Language.HM.Type

This module contains the abstract syntax of Hindley-Milner types.

Documentation

module Language.HM.Alpha

Monomorphic types.

data TauF r

Constructors

VarT String

ArrowT r r

Instances

Functor TauF

HasTypeVars Tau

CanApply Tau

CanApply TyTerm

Eq r => Eq (TauF r)

Show r => Show (TauF r)

type Tau = Fix TauF

Monomorphic types.

varT :: String -> Tau

varT x constructs a type variable named x.

arrowT :: Tau -> Tau -> Tau

arrowT t0 t1 constructs an arrow type from t0 to t1.

Polymorphic types.

data SigmaF r

Constructors

ForAllT String r

MonoT Tau

Instances

Functor SigmaF

Foldable SigmaF

Traversable SigmaF

AlphaEq Sigma

HasTypeVars Sigma

CanApply Sigma

CanApply TyTerm

Eq r => Eq (SigmaF r)

Show r => Show (SigmaF r)

type Sigma = Fix SigmaF

Polymorphic types.

forAllT :: String -> Sigma -> Sigma

forAllT x t universally quantifies x in t.

monoT :: Tau -> Sigma

monoT t lifts a monomorophic type t to a polymorphic one.

class HasTypeVars a where

The class of types which have free type variables.

Methods

tyVars :: a -> Set String

tyVars t calculates the set of free type variables in t.

tyVarsInOrder :: a -> [String]

tyVarsInOrder t is like tyVars t, except that the type variables are returned in the order in which they are encountered.

Instances

HasTypeVars Sigma

HasTypeVars Tau