:: a typeCtrl KGHC 9.10.3 · lts/ghc-9.10.x · 248f8f0 · 2026-10-05
ModuleBoolean-0.2.4Haskell98
A generalized version of the class hirarchy for numbers. All functions that would break a potential deep embedding are removed or generalized to support deep embeddings.
The class hierarchy for numeric types keeps as close as possible to the
Prelude hierarchy. A great part of the default implementation and comments
are copied and adopted from Prelude.
An extension of Num that supplies the integer type of a given number type and a way to create that number from the integer.
type family IntegerOf aThe accociated integer type of the number.
fromIntegerB :: IntegerOf a -> aConstruct the number from the associated integer.
A deep embedded version of Integral. Integral numbers, supporting integer division.
Minimal complete definition is either quotRem and divMod or the other four functions. Besides that toIntegerB always has to be implemented.
Deep embedded version of RealFloat. Extracting components of fractions.
Minimal complete definition: properFraction, round, floor and ceiling.
properFraction :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> (b, a)The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
n is an integral number with the same sign as x; and
f is a fraction with the same type and sign as x,
and with absolute value less than 1.
The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.
truncate :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> btruncate x returns the integer nearest x between zero and x
round :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> bround x returns the nearest integer to x;
the even integer if x is equidistant between two integers
ceiling :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> bceiling x returns the least integer not less than x
floor :: (IntegerOf a ~ IntegerOf b, IntegralB b) => a -> bfloor x returns the greatest integer not greater than x.
Deep embedded version of RealFloat. Efficient, machine-independent access to the components of a floating-point number.
A complete definition has to define all functions.
isNaN :: a -> BooleanOf atrue if the argument is an IEEE "not-a-number" (NaN) value.
isInfinite :: a -> BooleanOf atrue if the argument is an IEEE infinity or negative infinity.
isNegativeZero :: a -> BooleanOf atrue if the argument is an IEEE negative zero.
isIEEE :: a -> BooleanOf atrue if the argument is an IEEE floating point number.
atan2 :: a -> a -> aa version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x computes the angle
(from the positive x-axis) of the vector from the origin to the
point (x,y). atan2 y x returns a value in the range [-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1, with y in a type
that is RealFloatB, should return the same value as atan y.
RealFloatB DoubleDefined in Boolean-0.2.4 · Data.Boolean.NumbersRealFloatB FloatDefined in Boolean-0.2.4 · Data.Boolean.NumbersVariant of even for generalized booleans.
Variant of odd for generalized booleans.
Variant of fromIntegral for generalized booleans.