0 $ runNamesT (teleNames prob0) $ do
             phi <- open phi0
             g0 <- open $ raise (size prob0) prob0
             step0 <- open $ Abs "i" $ step0 `applySubst` teleArgs prob0
             leftInv0 <- open $ Abs "i" $ map unArg $ leftInv0 `applySubst` teleArgs prob0
             bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT tcm b
i -> (String, Dom Type)
-> NamesT tcm (Either (Closure (Abs Type)) [Term])
-> NamesT tcm (Either (Closure (Abs Type)) [Term])
forall b (m :: * -> *) a.
(AddContext b, MonadAddContext m) =>
b -> m a -> m a
forall (m :: * -> *) a.
MonadAddContext m =>
(String, Dom Type) -> m a -> m a
addContext (String
"i" :: String, Type -> Dom Type
forall a. a -> Dom a
defaultDom Type
interval) (NamesT tcm (Either (Closure (Abs Type)) [Term])
 -> NamesT tcm (Either (Closure (Abs Type)) [Term]))
-> NamesT tcm (Either (Closure (Abs Type)) [Term])
-> NamesT tcm (Either (Closure (Abs Type)) [Term])
forall a b. (a -> b) -> a -> b
$ do
              tel <- String
-> ((forall b. (Subst b, DeBruijn b) => NamesT tcm b)
    -> NamesT tcm Telescope)
-> NamesT tcm (Abs Telescope)
forall (m :: * -> *) a.
Monad m =>
String
-> ((forall b. (Subst b, DeBruijn b) => NamesT m b) -> NamesT m a)
-> NamesT m (Abs a)
bind String
"_" (((forall b. (Subst b, DeBruijn b) => NamesT tcm b)
  -> NamesT tcm Telescope)
 -> NamesT tcm (Abs Telescope))
-> ((forall b. (Subst b, DeBruijn b) => NamesT tcm b)
    -> NamesT tcm Telescope)
-> NamesT tcm (Abs Telescope)
forall a b. (a -> b) -> a -> b
$ \ (NamesT tcm Term
_ :: NamesT tcm Term) -> NamesT tcm Telescope
g0
              step0i <- lazyAbsApp <$> step0 <*> i
              face <- pure max <@> (pure neg <@> i) <@> phi
              leftInv0 <- leftInv0
              i <- i
              -- this composition could be optimized further whenever step0i is actually constant in i.
              lift $ runExceptT (map unArg <$> transpSysTel' True tel [(i, leftInv0)] face step0i)
  leftInv <- case result of
    Right Abs [Term]
x  -> Abs [Term] -> tcm (Abs [Term])
forall a. a -> tcm a
forall (f :: * -> *) a. Applicative f => a -> f a
pure Abs [Term]
x
    Left Closure (Abs Type)
cl -> do
      String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"impossible" Int
10 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
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
vcat
        [ TCMT IO Doc
"transpSysTel' errored with term"
        , Closure (Abs Type) -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Closure (Abs Type) -> m Doc
prettyTCM Closure (Abs Type)
cl
        ]
      tcm (Abs [Term])
forall a. HasCallStack => a
__IMPOSSIBLE__

  let sigma = Impossible -> [Term] -> Substitution
forall a. DeBruijn a => Impossible -> [a] -> Substitution' a
termsS Impossible
forall a. HasCallStack => a
__IMPOSSIBLE__ ([Term] -> Substitution) -> [Term] -> Substitution
forall a b. (a -> b) -> a -> b
$ Abs [Term] -> [Term]
forall a. Subst a => Abs a -> a
absBody Abs [Term]
leftInv
  verboseS "tc.lhs.unify.inv" 20 do
    addContext prob0 $ addContext ("r" :: String, __DUMMY_DOM__) do
      reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv    :" <+> prettyTCM (absBody leftInv)
      reportSDoc "tc.lhs.unify.inv" 40 $ "leftInv    :" <+> pretty (absBody leftInv)
      reportSDoc "tc.lhs.unify.inv" 40 $ "leftInvSub :" <+> pretty sigma
  return (prob, rho, tau, sigma)

buildEquiv :: forall tcm. (PureTCM tcm, MonadError TCErr tcm) => UnifyLogEntry -> UnifyState -> tcm (Either NoLeftInv (Retract,Term))
buildEquiv :: forall (tcm :: * -> *).
(PureTCM tcm, MonadError TCErr tcm) =>
UnifyLogEntry
-> UnifyState -> tcm (Either NoLeftInv (Retract, Term))
buildEquiv (UnificationStep UnifyState
st step :: UnifyStep
step@(Solution Int
k Dom Type
ty FlexibleVar Int
fx Term
tm Either () ()
side) UnifyOutput
output) UnifyState
next = ExceptT NoLeftInv tcm (Retract, Term)
-> tcm (Either NoLeftInv (Retract, Term))
forall e (m :: * -> *) a. ExceptT e m a -> m (Either e a)
runExceptT (ExceptT NoLeftInv tcm (Retract, Term)
 -> tcm (Either NoLeftInv (Retract, Term)))
-> ExceptT NoLeftInv tcm (Retract, Term)
-> tcm (Either NoLeftInv (Retract, Term))
forall a b. (a -> b) -> a -> b
$ do
        let
          errorToUnsupported :: ExceptT a tcm b -> ExceptT NoLeftInv tcm b
          errorToUnsupported :: forall a b. ExceptT a tcm b -> ExceptT NoLeftInv tcm b
errorToUnsupported ExceptT a tcm b
m = (a -> NoLeftInv) -> ExceptT a tcm b -> ExceptT NoLeftInv tcm b
forall (m :: * -> *) e e' a.
