Documentation

When comparing argument spines (in compareElims) where the first arguments don't match, we keep going, substituting the anti-unification of the two terms in the telescope. More precisely:

@ (u = v : A)[pid] w = antiUnify pid A u v us = vs : Δ[w/x] ------------------------------------------------------------- u us = v vs : (x : A) Δ @

The simplest case of anti-unification is to return a fresh metavariable (created by blockTermOnProblem), but if there's shared structure between the two terms we can expose that.

This is really a crutch that lets us get away with things that otherwise would require heterogenous conversion checking. See for instance issue #2384.

Try to assign meta. If meta is projected, try to eta-expand and run conversion check again.

coerce v a b coerces v : a to type b, returning a v' : b with maybe extra hidden applications or hidden abstractions.

In principle, this function can host coercive subtyping, but currently it only tries to fix problems with hidden function types.

Account for situations like k : (Size< j) <= (Size< k + 1)

Actually, the semantics is (Size<= k) ∩ (Size< j) ⊆ rhs which gives a disjunctive constraint. Mmmh, looks like stuff TODO.

For now, we do a cheap heuristics.

Type-directed equality on argument lists

Type directed equality on terms or types.

Syntax directed equality on atomic values

Check whether a1 cmp a2 and continue in context extended by a1.

compareElims pols a v els1 els2 performs type-directed equality on eliminator spines. t is the type of the head v.

Note: since TCM is lazy in return values from (>>=), it is important that compareElims in non-tail position be called as () <- compareElims pols a v e1 e2 so that any internal invariants upheld by returning IMPOSSIBLE actually get checked.

Compare two terms in irrelevant position. This always succeeds. However, we can dig for solutions of irrelevant metas in the terms we compare. (Certainly not the systematic solution, that'd be proof search...)

Check whether x xArgs cmp y yArgs

Type directed equality on values.

Equality on Types

Compute the head type of an elimination. For projection-like functions this requires inferring the type of the principal argument.

Compute the type of a rewrite rule head. For projection-like functions, this requires inferring the type of the principal argument, using the eliminations.

Ignore errors in irrelevant context.

Check that the first sort equal to the second.

equalTermOnFace φ A u v = _ , φ ⊢ u = v : A

guardPointerEquality x y s m behaves as m if x and y are equal as pointers, or does nothing otherwise. Use with care, see the documentation for unsafeComparePointers

intersectVars us vs checks whether all relevant elements in us and vs are variables, and if yes, returns a prune list which says True for arguments which are different and can be pruned.

leqConj r q = r ≤ q in the I lattice, when r and q are conjuctions. ' (∧ r_i) ≤ (∧ q_j) iff ' (∧ r_i) ∧ (∧ q_j) = (∧ r_i) iff ' {r_i | i} ∪ {q_j | j} = {r_i | i} iff ' {q_j | j} ⊆ {r_i | i}

leqInterval r q = r ≤ q in the I lattice. (∨ r_i) ≤ (∨ q_j) iff ∀ i. ∃ j. r_i ≤ q_j

Check that the first sort is less or equal to the second.

We can put SizeUniv below Inf, but otherwise, it is unrelated to the other universes.

Check if to lists of arguments are the same (and all variables). Precondition: the lists have the same length.

Try whether a computation runs without errors or new constraints (may create new metas, though). Restores state upon failure.

Try whether a computation runs without errors or new constraints (may create new metas, though). Return Just the result upon success. Return Nothing and restore state upon failure.

Throw a floating ConversionError, given the arguments of compareAs.