Top.Types.Primitive

This module contains a data type to represent (plain) types, some basic functionality for types, and an instance for Show.

Data type definition

type Tps = [Tp]

data Tp

A data type to represent monotypes. Note that Type is already in use in the Unified Haskell Architecture (UHA) which is used in the Helium compiler

Constructors

TVar Int

The type variables are numbered.

TCon String

A type constant is represented by a string.

TApp Tp Tp

The application of two Top.Types. Not all types that can be constructed are well-formed.

Instances

Eq Tp

Ord Tp

Read Tp

Show Tp

HasTypes Tp

Substitutable Tp

Substitution MapSubstitution

ShowQuantors Tp

HasSkolems Tp

IsSigmaPreds Tp

IsSigmaPreds QType

IsSigmaPreds TpScheme

IsTpScheme Tp

IsTpScheme QType

IsTpScheme TpScheme

Common types

intType, stringType, boolType, floatType, charType :: Tp

(.->.) :: Tp -> Tp -> Tp

Constructs a function type from one type to another. This operator is left associative.

listType :: Tp -> Tp

For instance, (listType intType) represents [Int]

ioType :: Tp -> Tp

For instance, (ioType boolType) represents (IO Bool)

tupleType :: Tps -> Tp

A cathesian product of zero or more Top.Types. For instance, (tupleType []) represents (), and (tupleType [charType, stringType]) represents (Char,String)

voidType :: Tp

The unit type. A special instance of of tuple type.

Basic functionality

variablesInType :: Tp -> [Int]

Returns the list of type variables of a type. (no duplicates)

constantsInType :: Tp -> [String]

Returns the list of type constants of a type. (no duplicates)

leftSpine :: Tp -> (Tp, Tps)

Returns the left spine of a type. For instance, if type t is Either Bool [Int], then leftSpine t is (Either,[Bool,[Int]]).

functionSpine :: Tp -> (Tps, Tp)

Returns the right spine of a function type. For instance, if type t is Int -> (Bool -> String), then functionSpine t is ([Int,Bool],String).

functionSpineOfLength :: Int -> Tp -> (Tps, Tp)

Returns the right spine of a function type of a maximal length.

arityOfTp :: Tp -> Int

Returns the arity of a type, that is, the number of expected arguments.

priorityOfType :: Tp -> Int

The priority of a type, primarily used for the insertion of parentheses in pretty printing.

freezeVariablesInType :: Tp -> Tp

All the type variables in a type are frozen by turning them into a type constant. The integer numeral is prefixed with an underscore ('_').

unfreezeVariablesInType :: Tp -> Tp

Recover the type variables that are frozen in a type.

Predicates on types

isTVar :: Tp -> Bool

isTCon :: Tp -> Bool

isTApp :: Tp -> Bool

isFunctionType :: Tp -> Bool

isTupleConstructor :: String -> Bool

isIOType :: Tp -> Bool

tpParser :: String -> [(Tp, String)]

class HasTypes a where

Methods

getTypes :: a -> Tps

changeTypes :: (Tp -> Tp) -> a -> a

Instances

HasTypes Tp

HasTypes Predicate

HasTypes a => HasTypes [a]

HasTypes a => HasTypes (Maybe a)

(HasTypes a, HasTypes b) => HasTypes (Either a b)

(HasTypes a, HasTypes b) => HasTypes (a, b)

(HasTypes q, HasTypes a) => HasTypes (Qualification q a)

HasTypes a => HasTypes (Quantification q a)