Functor m =>
(e -> e') -> ExceptT e m a -> ExceptT e' m a
withExceptT (\ a
_ -> UnifyStep -> NoLeftInv
UnsupportedYet UnifyStep
step) ExceptT a tcm b
m
        String -> Int -> TCMT IO Doc -> ExceptT NoLeftInv tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> ExceptT NoLeftInv tcm ())
-> TCMT IO Doc -> ExceptT NoLeftInv tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"step 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
st
        String -> Int -> TCMT IO Doc -> ExceptT NoLeftInv tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> ExceptT NoLeftInv tcm ())
-> TCMT IO Doc -> ExceptT NoLeftInv tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"step step:" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> 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 (UnifyState -> Telescope
varTel UnifyState
st) (UnifyStep -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => UnifyStep -> m Doc
prettyTCM UnifyStep
step)
        unview <- ExceptT NoLeftInv tcm (IntervalView -> Term)
forall (m :: * -> *). HasBuiltins m => m (IntervalView -> Term)
intervalUnview'
        cxt <- getContextTelescope
        reportSDoc "tc.lhs.unify.inv" 20 $ "context:" <+> prettyTCM cxt
        let
          -- k counds in eqs from the left
          m = UnifyState -> Int
varCount UnifyState
st
          gamma = UnifyState -> Telescope
varTel UnifyState
st
          eqs = UnifyState -> Telescope
eqTel UnifyState
st
          u = UnifyState -> [Arg Term]
eqLHS UnifyState
st [Arg Term] -> Int -> Arg Term
forall a. HasCallStack => [a] -> Int -> a
!! Int
k
          v = UnifyState -> [Arg Term]
eqRHS UnifyState
st [Arg Term] -> Int -> Arg Term
forall a. HasCallStack => [a] -> Int -> a
!! Int
k
          x = FlexibleVar Int -> Int
forall a. FlexibleVar a -> a
flexVar FlexibleVar Int
fx
          neqs = Telescope -> Int
forall a. Sized a => a -> Int
size Telescope
eqs
          phis = Int
1 -- neqs
        interval <- lift $ primIntervalType
         -- Γ, φs : I^phis
        let gamma_phis = Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
abstract Telescope
gamma (Telescope -> Telescope) -> Telescope -> Telescope
forall a b. (a -> b) -> a -> b
$ ListTel -> Telescope
telFromList (ListTel -> Telescope) -> ListTel -> Telescope
forall a b. (a -> b) -> a -> b
$
              (Int -> Dom (String, Type)) -> [Int] -> ListTel
forall a b. (a -> b) -> [a] -> [b]
map ((String, Type) -> Dom (String, Type)
forall a. a -> Dom a
defaultDom ((String, Type) -> Dom (String, Type))
-> (Int -> (String, Type)) -> Int -> Dom (String, Type)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,Type
interval) (String -> (String, Type))
-> (Int -> String) -> Int -> (String, Type)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (String
"phi" String -> ShowS
forall a. [a] -> [a] -> [a]
++) ShowS -> (Int -> String) -> Int -> String
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> String
forall a. Show a => a -> String
show) [Int
0 .. Int
phis Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1]
        working_tel <- abstract gamma_phis <$>
          errorToUnsupported (pathTelescope' (raise phis $ eqTel st) (raise phis $ eqLHS st) (raise phis $ eqRHS st))
        reportSDoc "tc.lhs.unify.inv" 20 $ vcat
          [ "working tel:" <+> prettyTCM (working_tel :: Telescope)
          , addContext working_tel $ "working tel args:" <+> prettyTCM (teleArgs working_tel :: [Arg Term])
          ]
        (tau,leftInv,phi) <- addContext working_tel $ runNamesT [] $ do
          let raiseFrom Telescope
tel Term
x = Int -> Term -> Term
forall a. Subst a => Int -> a -> a
raise (Telescope -> Int
forall a. Sized a => a -> Int
size Telescope
working_tel Int -> Int -> Int
forall a. Num a => a -> a -> a
- Telescope -> Int
forall a. Sized a => a -> Int
size Telescope
tel) Term
x
          u <- open . raiseFrom gamma . unArg $ u
          v <- open . raiseFrom gamma . unArg $ v
          -- φ
          let phi = Telescope -> Term -> Term
raiseFrom Telescope
gamma_phis (Term -> Term) -> Term -> Term
forall a b. (a -> b) -> a -> b
$ Int -> Term
var Int
0
          -- working_tel ⊢ γ₁,x,γ₂,φ,eqs
          let all_args = Telescope -> [Arg Term]
forall a t. DeBruijn a => Tele (Dom t) -> [Arg a]
teleArgs Telescope
working_tel
          -- Γ₁,x : A,Γ₂
--          gamma <- open $ raiseFrom EmptyTel gamma
          -- -- γ₁,x,γ₂,φ,eqs : W
          -- working_tel <- open $ raiseFrom EmptyTel working_tel

          -- eq_tel <- open $ raiseFrom gamma (eqTel st)

          -- [lhs,rhs] <- mapM (open . raiseFrom gamma) [eqLHS st,eqRHS st]
          let bindSplit (Telescope
tel1,a
tel2) = (Telescope
tel1,Names -> a -> AbsN a
forall a. Names -> a -> AbsN a
AbsN (Telescope -> Names
teleNames Telescope
tel1) a
tel2)
          -- . ⊢ Γ₁  ,  γ₁. (x : A),Γ₂,φ : I,[lhs ≡ rhs]
          let (gamma1, xxi) = bindSplit $ splitTelescopeAt (size gamma - x - 1) working_tel
          let (gamma1_args,xxi_args) = splitAt (size gamma1) all_args
              (_x_arg:xi_args) = xxi_args
              (x_arg:xi0,k_arg:xi1) = splitAt ((size gamma - size gamma1) + phis + k) xxi_args
              -- W ⊢ (x : A),Γ₂,φ : I,[lhs ≡ rhs]
          let
            xxi_here :: Telescope
            xxi_here = AbsN Telescope -> [SubstArg Telescope] -> Telescope
forall a. Subst a => AbsN a -> [SubstArg a] -> a
absAppN AbsN Telescope
xxi ([SubstArg Telescope] -> Telescope)
-> [SubstArg Telescope] -> Telescope
forall a b. (a -> b) -> a -> b
$ (Arg Term -> Term) -> [Arg Term] -> [Term]
forall a b. (a -> b) -> [a] -> [b]
map Arg Term -> Term
forall e. Arg e -> e
unArg [Arg Term]
gamma1_args
          --                                                      x:A,Γ₂                φ
          let (xpre,krest) = bindSplit $ splitTelescopeAt ((size gamma - size gamma1) + phis + k) xxi_here
          k_arg <- open $ unArg k_arg
          xpre <- open xpre
          krest <- open krest
          delta <- bindN ["x","eq"] $ \ [NamesT (ExceptT NoLeftInv tcm) Term
x,NamesT (ExceptT NoLeftInv tcm) Term
eq] -> do
                     let pre :: NamesT (ExceptT NoLeftInv tcm) Telescope
pre = Telescope -> Term -> Telescope
forall t. Apply t => t -> Term -> t
apply1 (Telescope -> Term -> Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Telescope
-> NamesT (ExceptT NoLeftInv tcm) (Term -> Telescope)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) Telescope
xpre NamesT (ExceptT NoLeftInv tcm) (Term -> Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
x
                     NamesT (ExceptT NoLeftInv tcm) Telescope
-> (Vars (ExceptT NoLeftInv tcm)
    -> NamesT (ExceptT NoLeftInv tcm) Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall (m :: * -> *) a.
