orbital.logic.functor
Class Functionals.Hylomorphism

java.lang.Object
  orbital.logic.functor.Functionals.Hylomorphism

All Implemented Interfaces:

java.io.Serializable, Function, Functor

Enclosing class:

Functionals

public static class Functionals.Hylomorphism
extends java.lang.Object
implements Function, java.io.Serializable

Hylomorphism recursion functional scheme (envelope).

A hylomorphism is denoted by envelopes.

this = [[(c,f),(g,p)]] = |[(c,f),(g,p)]| = 〚(c,f),(g,p)〛

A hylomorphism corresponds to the composition of an anamorphism and a catamorphism.

[[(c,f),(g,p)]] = (|c,f|) ∘ |(g,p)| So it is very much like an anamorphism except for basevalue c instead of nil, and f instead of list construction cons.

Author:

André Platzer

See Also:

Functionals.envelope(Object, BinaryFunction, Function, Predicate, Object), Meijer, E. and Fokkinga, M.M. and Paterson, R., Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire, FPCA91: Functional Programming Languages and Computer Architecture, pp. 124--144, volume 523, Lecture Notes in Computer Science, Springer-Verlag, 1991., Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface orbital.logic.functor.Function

Function.Composite

Nested classes/interfaces inherited from interface orbital.logic.functor.Functor

Functor.Specification

Field Summary

Fields inherited from interface orbital.logic.functor.Function

callTypeDeclaration

Constructor Summary

Functionals.Hylomorphism(java.lang.Object c, BinaryFunction f, Function g, Predicate p)
Constructs a new hylomorphism [[(c,f),(g,p)]]:A→C.

Method Summary

java.lang.Object	apply(java.lang.Object a) [[(c,f),(g,p)]] a.
boolean	equals(java.lang.Object o) .
int	hashCode()
java.lang.String	toString() Returns a string representation of the Functor.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Functionals.Hylomorphism

public Functionals.Hylomorphism(java.lang.Object c,
                                BinaryFunction f,
                                Function g,
                                Predicate p)

Constructs a new hylomorphism [[(c,f),(g,p)]]:A→C.

Parameters:

c - is an element ∈C that is the basevalue for p(a) = true.

f - is a binary function f:B||C→C.

g - is a function g:A→B||A that returns objects of type Pair.

p - is a predicate p⊆A saying whether to use the basevalue case.

Method Detail

equals

public boolean equals(java.lang.Object o)

Description copied from interface: Functor

.

Note that functors will often provide intensional equality only, since the mathematical notion of extensional equality for functions and predicates is undecidable anyway (Proposition of Rice). Nevertheless implementations are encouraged to provide a larger subset of extensional equality as far as possible.

Specified by:

equals in interface Functor

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Specified by:

hashCode in interface Functor

Overrides:

hashCode in class java.lang.Object

apply

public final java.lang.Object apply(java.lang.Object a)

[[(c,f),(g,p)]] a.

hylo a	=	c	⇐ p(a)
	=	f(b, hylo(a'))	⇐ ¬p(a)
		where (b, a') = g(a)
[[(c,f),(g,p)]] := hylo

Specified by:

apply in interface Function

Parameters:

a - value ∈A.

Returns:

the value [[(c,f),(g,p)]] a ∈ C.

toString

public java.lang.String toString()

Description copied from interface: Functor

Returns a string representation of the Functor.

This method is already provided in Object.toString(). If it is overwritten it should return a nice name for the functor.

Specified by:

toString in interface Functor

Overrides:

toString in class java.lang.Object

Returns:

a nice name for the functor.