Copyright	(c) Michal Konecny
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Numeric.MixedTypes.Bool

Contents

Conversion to/from Bool
Negation
- Tests
And and or
- Tests
Orphan instances

Description

Synopsis

type IsBool t = (HasBools t, CanNegSameType t, CanAndOrSameType t)
specIsBool :: (IsBool t, CanTestCertainly t, Show t, Serial IO t) => T t -> Spec
type HasBools t = ConvertibleExactly Bool t
class HasBools t => CanTestCertainly t where
- isCertainlyTrue :: t -> Bool
- isCertainlyFalse :: t -> Bool
specCanTestCertainly :: CanTestCertainly t => T t -> Spec
type CanTestCertainlyX t = (CanTestCertainly t, Show t, Serial IO t)
isNotTrue :: CanTestCertainly t => t -> Bool
isNotFalse :: CanTestCertainly t => t -> Bool
stronglyImplies :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool
stronglyEquivalentTo :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool
weaklyImplies :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool
weaklyEquivalentTo :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool
class CanNeg t where
- type NegType t
- negate :: t -> NegType t
not :: CanNeg t => t -> NegType t
type CanNegSameType t = (CanNeg t, NegType t ~ t)
specCanNegBool :: (CanTestCertainly t, CanTestCertainly (NegType t), CanTestCertainly (NegType (NegType t)), Serial IO t, Show t, Show (NegType (NegType t)), CanNeg t, CanNeg (NegType t)) => T t -> Spec
type CanAndOr t1 t2 = (CanAndOrAsymmetric t1 t2, CanAndOrAsymmetric t2 t1, AndOrType t1 t2 ~ AndOrType t2 t1)
class CanAndOrAsymmetric t1 t2 where
- type AndOrType t1 t2
- and2 :: t1 -> t2 -> AndOrType t1 t2
- or2 :: t1 -> t2 -> AndOrType t1 t2
(&&) :: CanAndOrAsymmetric a b => a -> b -> AndOrType a b
(||) :: CanAndOrAsymmetric a b => a -> b -> AndOrType a b
type CanAndOrWith t1 t2 = (CanAndOr t1 t2, AndOrType t1 t2 ~ t1)
type CanAndOrSameType t = CanAndOrWith t t
and :: (CanAndOrSameType t, CanTestCertainly t) => [t] -> t
or :: (CanAndOrSameType t, CanTestCertainly t) => [t] -> t
specCanAndOr :: (Serial IO t1, Serial IO t2, Serial IO t3, Show t1, Show t2, Show t3, Show (AndOrType t2 t1), Show (AndOrType t1 t1), Show (AndOrType t1 t2), Show (AndOrType t1 (AndOrType t2 t3)), Show (AndOrType (AndOrType t1 t2) t3), Show (AndOrType (AndOrType t1 t2) (AndOrType t1 t3)), Show (AndOrType (NegType t1) (NegType t2)), Show (NegType (AndOrType t1 t2)), CanTestCertainly t1, CanTestCertainly (AndOrType t2 t1), CanTestCertainly (AndOrType t1 t1), CanTestCertainly (AndOrType t1 t2), CanTestCertainly (AndOrType t1 (AndOrType t2 t3)), CanTestCertainly (AndOrType (AndOrType t1 t2) t3), CanTestCertainly (AndOrType (AndOrType t1 t2) (AndOrType t1 t3)), CanTestCertainly (AndOrType (NegType t1) (NegType t2)), CanTestCertainly (NegType (AndOrType t1 t2)), CanAndOrAsymmetric t2 t1, CanAndOrAsymmetric t2 t3, CanAndOrAsymmetric t1 t1, CanAndOrAsymmetric t1 t2, CanAndOrAsymmetric t1 t3, CanAndOrAsymmetric t1 (AndOrType t2 t3), CanAndOrAsymmetric (AndOrType t1 t2) t3, CanAndOrAsymmetric (AndOrType t1 t2) (AndOrType t1 t3), CanAndOrAsymmetric (NegType t1) (NegType t2), CanNeg t1, CanNeg t2, CanNeg (AndOrType t1 t2)) => T t1 -> T t2 -> T t3 -> Spec
specCanAndOrNotMixed :: (Serial IO t, Show t, Show (AndOrType t t), Show (AndOrType t (AndOrType t t)), Show (AndOrType (AndOrType t t) t), Show (AndOrType (AndOrType t t) (AndOrType t t)), Show (AndOrType (NegType t) (NegType t)), Show (NegType (AndOrType t t)), CanTestCertainly t, CanTestCertainly (AndOrType t t), CanTestCertainly (AndOrType t (AndOrType t t)), CanTestCertainly (AndOrType (AndOrType t t) t), CanTestCertainly (AndOrType (AndOrType t t) (AndOrType t t)), CanTestCertainly (AndOrType (NegType t) (NegType t)), CanTestCertainly (NegType (AndOrType t t)), CanAndOrAsymmetric t t, CanAndOrAsymmetric t (AndOrType t t), CanAndOrAsymmetric (AndOrType t t) t, CanAndOrAsymmetric (AndOrType t t) (AndOrType t t), CanAndOrAsymmetric (NegType t) (NegType t), CanNeg t, CanNeg (AndOrType t t)) => T t -> Spec