(Monad m, Abstract a) =>
NamesT m Telescope -> (Vars m -> NamesT m a) -> NamesT m a
abstractN NamesT (ExceptT NoLeftInv tcm) Telescope
pre ((Vars (ExceptT NoLeftInv tcm)
  -> NamesT (ExceptT NoLeftInv tcm) Telescope)
 -> NamesT (ExceptT NoLeftInv tcm) Telescope)
-> (Vars (ExceptT NoLeftInv tcm)
    -> NamesT (ExceptT NoLeftInv tcm) Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall a b. (a -> b) -> a -> b
$ \ Vars (ExceptT NoLeftInv tcm)
args ->
                       Telescope -> Term -> Telescope
forall t. Apply t => t -> Term -> t
apply1 (Telescope -> Term -> Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Telescope
-> NamesT (ExceptT NoLeftInv tcm) (Term -> Telescope)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) (AbsN Telescope)
-> [NamesT (ExceptT NoLeftInv tcm) (SubstArg Telescope)]
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall (m :: * -> *) a.
(Monad m, Subst a) =>
NamesT m (AbsN a) -> [NamesT m (SubstArg a)] -> NamesT m a
applyN NamesT (ExceptT NoLeftInv tcm) (AbsN Telescope)
krest (NamesT (ExceptT NoLeftInv tcm) Term
xNamesT (ExceptT NoLeftInv tcm) Term
-> [NamesT (ExceptT NoLeftInv tcm) Term]
-> [NamesT (ExceptT NoLeftInv tcm) Term]
forall a. a -> [a] -> [a]
:[NamesT (ExceptT NoLeftInv tcm) Term]
Vars (ExceptT NoLeftInv tcm)
args) NamesT (ExceptT NoLeftInv tcm) (Term -> Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
eq
--          let delta_zero = absAppN delta $ map unArg [x_arg,k_arg]
          let d_zero_args = [Arg Term]
xi0 [Arg Term] -> [Arg Term] -> [Arg Term]
forall a. [a] -> [a] -> [a]
++ [Arg Term]
xi1
          reportSDoc "tc.lhs.unify.inv" 20 $ "size delta:" <+> text (show $ size $ unAbsN delta)
          reportSDoc "tc.lhs.unify.inv" 20 $ "size d0args:" <+> text (show $ size d_zero_args)
          let appSide = case Either () ()
side of
                          Left{} -> Term -> Term
forall a. a -> a
id
                          Right{} -> IntervalView -> Term
unview (IntervalView -> Term) -> (Term -> IntervalView) -> Term -> Term
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Arg Term -> IntervalView
INeg (Arg Term -> IntervalView)
-> (Term -> Arg Term) -> Term -> IntervalView
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Term -> Arg Term
forall e. e -> Arg e
argN
          let
                  -- csingl :: NamesT tcm Term -> NamesT tcm [Arg Term]
                  csingl NamesT (ExceptT NoLeftInv tcm) Term
i = (NamesT (ExceptT NoLeftInv tcm) Term
 -> NamesT (ExceptT NoLeftInv tcm) (Arg Term))
-> [NamesT (ExceptT NoLeftInv tcm) Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
mapM ((Term -> Arg Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) (Arg Term)
forall a b.
(a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Term -> Arg Term
forall e. e -> Arg e
defaultArg) ([NamesT (ExceptT NoLeftInv tcm) Term]
 -> NamesT (ExceptT NoLeftInv tcm) [Arg Term])
-> [NamesT (ExceptT NoLeftInv tcm) Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b. (a -> b) -> a -> b
$ NamesT (ExceptT NoLeftInv tcm) Term
-> [NamesT (ExceptT NoLeftInv tcm) Term]
csingl' NamesT (ExceptT NoLeftInv tcm) Term
i
                  -- csingl' :: NamesT tcm Term -> [NamesT tcm Term]
                  csingl' NamesT (ExceptT NoLeftInv tcm) Term
i = [ NamesT (ExceptT NoLeftInv tcm) Term
k_arg NamesT (ExceptT NoLeftInv tcm) Term
-> (NamesT (ExceptT NoLeftInv tcm) Term,
    NamesT (ExceptT NoLeftInv tcm) Term,
    NamesT (ExceptT NoLeftInv tcm) Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
forall (m :: * -> *).
