Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

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 :: (Show t, Show (NegType (NegType t)), Serial IO t, CanTestCertainly t, CanTestCertainly (NegType t), CanTestCertainly (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 :: (Show t1, Show t2, Show t3, Show (AndOrType t1 t1), Show (AndOrType t1 t2), Show (AndOrType t2 t1), Show (AndOrType t1 (AndOrType t2 t3)), Show (AndOrType (AndOrType t1 t2) t3), Show (AndOrType (AndOrType t1 t2) (AndOrType t1 t3)), Show (NegType (AndOrType t1 t2)), Show (AndOrType (NegType t1) (NegType t2)), Serial IO t1, Serial IO t2, Serial IO t3, CanTestCertainly t1, CanTestCertainly (AndOrType t1 t1), CanTestCertainly (AndOrType t1 t2), CanTestCertainly (AndOrType t2 t1), CanTestCertainly (AndOrType t1 (AndOrType t2 t3)), CanTestCertainly (AndOrType (AndOrType t1 t2) t3), CanTestCertainly (AndOrType (AndOrType t1 t2) (AndOrType t1 t3)), CanTestCertainly (NegType (AndOrType t1 t2)), CanTestCertainly (AndOrType (NegType t1) (NegType t2)), CanNeg t1, CanNeg t2, CanNeg (AndOrType t1 t2), CanAndOrAsymmetric t1 t1, CanAndOrAsymmetric t1 t2, CanAndOrAsymmetric t1 t3, CanAndOrAsymmetric t1 (AndOrType t2 t3), CanAndOrAsymmetric t2 t1, CanAndOrAsymmetric t2 t3, CanAndOrAsymmetric (AndOrType t1 t2) t3, CanAndOrAsymmetric (AndOrType t1 t2) (AndOrType t1 t3), CanAndOrAsymmetric (NegType t1) (NegType t2)) => T t1 -> T t2 -> T t3 -> Spec
specCanAndOrNotMixed :: (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 (NegType (AndOrType t t)), Show (AndOrType (NegType t) (NegType t)), Serial IO 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 (NegType (AndOrType t t)), CanTestCertainly (AndOrType (NegType t) (NegType t)), CanNeg t, CanNeg (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)) => 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.

Examples: Bool, Maybe Bool, Maybe (Maybe Bool), 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

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

Methods

negate :: t -> NegType t Source #

Instances

CanNeg Bool Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type NegType Bool :: Type Source # Methods negate :: Bool -> NegType Bool Source #
CanNeg Double Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type NegType Double :: Type Source # Methods negate :: Double -> NegType Double Source #
CanNeg Int Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type NegType Int :: Type Source # Methods negate :: Int -> NegType Int Source #
CanNeg Integer Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type NegType Integer :: Type Source # Methods negate :: Integer -> NegType Integer Source #
CanNeg Rational Source #
Instance details Defined in Numeric.MixedTypes.MinMaxAbs Associated Types type NegType Rational :: Type Source # Methods negate :: Rational -> NegType Rational Source #
CanNeg t => CanNeg (Maybe t) Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type NegType (Maybe t) :: Type Source # Methods negate :: Maybe t -> NegType (Maybe t) Source #
CanNeg t => CanNeg (Complex t) Source #
Instance details Defined in Numeric.MixedTypes.Complex Associated Types type NegType (Complex t) :: Type Source # Methods negate :: Complex t -> NegType (Complex t) Source #
(CanNeg t, SuitableForCE es, CanEnsureCE es t, CanEnsureCE es (NegType t)) => CanNeg (CollectErrors es t) Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type NegType (CollectErrors es t) :: Type Source # 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 :: (Show t, Show (NegType (NegType t)), Serial IO t, CanTestCertainly t, CanTestCertainly (NegType t), CanTestCertainly (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