Documentation

type IsBool t = (HasBools t, CanNegSameType t, CanAndOrSameType t) Source #

A type constraint synonym that stipulates that the type behaves very much like Bool, except it does not necessarily satisfy the law of excluded middle, which means that the type can contain a "do-not-know" value or an error.

Examples: Bool, Kleenean, CollectErrors Bool

specIsBool :: (IsBool t, CanTestCertainly t, Show t, Serial IO t) => T t -> Spec Source #

HSpec properties that each implementation of IsBool should satisfy.

Conversion to/from Bool

type HasBools t = ConvertibleExactly Bool t Source #

class HasBools t => CanTestCertainly t where Source #

Tests for truth or falsity. Beware, when isCertainlyTrue returns False, it does not mean that the proposition is false. It usually means that we failed to prove the proposition.

Methods

isCertainlyTrue :: t -> Bool Source #

isCertainlyFalse :: t -> Bool Source #

Instances

Instances details

CanTestCertainly Bool Source #
Instance details Defined in Numeric.MixedTypes.Bool Methods isCertainlyTrue :: Bool -> Bool Source # isCertainlyFalse :: Bool -> Bool Source #
(CanTestCertainly t, CanBeErrors es) => CanTestCertainly (CollectErrors es t) Source #
Instance details Defined in Numeric.MixedTypes.Bool Methods isCertainlyTrue :: CollectErrors es t -> Bool Source # isCertainlyFalse :: CollectErrors es t -> Bool Source #

specCanTestCertainly :: CanTestCertainly t => T t -> Spec Source #

HSpec properties that each implementation of CanTestCertainly should satisfy.

type CanTestCertainlyX t = (CanTestCertainly t, Show t, Serial IO t) Source #

Compound type constraint useful for test definition.

isNotTrue :: CanTestCertainly t => t -> Bool Source #

isNotFalse :: CanTestCertainly t => t -> Bool Source #

stronglyImplies :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool Source #

If l is certainly True, then r is also certainly True.

stronglyEquivalentTo :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool Source #

weaklyImplies :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool Source #

If l is certainly True, then r is not certainly False.

weaklyEquivalentTo :: (CanTestCertainly t1, CanTestCertainly t2) => t1 -> t2 -> Bool Source #

Negation

class CanNeg t where Source #

This is negation is both the numeric negation as well as the Boolean negation. Example of non-standard Boolean negation:

 negate (Just True) = Just False

Associated Types

type NegType t Source #

type NegType t = t

Methods

negate :: t -> NegType t Source #

Instances

Instances details

CanNeg Rational Source #

Instance details

Defined in Numeric.MixedTypes.MinMaxAbs

Associated Types

type NegType Rational
Instance details Defined in Numeric.MixedTypes.MinMaxAbs type NegType Rational = Rational

Methods

negate :: Rational -> NegType Rational Source #

CanNeg Integer Source #

Instance details

Defined in Numeric.MixedTypes.MinMaxAbs

Associated Types

type NegType Integer
Instance details Defined in Numeric.MixedTypes.MinMaxAbs type NegType Integer = Integer

Methods

negate :: Integer -> NegType Integer Source #

CanNeg Bool Source #

Instance details

Defined in Numeric.MixedTypes.Bool

Associated Types

type NegType Bool
Instance details Defined in Numeric.MixedTypes.Bool type NegType Bool = Bool

Methods

negate :: Bool -> NegType Bool Source #

CanNeg Double Source #

Instance details

Defined in Numeric.MixedTypes.MinMaxAbs

Associated Types

type NegType Double
Instance details Defined in Numeric.MixedTypes.MinMaxAbs type NegType Double = Double

