Boolean-0.2: Generalized booleans and numbers

Stability experimental conal@conal.net Safe-Inferred

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 whereSource

Generalized boolean class

Methods

true, false :: bSource

notB :: b -> bSource

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

Instances

 Boolean Bool Boolean bool => Boolean (z -> bool)

type family BooleanOf a Source

`BooleanOf` computed the boolean analog of a specific type.

class Boolean (BooleanOf a) => IfB a whereSource

Types with conditionals

Methods

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

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 -> aSource

Expression-lifted conditional with condition last

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

Point-wise conditional

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

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

class Boolean (BooleanOf a) => EqB a whereSource

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

Methods

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

Instances

 EqB Bool EqB Char EqB Double EqB Float EqB Int EqB Integer EqB a => EqB (z -> a)

class Boolean (BooleanOf a) => OrdB a whereSource

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

Methods

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

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 -> aSource

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

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

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 -> bSource

A generalized replacement for guards and chained ifs.

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

A generalized version of a case like control structure.