Agda-2.6.0.1: A dependently typed functional programming language and proof assistant

Agda.TypeChecking.SizedTypes

Synopsis

SIZELT stuff

Check whether a type is either not a SIZELT or a SIZELT that is non-empty.

Precondition: Term is reduced and not blocked. Throws a patternViolation if undecided

Checks that a size variable is ensured to be > 0. E.g. variable i cannot be zero in context (i : Size) (j : Size< ↑ ↑ i) (k : Size< j) (k' : Size< k). Throws a patternViolation if undecided.

isBounded :: MonadTCM tcm => Nat -> tcm BoundedSize Source #

Check whether a variable in the context is bounded by a size expression. If x : Size< a, then a is returned.

Whenever we create a bounded size meta, add a constraint expressing the bound. In boundedSizeMetaHook v tel a, tel includes the current context.

trySizeUniv :: Comparison -> Type -> Term -> Term -> QName -> Elims -> QName -> Elims -> TCM () Source #

trySizeUniv cmp t m n x els1 y els2 is called as a last resort when conversion checking m cmp n : t failed for definitions m = x els1 and n = y els2, where the heads x and y are not equal.

trySizeUniv accounts for subtyping between SIZELT and SIZE, like Size< i =< Size.

If it does not succeed it reports failure of conversion check.

Size views that reduce.

Compute the deep size view of a term. Precondition: sized types are enabled.

Size comparison that might add constraints.

compareSizes :: Comparison -> Term -> Term -> TCM () Source #

Compare two sizes.

Compare two sizes in max view.

compareBelowMax u vs checks u <= max vs. Precondition: size vs >= 2

giveUp :: Comparison -> Type -> Term -> Term -> TCM () Source #

If envAssignMetas then postpone as constraint, otherwise, fail hard. Failing is required if we speculatively test several alternatives.

Checked whether a size constraint is trivial (like X <= X+1).

Size constraints.

Test whether a problem consists only of size constraints.

Test is a constraint speaks about sizes.

Take out all size constraints (DANGER!).

Find the size constraints.

Return a list of size metas and their context.

Size constraint solving.

Atomic size expressions.

Constructors

 SizeMeta MetaId [Int] A size meta applied to de Bruijn indices. Rigid Int A de Bruijn index.
Instances
 Source # Instance detailsDefined in Agda.TypeChecking.SizedTypes Methods Source # Instance detailsDefined in Agda.TypeChecking.SizedTypes MethodsshowList :: [OldSizeExpr] -> ShowS # Source # Instance detailsDefined in Agda.TypeChecking.SizedTypes MethodsprettyList :: [OldSizeExpr] -> Doc Source #

Size constraints we can solve.

Constructors

 Leq OldSizeExpr Int OldSizeExpr Leq a +n b represents a =< b + n. Leq a -n b represents a + n =< b.
Instances
 Source # Instance detailsDefined in Agda.TypeChecking.SizedTypes MethodsshowList :: [OldSizeConstraint] -> ShowS # Source # Instance detailsDefined in Agda.TypeChecking.SizedTypes Methods

Compute a set of size constraints that all live in the same context from constraints over terms of type size that may live in different contexts.

cf. simplifyLevelConstraint

Turn a constraint over de Bruijn indices into a size constraint.

Turn a term with de Bruijn indices into a size expression with offset.

Throws a patternViolation if the term isn't a proper size expression.

flexibleVariables :: OldSizeConstraint -> [(MetaId, [Int])] Source #

Compute list of size metavariables with their arguments appearing in a constraint.

Convert size constraint into form where each meta is applied to indices 0,1,..,n-1 where n is the arity of that meta.

X[σ] <= t becomes X[id] <= t[σ^-1]

X[σ] ≤ Y[τ] becomes X[id] ≤ Y[τ[σ^-1]] or X[σ[τ^1]] ≤ Y[id] whichever is defined. If none is defined, we give up.

Main function. Uses the old solver for size constraints using Agda.Utils.Warshall. This solver does not smartly use size hypotheses j : Size< i. It only checks that its computed solution is compatible

Arguments

 :: [(MetaId, Int)] Size metas and their arity. -> [OldSizeConstraint] Size constraints (in preprocessed form). -> TCM Bool Returns False if solver fails.

Old solver for size constraints using Agda.Utils.Warshall. This solver does not smartly use size hypotheses j : Size< i.