GHC.Core.Multiplicity

ghc-9.10.0.20240328: The GHC API

Safe Haskell | None
Language | GHC2021

GHC.Core.Multiplicity

Description

This module defines the semi-ring of multiplicities, and associated functions. Multiplicities annotate arrow types to indicate the linearity of the arrow (in the sense of linear types).

Mult is a type synonym for Type, used only when its kind is Multiplicity. To simplify dealing with multiplicities, functions such as mkMultMul perform simplifications such as Many * x = Many on the fly.

Synopsis

- type Mult = Type
- pattern OneTy :: Mult
- pattern ManyTy :: Mult
- isMultMul :: Mult -> Maybe (Mult, Mult)
- mkMultAdd :: Mult -> Mult -> Mult
- mkMultMul :: Mult -> Mult -> Mult
- mkMultSup :: Mult -> Mult -> Mult
- data Scaled a = Scaled !Mult a
- scaledMult :: Scaled a -> Mult
- scaledThing :: Scaled a -> a
- unrestricted :: a -> Scaled a
- linear :: a -> Scaled a
- tymult :: a -> Scaled a
- irrelevantMult :: Scaled a -> a
- mkScaled :: Mult -> a -> Scaled a
- scaledSet :: Scaled a -> b -> Scaled b
- scaleScaled :: Mult -> Scaled a -> Scaled a
- data IsSubmult
  - = Submult
  - | Unknown
- submult :: Mult -> Mult -> IsSubmult
- mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type
- pprArrowWithMultiplicity :: FunTyFlag -> Either Bool SDoc -> SDoc

# Documentation

type Mult = Type Source #

Mult is a type alias for Type.

Mult must contain Type because multiplicity variables are mere type variables (of kind Multiplicity) in Haskell. So the simplest implementation is to make Mult be Type.

Multiplicities can be formed with: - One: GHC.Types.One (= oneDataCon) - Many: GHC.Types.Many (= manyDataCon) - Multiplication: GHC.Types.MultMul (= multMulTyCon)

So that Mult feels a bit more structured, we provide pattern synonyms and smart constructors for these.

pattern OneTy :: Mult Source #

pattern ManyTy :: Mult Source #

isMultMul :: Mult -> Maybe (Mult, Mult) Source #

mkMultAdd :: Mult -> Mult -> Mult Source #

mkMultMul :: Mult -> Mult -> Mult Source #

mkMultSup :: Mult -> Mult -> Mult Source #

`mkMultSup w1 w2` returns a multiplicity such that `mkMultSup w1 w2 >= w1` and `mkMultSup w1 w2 >= w2`. See Note [Overapproximating multiplicities].

data Scaled a Source #

A shorthand for data with an attached `Mult` element (the multiplicity).

Constructors

Scaled !Mult a |

#### Instances

Instances details

Outputable a => Outputable (Scaled a) Source # |
Instance details Defined in GHC.Core.TyCo.Rep Methods ppr :: Scaled a -> SDoc Source #
Data a => Data (Scaled a) Source # |
Instance details Defined in GHC.Core.TyCo.Rep Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Scaled a -> c (Scaled a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scaled a) # toConstr :: Scaled a -> Constr # dataTypeOf :: Scaled a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scaled a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scaled a)) # gmapT :: (forall b. Data b => b -> b) -> Scaled a -> Scaled a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scaled a -> r # gmapQ :: (forall d. Data d => d -> u) -> Scaled a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Scaled a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Scaled a -> m (Scaled a) #

scaledMult :: Scaled a -> Mult Source #

scaledThing :: Scaled a -> a Source #

unrestricted :: a -> Scaled a Source #

Scale a payload by Many

linear :: a -> Scaled a Source #

Scale a payload by One

tymult :: a -> Scaled a Source #

Scale a payload by Many; used for type arguments in core

irrelevantMult :: Scaled a -> a Source #

mkScaled :: Mult -> a -> Scaled a Source #

scaledSet :: Scaled a -> b -> Scaled b Source #

scaleScaled :: Mult -> Scaled a -> Scaled a Source #

data IsSubmult Source #

Constructors

Submult |
Unknown |

#### Instances

Instances details

Outputable IsSubmult Source # |
Instance details Defined in GHC.Core.Multiplicity Methods ppr :: IsSubmult -> SDoc Source #
Show IsSubmult Source # |
Instance details Defined in GHC.Core.Multiplicity Methods showsPrec :: Int -> IsSubmult -> ShowS # show :: IsSubmult -> String # showList :: [IsSubmult] -> ShowS #
Eq IsSubmult Source # |
Instance details Defined in GHC.Core.Multiplicity Methods (==) :: IsSubmult -> IsSubmult -> Bool # (/=) :: IsSubmult -> IsSubmult -> Bool #

submult :: Mult -> Mult -> IsSubmult Source #

`submult w1 w2` check whether a value of multiplicity `w1` is allowed where a value of multiplicity `w2` is expected. This is a partial order.

mapScaledType :: (Type -> Type) -> Scaled Type -> Scaled Type Source #

Apply a function to both the Mult and the Type in a 'Scaled Type'

pprArrowWithMultiplicity :: FunTyFlag -> Either Bool SDoc -> SDoc Source #