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expressions-0.5: Expressions and Formulae a la carte

Copyright(C) 2017-18 Jakub Daniel
LicenseBSD-style (see the file LICENSE)
MaintainerJakub Daniel <jakub.daniel@protonmail.com>
Stabilityexperimental
Safe HaskellNone
LanguageHaskell2010

Data.Expression.Equality

Description

 
Synopsis

Documentation

data EqualityF a (s :: Sort) where Source #

A functor representing an equality predicate between two expressions of matching sort

Constructors

Equals :: Sing s -> a s -> a s -> EqualityF a BooleanSort 
Instances
IShow (EqualityF :: (k -> Type) -> Sort -> Type) Source # 
Instance details

Defined in Data.Expression.Equality

Methods

ishow :: EqualityF (Const String) i -> Const String i Source #

IEq1 (EqualityF :: (Sort -> Type) -> Sort -> Type) Source # 
Instance details

Defined in Data.Expression.Equality

Methods

ieq1 :: IEq a => EqualityF a j -> EqualityF a j -> Bool Source #

IFoldable (EqualityF :: (Sort -> Type) -> Sort -> Type) Source # 
Instance details

Defined in Data.Expression.Equality

Methods

ifold :: Monoid m => EqualityF (Const m) i' -> Const m 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 #

ITraversable (EqualityF :: (Sort -> Type) -> Sort -> Type) Source # 
Instance details

Defined in Data.Expression.Equality

Methods

itraverse :: Applicative f => (forall (i' :: i). a i' -> f (b i')) -> forall (i' :: i). EqualityF a i' -> f (EqualityF b i') Source #

Heyting (ALia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(==>) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #

neg :: ALia BooleanSort -> ALia BooleanSort #

(<=>) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #

Heyting (QFALia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(==>) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #

neg :: QFALia BooleanSort -> QFALia BooleanSort #

(<=>) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #

Heyting (Lia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(==>) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #

neg :: Lia BooleanSort -> Lia BooleanSort #

(<=>) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #

Heyting (QFLia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(==>) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #

neg :: QFLia BooleanSort -> QFLia BooleanSort #

(<=>) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #

Heyting (QFLogic BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(==>) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #

neg :: QFLogic BooleanSort -> QFLogic BooleanSort #

(<=>) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #

Lattice (ALia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(\/) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #

(/\) :: ALia BooleanSort -> ALia BooleanSort -> ALia BooleanSort #

Lattice (QFALia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(\/) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #

(/\) :: QFALia BooleanSort -> QFALia BooleanSort -> QFALia BooleanSort #

Lattice (Lia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(\/) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #

(/\) :: Lia BooleanSort -> Lia BooleanSort -> Lia BooleanSort #

Lattice (QFLia BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(\/) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #

(/\) :: QFLia BooleanSort -> QFLia BooleanSort -> QFLia BooleanSort #

Lattice (QFLogic BooleanSort) Source # 
Instance details

Defined in Data.Expression

Methods

(\/) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #

(/\) :: QFLogic BooleanSort -> QFLogic BooleanSort -> QFLogic BooleanSort #

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 #

(EqualityF :: (Sort -> Type) -> Sort -> Type) :<: f => Parseable (EqualityF :: (k -> Type) -> Sort -> Type) f Source # 
Instance details

Defined in Data.Expression.Equality

Methods

parser :: Proxy EqualityF -> Parser (DynamicallySortedFix f) -> Parser (DynamicallySortedFix f) Source #

(.=.) :: forall f s. (EqualityF :<: f, SingI s) => IFix f s -> IFix f s -> IFix f BooleanSort infix 7 Source #

A smart constructor for an equality predicate