Applicative m =>
m Term -> (m Term, m Term, m Term) -> m Term
<@@> (NamesT (ExceptT NoLeftInv tcm) Term
u, NamesT (ExceptT NoLeftInv tcm) Term
v, Term -> Term
appSide (Term -> Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) Term
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) Term
i)
                              , String
-> (NamesT (ExceptT NoLeftInv tcm) Term
    -> NamesT (ExceptT NoLeftInv tcm) Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
forall (m :: * -> *).
Monad m =>
String -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
lam String
"j" ((NamesT (ExceptT NoLeftInv tcm) Term
  -> NamesT (ExceptT NoLeftInv tcm) Term)
 -> NamesT (ExceptT NoLeftInv tcm) Term)
-> (NamesT (ExceptT NoLeftInv tcm) Term
    -> NamesT (ExceptT NoLeftInv tcm) Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
forall a b. (a -> b) -> a -> b
$ \ NamesT (ExceptT NoLeftInv tcm) Term
j ->
                                  let r :: Term -> Term -> Term
r Term
i Term
j = case Either () ()
side of
                                            Left{} -> IntervalView -> Term
unview (Arg Term -> Arg Term -> IntervalView
IMax (Term -> Arg Term
forall e. e -> Arg e
argN Term
j) (Term -> Arg Term
forall e. e -> Arg e
argN Term
i))
                                            Right{} -> IntervalView -> Term
unview (Arg Term -> Arg Term -> IntervalView
IMin (Term -> Arg Term
forall e. e -> Arg e
argN Term
j) (Term -> Arg Term
forall e. e -> Arg e
argN (Term -> Arg Term)
-> (IntervalView -> Term) -> IntervalView -> Arg Term
forall b c a. (b -> c) -> (a -> b) -> a -> c
. IntervalView -> Term
unview (IntervalView -> Arg Term) -> IntervalView -> Arg Term
forall a b. (a -> b) -> a -> b
$ Arg Term -> IntervalView
INeg (Arg Term -> IntervalView) -> Arg Term -> IntervalView
forall a b. (a -> b) -> a -> b
$ Term -> Arg Term
forall e. e -> Arg e
argN Term
i))
                                  in NamesT (ExceptT NoLeftInv tcm) Term
k_arg NamesT (ExceptT NoLeftInv tcm) Term
-> (NamesT (ExceptT NoLeftInv tcm) Term,
    NamesT (ExceptT NoLeftInv tcm) Term,
    NamesT (ExceptT NoLeftInv tcm) Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
forall (m :: * -> *).
Applicative m =>
m Term -> (m Term, m Term, m Term) -> m Term
<@@> (NamesT (ExceptT NoLeftInv tcm) Term
u, NamesT (ExceptT NoLeftInv tcm) Term
v, Term -> Term -> Term
r (Term -> Term -> Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) (Term -> Term)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) Term
i NamesT (ExceptT NoLeftInv tcm) (Term -> Term)
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) Term
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
j)
                              ]
          let replaceAt Int
n a
x [a]
xs = [a]
xs0 [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
xs1
                where ([a]
xs0,a
_:[a]
xs1) = Int -> [a] -> ([a], [a])
forall a. Int -> [a] -> ([a], [a])
splitAt Int
n [a]
xs
              dropAt Int
n [a]
xs = [a]
xs0 [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a]
xs1
                where ([a]
xs0,a
_:[a]
xs1) = Int -> [a] -> ([a], [a])
forall a. Int -> [a] -> ([a], [a])
splitAt Int
n [a]
xs
          delta <- open delta
          d <- bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i -> NamesT (ExceptT NoLeftInv tcm) (AbsN Telescope)
-> [NamesT (ExceptT NoLeftInv tcm) (SubstArg Telescope)]
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall (m :: * -> *) a.
(Monad m, Subst a) =>
NamesT m (AbsN a) -> [NamesT m (SubstArg a)] -> NamesT m a
applyN NamesT (ExceptT NoLeftInv tcm) (AbsN Telescope)
delta (NamesT (ExceptT NoLeftInv tcm) Term
-> [NamesT (ExceptT NoLeftInv tcm) Term]
csingl' NamesT (ExceptT NoLeftInv tcm) Term
forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i)

          -- Andrea 06/06/2018
          -- We do not actually add a transp/fill if the family is
          -- constant (TODO: postpone for metas) This is so variables
          -- whose types do not depend on "x" are left alone, in
          -- particular those the solution "t" depends on.
          --
          -- We might want to instead use the info discovered by the
          -- solver when checking if "t" depends on "x" to decide what
          -- to transp and what not to.
          let flag = Bool
True
                 {-   φ -}
          tau <- {-dropAt (size gamma - 1 + k) .-} (gamma1_args ++) <$>
                                                   lift (errorToUnsupported (transpTel' flag d phi d_zero_args))
          reportSDoc "tc.lhs.unify.inv" 20 $ "tau    :" <+> prettyTCM (map (setHiding NotHidden) tau)
          leftInv <- do
            gamma1_args <- open gamma1_args
            phi <- open phi
            -- xxi_here <- open xxi_here
            -- (xi_here_f :: Abs Telescope) <- bind "i" $ \ i -> apply <$> xxi_here <*> (take 1 `fmap` csingl i)
            -- xi_here_f <- open xi_here_f
            -- xi_args <- open xi_args
            -- xif <- bind "i" $ \ i -> do
            --                      m <- (runExceptT <$> (trFillTel' flag <$> xi_here_f <*> phi <*> xi_args <*> i))
            --                      either __IMPOSSIBLE__ id <$> lift m
            -- xif <- open xif

            xi0 <- open xi0
            xi1 <- open xi1
            delta0 <- bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i -> Telescope -> [Arg Term] -> Telescope
forall t. Apply t => t -> [Arg Term] -> t
apply (Telescope -> [Arg Term] -> Telescope)
-> NamesT (ExceptT NoLeftInv tcm) Telescope
-> NamesT (ExceptT NoLeftInv tcm) ([Arg Term] -> Telescope)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) Telescope
xpre NamesT (ExceptT NoLeftInv tcm) ([Arg Term] -> Telescope)
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) Telescope
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (Int -> [Arg Term] -> [Arg Term]
forall a. Int -> [a] -> [a]
take Int
1 ([Arg Term] -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b.
