Data.Boolean

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.

Documentation

class Boolean b where

Generalized boolean class

Methods

true, false :: b

notB :: b -> b

(&&*), (||*) :: b -> b -> b

Instances

Boolean Bool

Boolean bool => Boolean (z -> bool)

type family BooleanOf a

BooleanOf computed the boolean analog of a specific type.

class Boolean (BooleanOf a) => IfB a where

Types with conditionals

Methods

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

Instances

IfB Bool

IfB Char

IfB Double

IfB Float

IfB Int

IfB Integer

(Boolean (BooleanOf a), ~ * (BooleanOf a) Bool) => IfB [a]

IfB a => IfB (z -> a)

(~ * bool (BooleanOf p), ~ * bool (BooleanOf q), IfB p, IfB q) => IfB (p, q)

(~ * bool (BooleanOf p), ~ * bool (BooleanOf q), ~ * bool (BooleanOf r), IfB p, IfB q, IfB r) => IfB (p, q, r)

(~ * 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)

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

Expression-lifted conditional with condition last

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

Point-wise conditional

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

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

class Boolean (BooleanOf a) => EqB a where

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

Methods

(==*), (/=*) :: bool ~ BooleanOf a => a -> a -> bool

Instances

EqB Bool

EqB Char

EqB Double

EqB Float

EqB Int

EqB Integer

EqB a => EqB (z -> a)

class Boolean (BooleanOf a) => OrdB a where

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

Methods

(<*), (>=*), (>*), (<=*) :: bool ~ BooleanOf a => a -> a -> bool

Instances

OrdB Bool

OrdB Char

OrdB Double

OrdB Float

OrdB Int

OrdB Integer

OrdB a => OrdB (z -> a)

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

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

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

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

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

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

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

A generalized replacement for guards and chained ifs.

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

A generalized version of a case like control structure.