Boolean-0.2.4: Generalized booleans and numbers

Data.Boolean

Description

Some classes for generalized boolean operations.

In this design, for if-then-else, equality and inequality tests, the boolean type depends on the value type.

I also tried using a unary type constructor class. The class doesn't work for regular booleans, so generality is lost. Also, we'd probably have to wire class constraints in like: (==*) :: Eq a => f Bool -> f a -> f a -> f a, which disallows situations needing additional constraints, e.g., Show.

Starting with 0.1.0, this package uses type families. Up to version 0.0.2, it used MPTCs with functional dependencies. My thanks to Andy Gill for suggesting & helping with the change.

Synopsis

# Documentation

class Boolean b where Source #

Generalized boolean class

Minimal complete definition

Methods

true, false :: b Source #

notB :: b -> b Source #

(&&*), (||*) :: b -> b -> b infixr 3 &&*infixr 2 ||* Source #

Instances

 Source # Methods(&&*) :: Bool -> Bool -> Bool Source #(||*) :: Bool -> Bool -> Bool Source # Boolean bool => Boolean (z -> bool) Source # Methodstrue :: z -> bool Source #false :: z -> bool Source #notB :: (z -> bool) -> z -> bool Source #(&&*) :: (z -> bool) -> (z -> bool) -> z -> bool Source #(||*) :: (z -> bool) -> (z -> bool) -> z -> bool Source #

type family BooleanOf a Source #

BooleanOf computed the boolean analog of a specific type.

Instances

 type BooleanOf Bool Source # type BooleanOf Bool = Bool type BooleanOf Char Source # type BooleanOf Char = Bool type BooleanOf Double Source # type BooleanOf Double = Bool type BooleanOf Float Source # type BooleanOf Float = Bool type BooleanOf Int Source # type BooleanOf Int = Bool type BooleanOf Integer Source # type BooleanOf Integer = Bool type BooleanOf [a] Source # type BooleanOf [a] = BooleanOf a type BooleanOf (z -> a) Source # type BooleanOf (z -> a) = z -> BooleanOf a type BooleanOf (a, b) Source # type BooleanOf (a, b) = BooleanOf a type BooleanOf (a, b, c) Source # type BooleanOf (a, b, c) = BooleanOf a type BooleanOf (a, b, c, d) Source # type BooleanOf (a, b, c, d) = BooleanOf a

class Boolean (BooleanOf a) => IfB a where Source #

Types with conditionals

Minimal complete definition

ifB

Methods

ifB :: bool ~ BooleanOf a => bool -> a -> a -> a Source #

Instances

 Source # MethodsifB :: (* ~ bool) (BooleanOf Bool) => bool -> Bool -> Bool -> Bool Source # Source # MethodsifB :: (* ~ bool) (BooleanOf Char) => bool -> Char -> Char -> Char Source # Source # MethodsifB :: (* ~ bool) (BooleanOf Double) => bool -> Double -> Double -> Double Source # Source # MethodsifB :: (* ~ bool) (BooleanOf Float) => bool -> Float -> Float -> Float Source # Source # MethodsifB :: (* ~ bool) (BooleanOf Int) => bool -> Int -> Int -> Int Source # Source # MethodsifB :: (* ~ bool) (BooleanOf Integer) => bool -> Integer -> Integer -> Integer Source # (Boolean (BooleanOf a), (~) * (BooleanOf a) Bool) => IfB [a] Source # MethodsifB :: (* ~ bool) (BooleanOf [a]) => bool -> [a] -> [a] -> [a] Source # IfB a => IfB (z -> a) Source # MethodsifB :: (* ~ bool) (BooleanOf (z -> a)) => bool -> (z -> a) -> (z -> a) -> z -> a Source # ((~) * bool (BooleanOf p), (~) * bool (BooleanOf q), IfB p, IfB q) => IfB (p, q) Source # MethodsifB :: (* ~ bool) (BooleanOf (p, q)) => bool -> (p, q) -> (p, q) -> (p, q) Source # ((~) * bool (BooleanOf p), (~) * bool (BooleanOf q), (~) * bool (BooleanOf r), IfB p, IfB q, IfB r) => IfB (p, q, r) Source # MethodsifB :: (* ~ bool) (BooleanOf (p, q, r)) => bool -> (p, q, r) -> (p, q, r) -> (p, q, r) Source # ((~) * bool (BooleanOf p), (~) * bool (BooleanOf q), (~) * bool (BooleanOf r), (~) * bool (BooleanOf s), IfB p, IfB q, IfB r, IfB s) => IfB (p, q, r, s) Source # MethodsifB :: (* ~ bool) (BooleanOf (p, q, r, s)) => bool -> (p, q, r, s) -> (p, q, r, s) -> (p, q, r, s) Source #

boolean :: (IfB a, bool ~ BooleanOf a) => a -> a -> bool -> a Source #

Expression-lifted conditional with condition last

cond :: (Applicative f, IfB a, bool ~ BooleanOf a) => f bool -> f a -> f a -> f a Source #

Point-wise conditional

crop :: (Applicative f, Monoid (f a), IfB a, bool ~ BooleanOf a) => f bool -> f a -> f a Source #

Generalized cropping, filling in mempty where the test yields false.

class Boolean (BooleanOf a) => EqB a where Source #

Types with equality. Minimum definition: '(==*)'.