Methods

negate :: Double -> NegType Double Source #

CanNeg Int Source #

Instance details

Defined in Numeric.MixedTypes.MinMaxAbs

Associated Types

type NegType Int
Instance details Defined in Numeric.MixedTypes.MinMaxAbs type NegType Int = Int

Methods

negate :: Int -> NegType Int Source #

CanNeg t => CanNeg (Complex t) Source #

Instance details

Defined in Numeric.MixedTypes.Complex

Associated Types

type NegType (Complex t)
Instance details Defined in Numeric.MixedTypes.Complex type NegType (Complex t) = Complex (NegType t)

Methods

negate :: Complex t -> NegType (Complex t) Source #

(CanNeg t, CanBeErrors es) => CanNeg (CollectErrors es t) Source #

Instance details

Defined in Numeric.MixedTypes.Bool

Associated Types

type NegType (CollectErrors es t)
Instance details Defined in Numeric.MixedTypes.Bool type NegType (CollectErrors es t) = CollectErrors es (NegType t)

Methods

negate :: CollectErrors es t -> NegType (CollectErrors es t) Source #

not :: CanNeg t => t -> NegType t Source #

A synonym of negate.

type CanNegSameType t = (CanNeg t, NegType t ~ t) Source #

Tests

specCanNegBool :: (CanTestCertainly t, CanTestCertainly (NegType t), CanTestCertainly (NegType (NegType t)), Serial IO t, Show t, Show (NegType (NegType t)), CanNeg t, CanNeg (NegType t)) => T t -> Spec Source #

HSpec properties that each Boolean implementation of CanNeg should satisfy.

And and or

type CanAndOr t1 t2 = (CanAndOrAsymmetric t1 t2, CanAndOrAsymmetric t2 t1, AndOrType t1 t2 ~ AndOrType t2 t1) Source #

class CanAndOrAsymmetric t1 t2 where Source #

Binary logical and and or for generalised Booleans. For example:

 (Just True) && False = Just False
 (Just (Just True)) || False = (Just (Just True))

Associated Types

type AndOrType t1 t2 Source #

Methods

and2 :: t1 -> t2 -> AndOrType t1 t2 Source #

or2 :: t1 -> t2 -> AndOrType t1 t2 Source #

Instances

Instances details

CanAndOrAsymmetric Bool Bool Source #

Instance details

Defined in Numeric.MixedTypes.Bool

Associated Types

type AndOrType Bool Bool
Instance details Defined in Numeric.MixedTypes.Bool type AndOrType Bool Bool = Bool

Methods

and2 :: Bool -> Bool -> AndOrType Bool Bool Source #

or2 :: Bool -> Bool -> AndOrType Bool Bool Source #

(CanAndOrAsymmetric Bool t2, CanBeErrors es) => CanAndOrAsymmetric Bool (CollectErrors es t2) Source #

Instance details

Defined in Numeric.MixedTypes.Bool

Associated Types

type AndOrType Bool (CollectErrors es t2)
Instance details Defined in Numeric.MixedTypes.Bool type AndOrType Bool (CollectErrors es t2) = CollectErrors es (AndOrType Bool t2)

Methods

and2 :: Bool -> CollectErrors es t2 -> AndOrType Bool (CollectErrors es t2) Source #

or2 :: Bool -> CollectErrors es t2 -> AndOrType Bool (CollectErrors es t2) Source #

(CanAndOrAsymmetric t1 Bool, CanBeErrors es) => CanAndOrAsymmetric (CollectErrors es t1) Bool Source #

Instance details

Defined in Numeric.MixedTypes.Bool

Associated Types

type AndOrType (CollectErrors es t1) Bool
Instance details Defined in Numeric.MixedTypes.Bool type AndOrType (CollectErrors es t1) Bool = CollectErrors es (AndOrType t1 Bool)

Methods

and2 :: CollectErrors es t1 -> Bool -> AndOrType (CollectErrors es t1) Bool Source #

or2 :: CollectErrors es t1 -> Bool -> AndOrType (CollectErrors es t1) Bool Source #

(CanAndOrAsymmetric t1 t2, CanBeErrors es, HasBools t2, CanTestCertainly t1) => CanAndOrAsymmetric (CollectErrors es t1) (CollectErrors es t2) Source #

Instance details

Defined in Numeric.MixedTypes.Bool

Associated Types

type AndOrType (CollectErrors es t1) (CollectErrors es t2)
Instance details Defined in Numeric.MixedTypes.Bool type AndOrType (CollectErrors es t1) (CollectErrors es t2) = CollectErrors es (AndOrType t1 t2)