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.

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

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.

Run the given computation but turn any errors into blocked computations with the given blocker

Ignore errors in irrelevant context.

Type directed equality on values.

Type directed equality on terms or types.

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

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

Syntax directed equality on atomic values

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

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.

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

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...)

Type-directed equality on argument lists

Equality on Types

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.

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 that the first sort equal to the second.

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

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}

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