Agda- A dependently typed functional programming language and proof assistant

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Polarity lattice.

(/\) :: Polarity -> Polarity -> PolaritySource

Infimum on the information lattice. Invariant is bottom (dominant for inf), Nonvariant is top (neutral for inf).

neg :: Polarity -> PolaritySource

Polarity negation, swapping monotone and antitone.

composePol :: Polarity -> Polarity -> PolaritySource

What is the polarity of a function composition?

Auxiliary functions

nextPolarity :: [Polarity] -> (Polarity, [Polarity])Source

Get the next polarity from a list, Invariant if empty.

Computing the polarity of a symbol.

computePolarity :: QName -> TCM ()Source

Main function of this module.

enablePhantomTypes :: Defn -> [Polarity] -> [Polarity]Source

Data and record parameters are used as phantom arguments all over the test suite (and possibly in user developments). enablePhantomTypes turns Nonvariant parameters to Invariant to enable phantoms.

dependentPolarity :: Type -> [Polarity] -> TCM [Polarity]Source

Make arguments Invariant if the type of a not-Nonvariant later argument depends on it.

relevantInIgnoringNonvariant :: Nat -> Type -> [Polarity] -> TCM BoolSource

Check whether a variable is relevant in a type expression, ignoring domains of non-variant arguments.

Turn polarity Nonvariant into relevance UnusedArg

mkUnused :: Relevance -> RelevanceSource

Record information that an argument is unused in Relevance.

nonvariantToUnusedArg :: [Polarity] -> Type -> TCM TypeSource

Improve Relevance information in a type by polarity information. Nonvariant becomes UnusedArg.

nonvariantToUnusedArgInDef :: [Polarity] -> Defn -> DefnSource

Propagate Nonvariant Polarity to Relevance information in Args of a defined symbol.

Sized types

sizePolarity :: QName -> [Polarity] -> TCM [Polarity]Source

Hack for polarity of size indices.

class HasPolarity a whereSource

polarities i a computes the list of polarities of de Bruijn index i in syntactic entity a.


polarities :: Nat -> a -> TCM [Polarity]Source

polarity :: HasPolarity a => Nat -> a -> TCM PolaritySource

polarity i a computes the polarity of de Bruijn index i in syntactic entity a by taking the infimum of all polarities.