(a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
`fmap` NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
csingl NamesT (ExceptT NoLeftInv tcm) Term
forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i)
            delta0 <- open delta0
            xi0f <- bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i -> do
                                 m <- Bool
-> Abs Telescope
-> Term
-> [Arg Term]
-> Term
-> ExceptT (Closure (Abs Type)) tcm [Arg Term]
forall (m :: * -> *).
(PureTCM m, MonadError TCErr m) =>
Bool
-> Abs Telescope
-> Term
-> [Arg Term]
-> Term
-> ExceptT (Closure (Abs Type)) m [Arg Term]
trFillTel' Bool
flag (Abs Telescope
 -> Term
 -> [Arg Term]
 -> Term
 -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Abs Telescope)
-> NamesT
     (ExceptT NoLeftInv tcm)
     (Term
      -> [Arg Term]
      -> Term
      -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) (Abs Telescope)
delta0 NamesT
  (ExceptT NoLeftInv tcm)
  (Term
   -> [Arg Term]
   -> Term
   -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT
     (ExceptT NoLeftInv tcm)
     ([Arg Term] -> Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
phi NamesT
  (ExceptT NoLeftInv tcm)
  ([Arg Term] -> Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT
     (ExceptT NoLeftInv tcm)
     (Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
xi0 NamesT
  (ExceptT NoLeftInv tcm)
  (Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT
     (ExceptT NoLeftInv tcm)
     (ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i
                                 lift (errorToUnsupported m)
            xi0f <- open xi0f

            delta1 <- bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i -> do

                   args <- (Arg Term
 -> NamesT
      (ExceptT NoLeftInv tcm) (NamesT (ExceptT NoLeftInv tcm) Term))
-> [Arg Term]
-> NamesT
     (ExceptT NoLeftInv tcm) [NamesT (ExceptT NoLeftInv tcm) Term]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
mapM (Term
-> NamesT
     (ExceptT NoLeftInv tcm) (NamesT (ExceptT NoLeftInv tcm) Term)
forall (m :: * -> *) a.
(Monad m, Subst a) =>
a -> NamesT m (NamesT m a)
open (Term
 -> NamesT
      (ExceptT NoLeftInv tcm) (NamesT (ExceptT NoLeftInv tcm) Term))
-> (Arg Term -> Term)
-> Arg Term
-> NamesT
     (ExceptT NoLeftInv tcm) (NamesT (ExceptT NoLeftInv tcm) Term)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Arg Term -> Term
forall e. Arg e -> e
unArg) ([Arg Term]
 -> NamesT
      (ExceptT NoLeftInv tcm) [NamesT (ExceptT NoLeftInv tcm) Term])
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT
     (ExceptT NoLeftInv tcm) [NamesT (ExceptT NoLeftInv tcm) Term]
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< (Abs [Arg Term] -> Term -> [Arg Term]
Abs [Arg Term] -> SubstArg [Arg Term] -> [Arg Term]
forall a. Subst a => Abs a -> SubstArg a -> a
lazyAbsApp (Abs [Arg Term] -> Term -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Abs [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Term -> [Arg Term])
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) (Abs [Arg Term])
xi0f NamesT (ExceptT NoLeftInv tcm) (Term -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i)
                   apply <$> applyN krest (take 1 (csingl' i) ++ args) <*> (drop 1 `fmap` csingl i)
            delta1 <- open delta1
            xi1f <- bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i -> do
                                 m <- Bool
-> Abs Telescope
-> Term
-> [Arg Term]
-> Term
-> ExceptT (Closure (Abs Type)) tcm [Arg Term]
forall (m :: * -> *).
(PureTCM m, MonadError TCErr m) =>
Bool
-> Abs Telescope
-> Term
-> [Arg Term]
-> Term
-> ExceptT (Closure (Abs Type)) m [Arg Term]
trFillTel' Bool
flag (Abs Telescope
 -> Term
 -> [Arg Term]
 -> Term
 -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Abs Telescope)
-> NamesT
     (ExceptT NoLeftInv tcm)
     (Term
      -> [Arg Term]
      -> Term
      -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) (Abs Telescope)
delta1 NamesT
  (ExceptT NoLeftInv tcm)
  (Term
   -> [Arg Term]
   -> Term
   -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT
     (ExceptT NoLeftInv tcm)
     ([Arg Term] -> Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
phi NamesT
  (ExceptT NoLeftInv tcm)
  ([Arg Term] -> Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT
     (ExceptT NoLeftInv tcm)
     (Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
xi1 NamesT
  (ExceptT NoLeftInv tcm)
  (Term -> ExceptT (Closure (Abs Type)) tcm [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT
     (ExceptT NoLeftInv tcm)
     (ExceptT (Closure (Abs Type)) tcm [Arg Term])
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i
                                 lift (errorToUnsupported m)
            xi1f <- open xi1f
            fmap absBody $ bind "i" $ \ forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i' -> do
              let +++ :: m [a] -> m [a] -> m [a]
(+++) m [a]
m = ([a] -> [a] -> [a]) -> m [a] -> m [a] -> m [a]
forall (m :: * -> *) a1 a2 r.