CanAndOrAsymmetric Bool Bool Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type AndOrType Bool Bool :: Type Source # Methods and2 :: Bool -> Bool -> AndOrType Bool Bool Source # or2 :: Bool -> Bool -> AndOrType Bool Bool Source #
(CanAndOrAsymmetric Bool t2, CanTestCertainly t2, CanTestCertainly (AndOrType Bool t2)) => CanAndOrAsymmetric Bool (Maybe t2) Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type AndOrType Bool (Maybe t2) :: Type Source # Methods and2 :: Bool -> Maybe t2 -> AndOrType Bool (Maybe t2) Source # or2 :: Bool -> Maybe t2 -> AndOrType Bool (Maybe t2) Source #
(CanAndOrAsymmetric Bool t2, SuitableForCE es, CanEnsureCE es t2, CanEnsureCE es (AndOrType Bool t2)) => CanAndOrAsymmetric Bool (CollectErrors es t2) Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type AndOrType Bool (CollectErrors es t2) :: Type Source # 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, CanTestCertainly t1, CanTestCertainly (AndOrType t1 Bool)) => CanAndOrAsymmetric (Maybe t1) Bool Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type AndOrType (Maybe t1) Bool :: Type Source # Methods and2 :: Maybe t1 -> Bool -> AndOrType (Maybe t1) Bool Source # or2 :: Maybe t1 -> Bool -> AndOrType (Maybe t1) Bool Source #
(CanAndOrAsymmetric t1 t2, CanTestCertainly t1, CanTestCertainly t2, CanTestCertainly (AndOrType t1 t2)) => CanAndOrAsymmetric (Maybe t1) (Maybe t2) Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type AndOrType (Maybe t1) (Maybe t2) :: Type Source # Methods and2 :: Maybe t1 -> Maybe t2 -> AndOrType (Maybe t1) (Maybe t2) Source # or2 :: Maybe t1 -> Maybe t2 -> AndOrType (Maybe t1) (Maybe t2) Source #
(CanAndOrAsymmetric t1 Bool, SuitableForCE es, CanEnsureCE es t1, CanEnsureCE es (AndOrType t1 Bool)) => CanAndOrAsymmetric (CollectErrors es t1) Bool Source #
Instance details Defined in Numeric.MixedTypes.Bool Associated Types type AndOrType (CollectErrors es t1) Bool :: Type Source # 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, SuitableForCE es, CanEnsureCE es t1, CanEnsureCE es t2, CanEnsureCE es (AndOrType t1 t2)) => 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) :: Type Source # Methods and2 :: CollectErrors es t1 -> CollectErrors es t2 -> AndOrType (CollectErrors es t1) (CollectErrors es t2) Source # or2 :: CollectErrors es t1 -> CollectErrors es t2 -> AndOrType (CollectErrors es t1) (CollectErrors es t2) Source #

(&&) :: CanAndOrAsymmetric a b => a -> b -> AndOrType a b infixr 3 Source #

A synonym of and2.

(||) :: CanAndOrAsymmetric a b => a -> b -> AndOrType a b infixr 2 Source #

A synonym of or2.

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

type CanAndOrSameType t = CanAndOrWith t t Source #

and :: (CanAndOrSameType t, CanTestCertainly t) => [t] -> t Source #

or :: (CanAndOrSameType t, CanTestCertainly t) => [t] -> t Source #

Tests

specCanAndOr :: (Show t1, Show t2, Show t3, Show (AndOrType t1 t1), Show (AndOrType t1 t2), Show (AndOrType t2 t1), Show (AndOrType t1 (AndOrType t2 t3)), Show (AndOrType (AndOrType t1 t2) t3), Show (AndOrType (AndOrType t1 t2) (AndOrType t1 t3)), Show (NegType (AndOrType t1 t2)), Show (AndOrType (NegType t1) (NegType t2)), Serial IO t1, Serial IO t2, Serial IO t3, CanTestCertainly t1, CanTestCertainly (AndOrType t1 t1), CanTestCertainly (AndOrType t1 t2), CanTestCertainly (AndOrType t2 t1), CanTestCertainly (AndOrType t1 (AndOrType t2 t3)), CanTestCertainly (AndOrType (AndOrType t1 t2) t3), CanTestCertainly (AndOrType (AndOrType t1 t2) (AndOrType t1 t3)), CanTestCertainly (NegType (AndOrType t1 t2)), CanTestCertainly (AndOrType (NegType t1) (NegType t2)), CanNeg t1, CanNeg t2, CanNeg (AndOrType t1 t2), CanAndOrAsymmetric t1 t1, CanAndOrAsymmetric t1 t2, CanAndOrAsymmetric t1 t3, CanAndOrAsymmetric t1 (AndOrType t2 t3), CanAndOrAsymmetric t2 t1, CanAndOrAsymmetric t2 t3, CanAndOrAsymmetric (AndOrType t1 t2) t3, CanAndOrAsymmetric (AndOrType t1 t2) (AndOrType t1 t3), CanAndOrAsymmetric (NegType t1) (NegType t2)) => T t1 -> T t2 -> T t3 -> Spec Source #

HSpec properties that each implementation of CanAndOr should satisfy.

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

HSpec properties that each implementation of CanAndOr should satisfy.

Orphan instances

ConvertibleExactly Bool Bool Source #
Instance details Methods safeConvertExactly :: Bool -> ConvertResult Bool Source #
ConvertibleExactly Bool t => ConvertibleExactly Bool (Maybe t) Source #
Instance details Methods safeConvertExactly :: Bool -> ConvertResult (Maybe t) Source #