orbital.logic.functor
Class Functionals.Catamorphism

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

All Implemented Interfaces:

java.io.Serializable, Function, Functor

Enclosing class:

Functionals

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

Catamorphism recursion functional scheme (banana).

A catamorphism is denoted by bananas and is the same as the iterative foldRight.

this := (|c,f|)

Fusion Law:

h((|c,f|)) = (|h(c),g|) ⇐ h(f(first,rest)) = g(first, h(rest))

Also known as fold, reduce. Usually implemented as a linear right tail-recurrence, however, associative f permit parallelising.

This function takes values ∈A^* represented as a generalized iteratable, like f.ex. Iterator.

See Also:

Functionals.banana(Object, BinaryFunction, Iterator), Functionals.foldRight(BinaryFunction, Object, Iterator), Functionals.foldRight(BinaryFunction, Object, List), 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

protected java.lang.Object	c the right (second) argument basevalue in B to start with.
protected BinaryFunction	f the function f:A×B=A||B→B used to fold the list a with.

Fields inherited from interface orbital.logic.functor.Function

callTypeDeclaration

Constructor Summary

Functionals.Catamorphism(java.lang.Object c, BinaryFunction f)
Constructs a new catamorphism (|c,f|):A^*→B.

Method Summary

java.lang.Object	apply(java.lang.Object a) (|c,f|) 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

Field Detail

c

protected final java.lang.Object c

the right (second) argument basevalue in B to start with. The result of the application of f will progressively build the next right (second) argument.

f

protected final BinaryFunction f

the function f:A×B=A||B→B used to fold the list a with.

Constructor Detail

Functionals.Catamorphism

public Functionals.Catamorphism(java.lang.Object c,
                                BinaryFunction f)

Constructs a new catamorphism (|c,f|):A^*→B.

Parameters:

f - the function f:A×B=A||B→B used to fold the list a with.

c - the right (second) argument basevalue in B to start with. The result of the application of f will progressively build the next right (second) argument.

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|) a.

cata ∅	=	c
cata ([first|rest])	=	f(first, cata(rest))
(|c,f|) := cata

Specified by:

apply in interface Function

Parameters:

a - a value ∈A^* represented as a generalized iteratable, like f.ex. Iterator.

Returns:

the value (|c,f|) a ∈ B.

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.