Portability	non-portable
Stability	experimental (MPTC, non-standarad instances)
Maintainer	alfonso.acosta@gmail.com

Data.TypeLevel.Bool

Contents

Type-level boolean values
Type-level boolean operations

Description

Type-level Booleans.

Synopsis

Type-level boolean values

class BoolI b => Bool b

Type-level Booleans

Instances

BoolI b => Bool b

toBool :: BoolI b => b -> Bool

data False

False type-level value

Instances

Show False
Typeable False
BoolI False
Not False True
Not True False
IsZero D9 False
IsZero D8 False
IsZero D7 False
IsZero D6 False
IsZero D5 False
IsZero D4 False
IsZero D3 False
IsZero D2 False
IsZero D1 False
Eq False False True
Eq False True False
Eq True False False
Imp False False True
Imp False True True
Imp True False False
Xor False False False
Xor False True True
Xor True False True
Xor True True False
Or False False False
Or False True True
Or True False True
And False False False
And False True False
And True False False
(Nat x, Nat y, Sub x y x', GCD x' y gcd) => GCD' x y False GT gcd
Nat x => GCD' x x False EQ x
(Nat x, Nat y, GCD y x gcd) => GCD' x y False LT gcd
(Pos b, b :>=: D2, Pos x) => LogBaseF' b x D0 False LT
Succ xi yi => Succ' xi D9 yi D0 False
Succ' xi D8 xi D9 False
Succ' xi D7 xi D8 False
Succ' xi D6 xi D7 False
Succ' xi D5 xi D6 False
Succ' xi D4 xi D5 False
Succ' xi D3 xi D4 False
Succ' xi D2 xi D3 False
Succ' xi D1 xi D2 False
Succ' xi D0 xi D1 False
Pos x => IsZero (:* x d) False

false :: False

False value-level reflecting function

data True

True type-level value

Instances

Show True
Typeable True
BoolI True
Not False True
Not True False
IsZero D0 True
Eq False False True
Eq False True False
Eq True False False
Eq True True True
Imp False False True
Imp False True True
Imp True False False
Imp True True True
Xor False True True
Xor True False True
Xor True True False
Or False True True
Or True False True
Or True True True
And False True False
And True False False
And True True True
Nat x => GCD' x D0 True cmp D0
(Pos b, b :>=: D2) => LogBaseF' b b D1 True EQ
Failure (PredecessorOfZeroError x) => Succ' (x, x) (x, x) D0 D0 True

true :: True

True value-level reflecting function

reifyBool :: Bool -> (forall b. Bool b => b -> r) -> r

Reification function. In CPS style (best possible solution)

Type-level boolean operations

class (BoolI b1, BoolI b2) => Not b1 b2 | b1 -> b2, b2 -> b1

Boolean negation type-level relation. Not b1 b2 establishes that not b1 = b2

Instances

Not False True
Not True False

not :: Not b1 b2 => b1 -> b2

value-level reflection function for the Not type-level relation

class (BoolI b1, BoolI b2, BoolI b3) => And b1 b2 b3 | b1 b2 -> b3

And type-level relation. And b1 b2 b3 establishes that b1 && b2 = b3

Instances

And False False False
And False True False
And True False False
And True True True

(&&) :: And b1 b2 b3 => b1 -> b2 -> b3

value-level reflection function for the And type-level relation

class (BoolI b1, BoolI b2, BoolI b3) => Or b1 b2 b3 | b1 b2 -> b3

Or type-level relation. Or b1 b2 b3 establishes that b1 || b2 = b3

Instances

Or False False False
Or False True True
Or True False True
Or True True True

(||) :: Or b1 b2 b3 => b1 -> b2 -> b3

value-level reflection function for the Or type-level relation

class (BoolI b1, BoolI b2, BoolI b3) => Xor b1 b2 b3 | b1 b2 -> b3

Exclusive or type-level relation. Xor b1 b2 b3 establishes that xor b1 b2 = b3

Instances

Xor False False False
Xor False True True
Xor True False True
Xor True True False

xor :: Xor b1 b2 b3 => b1 -> b2 -> b3

value-level reflection function for the Xor type-level relation

class (BoolI b1, BoolI b2, BoolI b3) => Imp b1 b2 b3 | b1 b2 -> b3

Implication type-level relation. Imp b1 b2 b3 establishes that b1 =>b2 = b3

Instances

Imp False False True
Imp False True True
Imp True False False
Imp True True True

imp :: Imp b1 b2 b3 => b1 -> b2 -> b3

value-level reflection function for the Imp type-level relation

class (BoolI b1, BoolI b2, BoolI b3) => Eq b1 b2 b3 | b1 b2 -> b3

Boolean equality type-level relation

Instances

Eq False False True
Eq False True False
Eq True False False
Eq True True True

eq :: Eq b1 b2 b3 => b1 -> b2 -> b3

value-level reflection function for the Eq type-level relation