hets -- a heterogenous Specification (CASL) tool set Contents Index

HasCASL.Unify Portability portable Stability experimental Maintainer hets@tzi.de

Description

substitution and unification of types

Synopsis

varsOf :: Type -> [TypeArg] generalize :: TypeScheme -> TypeScheme compSubst :: Subst -> Subst -> Subst isUnifiable :: TypeMap -> Int -> TypeScheme -> TypeScheme -> Bool instScheme :: TypeMap -> Int -> TypeScheme -> TypeScheme -> Bool toEnvState :: State Int a -> State Env a toSchemes :: (Type -> Type -> a) -> TypeScheme -> TypeScheme -> State Int a asSchemes :: Int -> (Type -> Type -> a) -> TypeScheme -> TypeScheme -> a freshInst :: TypeScheme -> State Int Type freshVar :: State Int Id mkSingleSubst :: TypeArg -> State Int Subst mkSubst :: [TypeArg] -> State Int Subst type Subst = Map TypeArg Type eps :: Subst class Unifiable a where subst :: Subst -> a -> a match :: TypeMap -> (Bool, a) -> (Bool, a) -> Result Subst mgu :: Unifiable a => TypeMap -> a -> a -> Result Subst unify :: Unifiable a => TypeMap -> a -> a -> Bool subsume :: Unifiable a => TypeMap -> a -> a -> Bool equalSubs :: Unifiable a => TypeMap -> a -> a -> Bool starTypeInfo :: TypeInfo showPrettyWithPos :: (PrettyPrint a, PosItem a) => a -> ShowS uniResult :: (PrettyPrint a, PosItem a, PrettyPrint b, PosItem b) => String -> a -> String -> b -> Result Subst occursIn :: TypeMap -> TypeId -> Type -> Bool expandAlias :: TypeMap -> Type -> (Type, Bool) expandAliases :: TypeMap -> Type -> ([TypeArg], [Type], Type, Bool)

Documentation

varsOf :: Type -> [TypeArg]

generalize :: TypeScheme -> TypeScheme

compSubst :: Subst -> Subst -> Subst

composition (reversed: first substitution first!)

isUnifiable :: TypeMap -> Int -> TypeScheme -> TypeScheme -> Bool

unifiability of type schemes including instantiation with fresh variables (and looking up type aliases)

instScheme :: TypeMap -> Int -> TypeScheme -> TypeScheme -> Bool

test if second scheme is a substitution instance

toEnvState :: State Int a -> State Env a

lift State Int to State Env

toSchemes :: (Type -> Type -> a) -> TypeScheme -> TypeScheme -> State Int a

asSchemes :: Int -> (Type -> Type -> a) -> TypeScheme -> TypeScheme -> a

freshInst :: TypeScheme -> State Int Type

freshVar :: State Int Id

mkSingleSubst :: TypeArg -> State Int Subst

mkSubst :: [TypeArg] -> State Int Subst

type Subst = Map TypeArg Type

eps :: Subst

class Unifiable a where

Methods subst :: Subst -> a -> a match :: TypeMap -> (Bool, a) -> (Bool, a) -> Result Subst Instances Unifiable Type (Unifiable a, Unifiable b) => Unifiable (a, b) (PrettyPrint a, PosItem a, Unifiable a) => Unifiable [a] (PrettyPrint a, PosItem a, Unifiable a) => Unifiable (Maybe a)

mgu :: Unifiable a => TypeMap -> a -> a -> Result Subst

most general unifier via match where both sides may contribute substitutions

unify :: Unifiable a => TypeMap -> a -> a -> Bool

subsume :: Unifiable a => TypeMap -> a -> a -> Bool

equalSubs :: Unifiable a => TypeMap -> a -> a -> Bool

starTypeInfo :: TypeInfo

showPrettyWithPos :: (PrettyPrint a, PosItem a) => a -> ShowS

uniResult :: (PrettyPrint a, PosItem a, PrettyPrint b, PosItem b) => String -> a -> String -> b -> Result Subst

occursIn :: TypeMap -> TypeId -> Type -> Bool

expandAlias :: TypeMap -> Type -> (Type, Bool)

expandAliases :: TypeMap -> Type -> ([TypeArg], [Type], Type, Bool)

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