Monad m =>
(a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM2 [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
(++) m [a]
m
                  i :: NamesT (ExceptT NoLeftInv tcm) Term
i = ExceptT NoLeftInv tcm Term -> NamesT (ExceptT NoLeftInv tcm) Term
forall (m :: * -> *) a. Monad m => m a -> NamesT m a
cl (tcm Term -> ExceptT NoLeftInv tcm Term
forall (m :: * -> *) a. Monad m => m a -> ExceptT NoLeftInv m a
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift tcm Term
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Term
primINeg) NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) Term
forall (m :: * -> *). Applicative m => m Term -> m Term -> m Term
<@> NamesT (ExceptT NoLeftInv tcm) Term
forall b. (Subst b, DeBruijn b) => NamesT (ExceptT NoLeftInv tcm) b
i'
--              replaceAt (size gamma + k) <$> (fmap defaultArg $ cl primIMax <@> phi <@> i) <*> do
              do
                NamesT (ExceptT NoLeftInv tcm) [Arg Term]
gamma1_args NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall {m :: * -> *} {a}. Monad m => m [a] -> m [a] -> m [a]
+++ (Int -> [Arg Term] -> [Arg Term]
forall a. Int -> [a] -> [a]
take Int
1 ([Arg Term] -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b.
(a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
`fmap` NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
csingl NamesT (ExceptT NoLeftInv tcm) Term
i NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall {m :: * -> *} {a}. Monad m => m [a] -> m [a] -> m [a]
+++ ((Abs [Arg Term] -> Term -> [Arg Term]
Abs [Arg Term] -> SubstArg [Arg Term] -> [Arg Term]
forall a. Subst a => Abs a -> SubstArg a -> a
lazyAbsApp (Abs [Arg Term] -> Term -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Abs [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Term -> [Arg Term])
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) (Abs [Arg Term])
xi0f NamesT (ExceptT NoLeftInv tcm) (Term -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
i) NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall {m :: * -> *} {a}. Monad m => m [a] -> m [a] -> m [a]
+++ (Int -> [Arg Term] -> [Arg Term]
forall a. Int -> [a] -> [a]
drop Int
1 ([Arg Term] -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b.
(a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
`fmap` NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
csingl NamesT (ExceptT NoLeftInv tcm) Term
i NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall {m :: * -> *} {a}. Monad m => m [a] -> m [a] -> m [a]
+++ (Abs [Arg Term] -> Term -> [Arg Term]
Abs [Arg Term] -> SubstArg [Arg Term] -> [Arg Term]
forall a. Subst a => Abs a -> SubstArg a -> a
lazyAbsApp (Abs [Arg Term] -> Term -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Abs [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) (Term -> [Arg Term])
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> NamesT (ExceptT NoLeftInv tcm) (Abs [Arg Term])
xi1f NamesT (ExceptT NoLeftInv tcm) (Term -> [Arg Term])
-> NamesT (ExceptT NoLeftInv tcm) Term
-> NamesT (ExceptT NoLeftInv tcm) [Arg Term]
forall a b.
NamesT (ExceptT NoLeftInv tcm) (a -> b)
-> NamesT (ExceptT NoLeftInv tcm) a
-> NamesT (ExceptT NoLeftInv tcm) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> NamesT (ExceptT NoLeftInv tcm) Term
i))))
          return (tau,leftInv,phi)
        iz <- lift $ primIZero
        io <- lift $ primIOne
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau    :" <+> prettyTCM (map (setHiding NotHidden) tau)
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tauS   :" <+> prettyTCM (termsS __IMPOSSIBLE__ $ map unArg tau)
        addContext working_tel $ addContext ("r" :: String, defaultDom interval)
                               $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv:   " <+> prettyTCM (map (setHiding NotHidden) leftInv)
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv[0]:" <+> (prettyTCM =<< reduce (subst 0 iz $ map (setHiding NotHidden) leftInv))
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv[1]:" <+> (prettyTCM =<< reduce  (subst 0 io $ map (setHiding NotHidden) leftInv))
        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "[rho]tau :" <+>
                                                                                  -- k   φ
          prettyTCM (applySubst (termsS __IMPOSSIBLE__ $ map unArg tau) $ fromPatternSubstitution
                                                                      $ raise (size (eqTel st) - 1{-k-} + phis {-neqs{-φs-} - 1{-φ0-}-})
                                                                      $ unifySubst output)
        reportSDoc "tc.lhs.unify.inv" 20 $ "."
        let rho0 = PatternSubstitution -> Substitution
fromPatternSubstitution (PatternSubstitution -> Substitution)
-> PatternSubstitution -> Substitution
forall a b. (a -> b) -> a -> b
$ UnifyOutput -> PatternSubstitution
unifySubst UnifyOutput
output
        addContext (varTel next) $ addContext (eqTel next) $ reportSDoc "tc.lhs.unify.inv" 20 $
          "prf :" <+> prettyTCM (fromPatternSubstitution $ unifyProof output)
        let c0 = ArgInfo -> Abs Term -> Term
Lam ArgInfo
defaultArgInfo (Abs Term -> Term) -> Abs Term -> Term
forall a b. (a -> b) -> a -> b
$ String -> Term -> Abs Term
forall a. String -> a -> Abs a
Abs String
"i" (Term -> Abs Term) -> Term -> Abs Term
forall a b. (a -> b) -> a -> b
$ Int -> Term -> Term
forall a. Subst a => Int -> a -> a
raise Int
1 (Term -> Term) -> Term -> Term
forall a b. (a -> b) -> a -> b
$ Substitution -> Int -> Term
forall a. EndoSubst a => Substitution' a -> Int -> a
lookupS (PatternSubstitution -> Substitution
fromPatternSubstitution (PatternSubstitution -> Substitution)
-> PatternSubstitution -> Substitution
forall a b. (a -> b) -> a -> b
$ UnifyOutput -> PatternSubstitution
unifyProof UnifyOutput
output) (Int
neqs Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
k Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1)
        let c = Int -> Substitution -> Substitution
forall a. Int -> Substitution' a -> Substitution' a
liftS (Telescope -> Int
forall a. Sized a => a -> Int
size (Telescope -> Int) -> Telescope -> Int
forall a b. (a -> b) -> a -> b
$ UnifyState -> Telescope
eqTel UnifyState
next) (Int -> Substitution
forall a. Int -> Substitution' a
raiseS Int
1) Substitution' (SubstArg Term) -> Term -> Term
forall a. Subst a => Substitution' (SubstArg a) -> a -> a
`applySubst` Term
c0
        addContext (varTel next) $ addContext ("φ" :: String, __DUMMY_DOM__) $ addContext (raise 1 $ eqTel next) $
          reportSDoc "tc.lhs.unify.inv" 20 $ "c :" <+> prettyTCM c
--        let rho = liftS (neqs - k - 1) $ consS (raise (1 + k) c) $ liftS (1 + k) rho0
        let rho = Int -> Term -> Substitution
forall a. DeBruijn a => Int -> a -> Substitution' a
singletonS (Int
neqs Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
k Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1) Term
c  Substitution -> Substitution -> Substitution
forall a.
