Portability	non-portable
Stability	experimental (MPTC, non-standarad instances)
Maintainer	alfonso.acosta@gmail.com
Safe Haskell	None

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

false :: False

False value-level reflecting function

data True

True type-level value

Instances

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

Show False
Typeable False
Not False True
Not True 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

Show True
Typeable True
Not False True
Not True False
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