Data.Sign

This module provides arithmetic over signs (i.e. {-, 0, +}) and set of signs.

For the purpose of abstract interpretation, it might be convenient to use Lattice instance. See also lattices package (http://hackage.haskell.org/package/lattices).

The Sign data type

data Sign

Signs of real numbers.

Constructors

Neg

negative

Zero

zero

Pos

positive

Instances

Bounded Sign

Enum Sign

Eq Sign

Data Sign

Ord Sign

Read Sign

Show Sign

Typeable Sign

Commutative Sign

Division Sign

Unital Sign

Multiplicative Sign

NFData Sign

Hashable Sign

Enumerable Sign

Fractional (Set Sign)

Num (Set Sign)

Commutative (Set Sign)

Division (Set Sign)

Unital (Set Sign)

Multiplicative (Set Sign)

Additive (Set Sign)

Abelian (Set Sign)

MeetSemiLattice (Set Sign)

Lattice (Set Sign)

BoundedMeetSemiLattice (Set Sign)

BoundedLattice (Set Sign)

Operations over signs

negate :: Sign -> Sign

Unary negation.

abs :: Sign -> Sign

Absolute value.

mult :: Sign -> Sign -> Sign

Multiplication.

recip :: Sign -> Sign

Reciprocal fraction.

div :: Sign -> Sign -> Sign

Fractional division.

pow :: Integral x => Sign -> x -> Sign

Fractional division.

signOf :: Real a => a -> Sign

Sign of a number.

symbol :: Sign -> String

Mnemonic symbol of a number.

This function returns "-", "0", "+" respectively for Neg, Zero, Pos.

Operations over sets of signs

Set Sign is equipped with instances of Num and Fractional. Therefore arithmetic operations can be applied to Set Sign.

Instances of Lattice and BoundedLattice are also provided for the purpose of abstract interpretation.