Copyright	(C) 2017-18 Jakub Daniel
License	BSD-style (see the file LICENSE)
Maintainer	Jakub Daniel <jakub.daniel@protonmail.com>
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Data.Expression.Utils.Indexed.Functor

Description

Synopsis

newtype IFix f i = IFix {
- unIFix :: f (IFix f) i
}
class IFunctor (f :: (i -> *) -> i -> *) where
- imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i'
- index :: forall a i'. f a i' -> Sing i'
icata :: IFunctor f => (forall i. f a i -> a i) -> forall i. IFix f i -> a i

Documentation

newtype IFix f i Source #

A fixpoint of a functor in indexed category

Constructors

IFix
Fields unIFix :: f (IFix f) i

Instances

IEq1 f => IEq (IFix f :: i -> Type) Source #
Instance details Defined in Data.Expression.Utils.Indexed.Functor Methods ieq :: IFix f j -> IFix f j -> Bool Source #
JoinSemiLattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (\/) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort # join :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #
JoinSemiLattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (\/) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort # join :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #
JoinSemiLattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (\/) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort # join :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #
JoinSemiLattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (\/) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort # join :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #
JoinSemiLattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression Methods (\/) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort # join :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #
MeetSemiLattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (/\) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort # meet :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #
MeetSemiLattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (/\) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort # meet :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #
MeetSemiLattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (/\) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort # meet :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #
MeetSemiLattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression Methods (/\) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort # meet :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #
MeetSemiLattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression Methods (/\) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort # meet :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #
Lattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression
Lattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression
Lattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression
Lattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression
Lattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression
BoundedJoinSemiLattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods bottom :: ALia BooleanSort #
BoundedJoinSemiLattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods bottom :: QFALia BooleanSort #
BoundedJoinSemiLattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression Methods bottom :: Lia BooleanSort #
BoundedJoinSemiLattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression Methods bottom :: QFLia BooleanSort #
BoundedJoinSemiLattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression Methods bottom :: QFLogic BooleanSort #
BoundedMeetSemiLattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods top :: ALia BooleanSort #
BoundedMeetSemiLattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods top :: QFALia BooleanSort #
BoundedMeetSemiLattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression Methods top :: Lia BooleanSort #
BoundedMeetSemiLattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression Methods top :: QFLia BooleanSort #
BoundedMeetSemiLattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression Methods top :: QFLogic BooleanSort #
BoundedLattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression
BoundedLattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression
BoundedLattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression
BoundedLattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression
BoundedLattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression
ComplementedLattice (ALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods complement :: ALia BooleanSort -> ALia BooleanSort Source #
ComplementedLattice (QFALia BooleanSort) Source #
Instance details Defined in Data.Expression Methods complement :: QFALia BooleanSort -> QFALia BooleanSort Source #
ComplementedLattice (Lia BooleanSort) Source #
Instance details Defined in Data.Expression Methods complement :: Lia BooleanSort -> Lia BooleanSort Source #
ComplementedLattice (QFLia BooleanSort) Source #
Instance details Defined in Data.Expression Methods complement :: QFLia BooleanSort -> QFLia BooleanSort Source #
ComplementedLattice (QFLogic BooleanSort) Source #
Instance details Defined in Data.Expression Methods complement :: QFLogic BooleanSort -> QFLogic BooleanSort Source #
IEq1 f => Eq (IFix f i) Source #
Instance details Defined in Data.Expression.Utils.Indexed.Functor Methods (==) :: IFix f i -> IFix f i -> Bool # (/=) :: IFix f i -> IFix f i -> Bool #
(IFunctor f, IShow f) => Show (IFix f i) Source #
Instance details Defined in Data.Expression.Utils.Indexed.Functor Methods showsPrec :: Int -> IFix f i -> ShowS # show :: IFix f i -> String # showList :: [IFix f i] -> ShowS #

class IFunctor (f :: (i -> *) -> i -> *) where Source #

A functor in indexed category

Methods

imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source #

index :: forall a i'. f a i' -> Sing i' Source #

Instances

IFunctor IfThenElseF Source #
Instance details Defined in Data.Expression.IfThenElse Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). IfThenElseF a i' -> IfThenElseF b i' Source # index :: IfThenElseF a i' -> Sing i' Source #
IFunctor ArrayF Source #
Instance details Defined in Data.Expression.Array Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). ArrayF a i' -> ArrayF b i' Source # index :: ArrayF a i' -> Sing i' Source #
IFunctor ArithmeticF Source #
Instance details Defined in Data.Expression.Arithmetic Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). ArithmeticF a i' -> ArithmeticF b i' Source # index :: ArithmeticF a i' -> Sing i' Source #
IFunctor NegationF Source #
Instance details Defined in Data.Expression Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). NegationF a i' -> NegationF b i' Source # index :: NegationF a i' -> Sing i' Source #
IFunctor DisjunctionF Source #
Instance details Defined in Data.Expression Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). DisjunctionF a i' -> DisjunctionF b i' Source # index :: DisjunctionF a i' -> Sing i' Source #
IFunctor ConjunctionF Source #
Instance details Defined in Data.Expression Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). ConjunctionF a i' -> ConjunctionF b i' Source # index :: ConjunctionF a i' -> Sing i' Source #
IFunctor (EqualityF :: (Sort -> Type) -> Sort -> Type) Source #
Instance details Defined in Data.Expression.Equality Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). EqualityF a i' -> EqualityF b i' Source # index :: EqualityF a i' -> Sing i' Source #
IFunctor (ExistentialF v :: (Sort -> Type) -> Sort -> Type) Source #
Instance details Defined in Data.Expression Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). ExistentialF v a i' -> ExistentialF v b i' Source # index :: ExistentialF v a i' -> Sing i' Source #
IFunctor (UniversalF v :: (Sort -> Type) -> Sort -> Type) Source #
Instance details Defined in Data.Expression Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). UniversalF v a i' -> UniversalF v b i' Source # index :: UniversalF v a i' -> Sing i' Source #
IFunctor (VarF :: (Sort -> Type) -> Sort -> Type) Source #
Instance details Defined in Data.Expression Methods imap :: (forall (i' :: i). a i' -> b i') -> forall (i' :: i). VarF a i' -> VarF b i' Source # index :: VarF a i' -> Sing i' Source #
(IFunctor f, IFunctor g) => IFunctor (f :+: g :: (i -> Type) -> i -> Type) Source #
Instance details Defined in Data.Expression.Utils.Indexed.Sum Methods imap :: (forall (i' :: i0). a i' -> b i') -> forall (i' :: i0). (f :+: g) a i' -> (f :+: g) b i' Source # index :: (f :+: g) a i' -> Sing i' Source #

icata :: IFunctor f => (forall i. f a i -> a i) -> forall i. IFix f i -> a i Source #

Indexed catamorphism