EndoSubst a =>
Substitution' a -> Substitution' a -> Substitution' a
`composeS` Int -> Substitution -> Substitution
forall a. Int -> Substitution' a -> Substitution' a
liftS (Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
neqs) Substitution
rho0
        reportSDoc "tc.lhs.unify.inv" 20 $ text "old_sizes: " <+> pretty (size $ varTel st, size $ eqTel st)
        reportSDoc "tc.lhs.unify.inv" 20 $ text "new_sizes: " <+> pretty (size $ varTel next, size $ eqTel next)
--        addContext (abstract (varTel next) $ ExtendTel __DUMMY_DOM__ (Abs "φ" $ raise 1 $ eqTel next)) $
        addContext (varTel next) $ addContext ("φ" :: String, __DUMMY_DOM__) $ addContext (raise 1 $ eqTel next) $
          reportSDoc "tc.lhs.unify.inv" 20 $ "rho   :" <+> prettyTCM rho
        return $ ((working_tel
                 , rho
                 , termsS __IMPOSSIBLE__ $ map unArg tau
                 , termsS __IMPOSSIBLE__ $ map unArg leftInv)
                 , phi)
buildEquiv (UnificationStep UnifyState
st step :: UnifyStep
step@(EtaExpandVar FlexibleVar Int
fv QName
_d [Arg Term]
_args) UnifyOutput
output) UnifyState
next = ((Retract, Term) -> Either NoLeftInv (Retract, Term))
-> tcm (Retract, Term) -> tcm (Either NoLeftInv (Retract, Term))
forall a b. (a -> b) -> tcm a -> tcm b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Retract, Term) -> Either NoLeftInv (Retract, Term)
forall a b. b -> Either a b
Right (tcm (Retract, Term) -> tcm (Either NoLeftInv (Retract, Term)))
-> tcm (Retract, Term) -> tcm (Either NoLeftInv (Retract, Term))
forall a b. (a -> b) -> a -> b
$ do
        String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 TCMT IO Doc
"buildEquiv EtaExpandVar"
        let
          gamma :: Telescope
gamma = UnifyState -> Telescope
varTel UnifyState
st
          eqs :: Telescope
eqs = UnifyState -> Telescope
eqTel UnifyState
st
          x :: Int
x = FlexibleVar Int -> Int
forall a. FlexibleVar a -> a
flexVar FlexibleVar Int
fv
          neqs :: Int
neqs = Telescope -> Int
forall a. Sized a => a -> Int
size Telescope
eqs
          phis :: Int
phis = Int
1
        interval <- tcm Type
forall (m :: * -> *).
(HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) =>
m Type
primIntervalType
         -- Γ, φs : I^phis
        let gamma_phis = Telescope -> Telescope -> Telescope
forall t. Abstract t => Telescope -> t -> t
abstract Telescope
gamma (Telescope -> Telescope) -> Telescope -> Telescope
forall a b. (a -> b) -> a -> b
$ ListTel -> Telescope
telFromList (ListTel -> Telescope) -> ListTel -> Telescope
forall a b. (a -> b) -> a -> b
$
              (Int -> Dom (String, Type)) -> [Int] -> ListTel
forall a b. (a -> b) -> [a] -> [b]
map ((String, Type) -> Dom (String, Type)
forall a. a -> Dom a
defaultDom ((String, Type) -> Dom (String, Type))
-> (Int -> (String, Type)) -> Int -> Dom (String, Type)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (,Type
interval) (String -> (String, Type))
-> (Int -> String) -> Int -> (String, Type)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (String
"phi" String -> ShowS
forall a. [a] -> [a] -> [a]
++) ShowS -> (Int -> String) -> Int -> String
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> String
forall a. Show a => a -> String
show) [Int
0 .. Int
phis Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1]
        working_tel <- abstract gamma_phis <$>
          pathTelescope (raise phis $ eqTel st) (raise phis $ eqLHS st) (raise phis $ eqRHS st)
        let raiseFrom Telescope
tel Int
x = (Telescope -> Int
forall a. Sized a => a -> Int
size Telescope
working_tel Int -> Int -> Int
forall a. Num a => a -> a -> a
- Telescope -> Int
forall a. Sized a => a -> Int
size Telescope
tel) Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
x
        let phi = Int -> Term
var (Int -> Term) -> Int -> Term
forall a b. (a -> b) -> a -> b
$ Telescope -> Int -> Int
raiseFrom Telescope
gamma_phis Int
0

        caseMaybeM (expandRecordVar (raiseFrom gamma x) working_tel) __IMPOSSIBLE__ $ \ (Telescope
_,Substitution
tau,Substitution
rho,Telescope
_) -> do
          String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
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
working_tel (TCMT IO Doc -> TCMT IO Doc) -> TCMT IO Doc -> TCMT IO Doc
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"tau    :" TCMT IO Doc -> TCMT IO Doc -> TCMT IO Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> Substitution -> TCMT IO Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => Substitution -> m Doc
prettyTCM Substitution
tau
          (Retract, Term) -> tcm (Retract, Term)
forall a. a -> tcm a
forall (m :: * -> *) a. Monad m => a -> m a
return ((Retract, Term) -> tcm (Retract, Term))
-> (Retract, Term) -> tcm (Retract, Term)
forall a b. (a -> b) -> a -> b
$ ((Telescope
working_tel,Substitution
rho,Substitution
tau,Int -> Substitution
forall a. Int -> Substitution' a
raiseS Int
1),Term
phi)

buildEquiv (UnificationStep UnifyState
st UnifyStep
step UnifyOutput
output) UnifyState
_ = do
  String -> Int -> TCMT IO Doc -> tcm ()
forall (m :: * -> *).