Minimal complete definition

(==*)

Methods

(==*), (/=*) :: bool ~ BooleanOf a => a -> a -> bool infix 4 ==*, /=* Source #

Instances

 Source # Methods(==*) :: (* ~ bool) (BooleanOf Bool) => Bool -> Bool -> bool Source #(/=*) :: (* ~ bool) (BooleanOf Bool) => Bool -> Bool -> bool Source # Source # Methods(==*) :: (* ~ bool) (BooleanOf Char) => Char -> Char -> bool Source #(/=*) :: (* ~ bool) (BooleanOf Char) => Char -> Char -> bool Source # Source # Methods(==*) :: (* ~ bool) (BooleanOf Double) => Double -> Double -> bool Source #(/=*) :: (* ~ bool) (BooleanOf Double) => Double -> Double -> bool Source # Source # Methods(==*) :: (* ~ bool) (BooleanOf Float) => Float -> Float -> bool Source #(/=*) :: (* ~ bool) (BooleanOf Float) => Float -> Float -> bool Source # Source # Methods(==*) :: (* ~ bool) (BooleanOf Int) => Int -> Int -> bool Source #(/=*) :: (* ~ bool) (BooleanOf Int) => Int -> Int -> bool Source # Source # Methods(==*) :: (* ~ bool) (BooleanOf Integer) => Integer -> Integer -> bool Source #(/=*) :: (* ~ bool) (BooleanOf Integer) => Integer -> Integer -> bool Source # EqB a => EqB (z -> a) Source # Methods(==*) :: (* ~ bool) (BooleanOf (z -> a)) => (z -> a) -> (z -> a) -> bool Source #(/=*) :: (* ~ bool) (BooleanOf (z -> a)) => (z -> a) -> (z -> a) -> bool Source #

class Boolean (BooleanOf a) => OrdB a where Source #

Types with inequality. Minimum definition: '(<*)'.

Minimal complete definition

(<*)

Methods

(<*), (<=*), (>*), (>=*) :: bool ~ BooleanOf a => a -> a -> bool infix 4 <*, <=*, >*, >=* Source #

Instances

 Source # Methods(<*) :: (* ~ bool) (BooleanOf Bool) => Bool -> Bool -> bool Source #(<=*) :: (* ~ bool) (BooleanOf Bool) => Bool -> Bool -> bool Source #(>*) :: (* ~ bool) (BooleanOf Bool) => Bool -> Bool -> bool Source #(>=*) :: (* ~ bool) (BooleanOf Bool) => Bool -> Bool -> bool Source # Source # Methods(<*) :: (* ~ bool) (BooleanOf Char) => Char -> Char -> bool Source #(<=*) :: (* ~ bool) (BooleanOf Char) => Char -> Char -> bool Source #(>*) :: (* ~ bool) (BooleanOf Char) => Char -> Char -> bool Source #(>=*) :: (* ~ bool) (BooleanOf Char) => Char -> Char -> bool Source # Source # Methods(<*) :: (* ~ bool) (BooleanOf Double) => Double -> Double -> bool Source #(<=*) :: (* ~ bool) (BooleanOf Double) => Double -> Double -> bool Source #(>*) :: (* ~ bool) (BooleanOf Double) => Double -> Double -> bool Source #(>=*) :: (* ~ bool) (BooleanOf Double) => Double -> Double -> bool Source # Source # Methods(<*) :: (* ~ bool) (BooleanOf Float) => Float -> Float -> bool Source #(<=*) :: (* ~ bool) (BooleanOf Float) => Float -> Float -> bool Source #(>*) :: (* ~ bool) (BooleanOf Float) => Float -> Float -> bool Source #(>=*) :: (* ~ bool) (BooleanOf Float) => Float -> Float -> bool Source # Source # Methods(<*) :: (* ~ bool) (BooleanOf Int) => Int -> Int -> bool Source #(<=*) :: (* ~ bool) (BooleanOf Int) => Int -> Int -> bool Source #(>*) :: (* ~ bool) (BooleanOf Int) => Int -> Int -> bool Source #(>=*) :: (* ~ bool) (BooleanOf Int) => Int -> Int -> bool Source # Source # Methods(<*) :: (* ~ bool) (BooleanOf Integer) => Integer -> Integer -> bool Source #(<=*) :: (* ~ bool) (BooleanOf Integer) => Integer -> Integer -> bool Source #(>*) :: (* ~ bool) (BooleanOf Integer) => Integer -> Integer -> bool Source #(>=*) :: (* ~ bool) (BooleanOf Integer) => Integer -> Integer -> bool Source # OrdB a => OrdB (z -> a) Source # Methods(<*) :: (* ~ bool) (BooleanOf (z -> a)) => (z -> a) -> (z -> a) -> bool Source #(<=*) :: (* ~ bool) (BooleanOf (z -> a)) => (z -> a) -> (z -> a) -> bool Source #(>*) :: (* ~ bool) (BooleanOf (z -> a)) => (z -> a) -> (z -> a) -> bool Source #(>=*) :: (* ~ bool) (BooleanOf (z -> a)) => (z -> a) -> (z -> a) -> bool Source #

minB :: (IfB a, OrdB a) => a -> a -> a Source #

Variant of min using ifB and '(<=*)'

maxB :: (IfB a, OrdB a) => a -> a -> a Source #

Variant of max using ifB and '(>=*)'

sort2B :: (IfB a, OrdB a) => (a, a) -> (a, a) Source #

Variant of min and max using ifB and '(<=*)'

guardedB :: (IfB b, bool ~ BooleanOf b) => bool -> [(bool, b)] -> b -> b Source #

A generalized replacement for guards and chained ifs.

caseB :: (IfB b, bool ~ BooleanOf b) => a -> [(a -> bool, b)] -> b -> b Source #

A generalized version of a case like control structure.