orbital.moon.logic.functor
Interface Operations

public interface Operations

Provides central logical operations for truth-value types.

Operations contains BinaryFunction abstractions of mathematical operations like ∧ ∨ ¬ ⇒ ⇔ etc. All function objects in this class provide canonical equality:

a.equals(b) if and only if a == b

From now on, a set D of designated truth-values is fixed. It contains the values true and false of classical logic.

Author:

André Platzer

See Also:

Functionals.compose(Function, Function), Functionals.genericCompose(BinaryFunction, Object, Object)

Field Summary

static BinaryFunction	and Conjunction and ∧:Dt×Dt→Dt; (x,y) ↦ x∧y.
static Function	andFold n-ary and ⋀: Dtn→Dt; (xi) ↦ ⋀i xi = (|true,∧|) (xi).
static Type	BINARY_LOGICAL_JUNCTOR
static BinaryFunction	equiv
static Type	FOLD_LOGICAL_JUNCTOR
static BinaryFunction	impl
static Function	not Negation not ¬:Dt→Dt; x ↦ ¬x.
static Operations	operations Class alias object.
static BinaryFunction	or
static Function	orFold
static BinaryFunction	reverseImpl
static TypeSystem	typeSystem
static Type	UNARY_LOGICAL_JUNCTOR
static BinaryFunction	xor

Field Detail

operations

static final Operations operations

Class alias object.

typeSystem

static final TypeSystem typeSystem

UNARY_LOGICAL_JUNCTOR

static final Type UNARY_LOGICAL_JUNCTOR

BINARY_LOGICAL_JUNCTOR

static final Type BINARY_LOGICAL_JUNCTOR

FOLD_LOGICAL_JUNCTOR

static final Type FOLD_LOGICAL_JUNCTOR

not

static final Function not

Negation not ¬:D_t→D_t; x ↦ ¬x.

and

static final BinaryFunction and

Conjunction and ∧:D_t×D_t→D_t; (x,y) ↦ x∧y.

andFold

static final Function andFold

n-ary and ⋀: D_tⁿ→D_t; (x_i) ↦ ⋀_i x_i = (|true,∧|) (x_i).

Treats its argument as a list like Functionals.Catamorphism.

See Also:

Functionals.Catamorphism, Predicates.TRUE, and

or

static final BinaryFunction or

orFold

static final Function orFold

xor

static final BinaryFunction xor

impl

static final BinaryFunction impl

reverseImpl

static final BinaryFunction reverseImpl

equiv

static final BinaryFunction equiv