MonadDebug m =>
String -> Int -> TCMT IO Doc -> m ()
reportSDoc String
"tc.lhs.unify.inv" Int
20 (TCMT IO Doc -> tcm ()) -> TCMT IO Doc -> tcm ()
forall a b. (a -> b) -> a -> b
$ TCMT IO Doc
"steps"
  let illegal :: tcm (Either NoLeftInv (Retract, Term))
illegal     = Either NoLeftInv (Retract, Term)
-> tcm (Either NoLeftInv (Retract, Term))
forall a. a -> tcm a
forall (m :: * -> *) a. Monad m => a -> m a
return (Either NoLeftInv (Retract, Term)
 -> tcm (Either NoLeftInv (Retract, Term)))
-> Either NoLeftInv (Retract, Term)
-> tcm (Either NoLeftInv (Retract, Term))
forall a b. (a -> b) -> a -> b
$ NoLeftInv -> Either NoLeftInv (Retract, Term)
forall a b. a -> Either a b
Left (NoLeftInv -> Either NoLeftInv (Retract, Term))
-> NoLeftInv -> Either NoLeftInv (Retract, Term)
forall a b. (a -> b) -> a -> b
$ UnifyStep -> NoLeftInv
Illegal UnifyStep
step
      unsupported :: tcm (Either NoLeftInv (Retract, Term))
unsupported = Either NoLeftInv (Retract, Term)
-> tcm (Either NoLeftInv (Retract, Term))
forall a. a -> tcm a
forall (m :: * -> *) a. Monad m => a -> m a
return (Either NoLeftInv (Retract, Term)
 -> tcm (Either NoLeftInv (Retract, Term)))
-> Either NoLeftInv (Retract, Term)
-> tcm (Either NoLeftInv (Retract, Term))
forall a b. (a -> b) -> a -> b
$ NoLeftInv -> Either NoLeftInv (Retract, Term)
forall a b. a -> Either a b
Left (NoLeftInv -> Either NoLeftInv (Retract, Term))
-> NoLeftInv -> Either NoLeftInv (Retract, Term)
forall a b. (a -> b) -> a -> b
$ UnifyStep -> NoLeftInv
UnsupportedYet UnifyStep
step
  case UnifyStep
step of
    Deletion{}           -> tcm (Either NoLeftInv (Retract, Term))
illegal
    TypeConInjectivity{} -> tcm (Either NoLeftInv (Retract, Term))
illegal
    -- These should end up in a NoUnify
    Conflict{}    -> tcm (Either NoLeftInv (Retract, Term))
forall a. HasCallStack => a
__IMPOSSIBLE__
    LitConflict{} -> tcm (Either NoLeftInv (Retract, Term))
forall a. HasCallStack => a
__IMPOSSIBLE__
    Cycle{}       -> tcm (Either NoLeftInv (Retract, Term))
forall a. HasCallStack => a
__IMPOSSIBLE__
    UnifyStep
_ -> tcm (Either NoLeftInv (Retract, Term))
unsupported

{-# SPECIALIZE explainStep :: UnifyStep -> TCM Doc #-}
explainStep :: MonadPretty m => UnifyStep -> m Doc
explainStep :: forall (m :: * -> *). MonadPretty m => UnifyStep -> m Doc
explainStep Injectivity{injectConstructor :: UnifyStep -> ConHead
injectConstructor = ConHead
ch} =
  m Doc
"injectivity of the data constructor" m Doc -> m Doc -> m Doc
forall (m :: * -> *). Applicative m => m Doc -> m Doc -> m Doc
<+> QName -> m Doc
forall a (m :: * -> *). (PrettyTCM a, MonadPretty m) => a -> m Doc
forall (m :: * -> *). MonadPretty m => QName -> m Doc
prettyTCM (ConHead -> QName
conName ConHead
ch)
explainStep TypeConInjectivity{} = m Doc
"injectivity of type constructors"
explainStep Deletion{}           = m Doc
"the K rule"
explainStep Solution{}           = m Doc
"substitution in Setω"
-- Note: this is the actual reason that a Solution step can fail, rather
-- than the explanation for the actual step
explainStep Conflict{}          = m Doc
"the disjointness of data constructors"
explainStep LitConflict{}       = m Doc
"the disjointness of literal values"
explainStep Cycle{}             = m Doc
"the impossibility of cyclic values"
explainStep EtaExpandVar{}      = m Doc
"eta-expansion of variables"
explainStep EtaExpandEquation{} = m Doc
"eta-expansion of equations"
explainStep StripSizeSuc{}      = m Doc
"the injectivity of size successors"
explainStep SkipIrrelevantEquation{} = m Doc
"ignoring irrelevant equations"