# BooleanΒΆ

Boolean is the elementary logic with 2 values: `true` and `false`

/\: (%, %) -> %

from MeetSemilattice

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

\/: (%, %) -> %

from JoinSemilattice

_|_: %
~=: (%, %) -> Boolean

from BasicType

~: % -> %

from Logic

and: (%, %) -> %

`a and b` returns the logical and of Boolean `a` and `b`.

coerce: % -> OutputForm
convert: % -> InputForm
enumerate: () -> List %

from Finite

false: %

from Logic

hash: % -> SingleInteger

from Hashable

hashUpdate!: (HashState, %) -> HashState

from Hashable

implies: (%, %) -> %

`implies(a, b)` returns the logical implication of Boolean `a` and `b`.

index: PositiveInteger -> %

from Finite

latex: % -> String

from SetCategory

lookup: % -> PositiveInteger

from Finite

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

nand: (%, %) -> %

`nand(a, b)` returns the logical negation of `a` and `b`.

nor: (%, %) -> %

`nor(a, b)` returns the logical negation of `a` or `b`.

not: % -> %

`not n` returns the negation of `n`.

or: (%, %) -> %

`a or b` returns the logical inclusive or of Boolean `a` and `b`.

random: () -> %

from Finite

size: () -> NonNegativeInteger

from Finite

smaller?: (%, %) -> Boolean

from Comparable

T: %
test: % -> Boolean

`test(b)` returns `b` and is provided for compatibility with the new compiler.

true: %

from Logic

xor: (%, %) -> %

`xor(a, b)` returns the logical exclusive or of Boolean `a` and `b`.

BasicType

BoundedDistributiveLattice

BoundedJoinSemilattice

BoundedLattice

BoundedMeetSemilattice

Comparable

DistributiveLattice

Finite

Hashable

JoinSemilattice

Lattice

Logic

MeetSemilattice

OrderedSet

PartialOrder

SetCategory