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

Documentation

newtype IFix f i Source #

A fixpoint of a functor in indexed category

Constructors

IFix
Fields unIFix :: f (IFix f) i

Instances

IEq1 i f => IEq i (IFix i f) Source #
Methods ieq :: a j -> a j -> Bool Source #
JoinSemiLattice (ALia BooleanSort) #
Methods (\/) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort # join :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #
JoinSemiLattice (QFALia BooleanSort) #
Methods (\/) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort # join :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #
JoinSemiLattice (Lia BooleanSort) #
Methods (\/) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort # join :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #
JoinSemiLattice (QFLia BooleanSort) #
Methods (\/) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort # join :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #
JoinSemiLattice (QFLogic BooleanSort) #
Methods (\/) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort # join :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #
MeetSemiLattice (ALia BooleanSort) #
Methods (/\) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort # meet :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #
MeetSemiLattice (QFALia BooleanSort) #
Methods (/\) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort # meet :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #
MeetSemiLattice (Lia BooleanSort) #
Methods (/\) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort # meet :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #
MeetSemiLattice (QFLia BooleanSort) #
Methods (/\) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort # meet :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #
MeetSemiLattice (QFLogic BooleanSort) #
Methods (/\) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort # meet :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #
Lattice (ALia BooleanSort) #

Lattice (QFALia BooleanSort) #

Lattice (Lia BooleanSort) #

Lattice (QFLia BooleanSort) #

Lattice (QFLogic BooleanSort) #

BoundedJoinSemiLattice (ALia BooleanSort) #
Methods bottom :: ALia BooleanSort #
BoundedJoinSemiLattice (QFALia BooleanSort) #
Methods bottom :: QFALia BooleanSort #
BoundedJoinSemiLattice (Lia BooleanSort) #
Methods bottom :: Lia BooleanSort #
BoundedJoinSemiLattice (QFLia BooleanSort) #
Methods bottom :: QFLia BooleanSort #
BoundedJoinSemiLattice (QFLogic BooleanSort) #
Methods bottom :: QFLogic BooleanSort #
BoundedMeetSemiLattice (ALia BooleanSort) #
Methods top :: ALia BooleanSort #
BoundedMeetSemiLattice (QFALia BooleanSort) #
Methods top :: QFALia BooleanSort #
BoundedMeetSemiLattice (Lia BooleanSort) #
Methods top :: Lia BooleanSort #
BoundedMeetSemiLattice (QFLia BooleanSort) #
Methods top :: QFLia BooleanSort #
BoundedMeetSemiLattice (QFLogic BooleanSort) #
Methods top :: QFLogic BooleanSort #
BoundedLattice (ALia BooleanSort) #

BoundedLattice (QFALia BooleanSort) #

BoundedLattice (Lia BooleanSort) #

BoundedLattice (QFLia BooleanSort) #

BoundedLattice (QFLogic BooleanSort) #

ComplementedLattice (ALia BooleanSort) Source #
Methods complement :: ALia BooleanSort -> ALia BooleanSort Source #
ComplementedLattice (QFALia BooleanSort) Source #
Methods complement :: QFALia BooleanSort -> QFALia BooleanSort Source #
ComplementedLattice (Lia BooleanSort) Source #
Methods complement :: Lia BooleanSort -> Lia BooleanSort Source #
ComplementedLattice (QFLia BooleanSort) Source #
Methods complement :: QFLia BooleanSort -> QFLia BooleanSort Source #
ComplementedLattice (QFLogic BooleanSort) Source #
Methods complement :: QFLogic BooleanSort -> QFLogic BooleanSort Source #
IEq1 k f => Eq (IFix k f i) Source #
Methods (==) :: IFix k f i -> IFix k f i -> Bool # (/=) :: IFix k f i -> IFix k f i -> Bool #
(IFunctor k f, IShow k k f) => Show (IFix k f i) Source #
Methods showsPrec :: Int -> IFix k f i -> ShowS # show :: IFix k f i -> String # showList :: [IFix k f i] -> ShowS #

class IFunctor f where Source #

A functor in indexed category

Minimal complete definition

imap, index

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 Sort ArrayF Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing ArrayF i' Source #
IFunctor Sort ArithmeticF Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing ArithmeticF i' Source #
IFunctor Sort NegationF Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing NegationF i' Source #
IFunctor Sort DisjunctionF Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing DisjunctionF i' Source #
IFunctor Sort ConjunctionF Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing ConjunctionF i' Source #
IFunctor Sort (EqualityF Sort) Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing (EqualityF Sort) i' Source #
IFunctor Sort (ExistentialF v) Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing (ExistentialF v) i' Source #
IFunctor Sort (UniversalF v) Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing (UniversalF v) i' Source #
IFunctor Sort (VarF (Sort -> *)) Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing (VarF (Sort -> *)) i' Source #
(IFunctor i f, IFunctor i g) => IFunctor i ((:+:) i (i -> *) f g) Source #
Methods imap :: (forall i'. a i' -> b i') -> forall i'. f a i' -> f b i' Source # index :: f a i' -> Sing ((i :+: (i -> *)) f g) i' Source #

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

Indexed catamorphism