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Expedited Broda-Damas Bracket Abstraction, Martin W. Bunder
Expedited Broda-Damas Bracket Abstraction, Martin W. Bunder
Faculty of Engineering and Information Sciences - Papers: Part A
A bracket abstraction algorithm is a means of translating λ-terms into combinators. Broda and Damas, in [1], introduce a new, rather natural set of combinators and a new form of bracket abstraction which introduces at most one combinator for each λ-abstraction. This leads to particularly compact combinatory terms. A disadvantage of their abstraction process is that it includes the whole Schonfinkel [4] algorithm plus two mappings which convert the Schonfinkel abstract into the new abstract. This paper shows how the new abstraction can be done more directly, in fact, using only 2n - 1 algorithm steps if there are n …
Some Improvements To Turner's Algorithm For Bracket Abstraction, Martin W. Bunder
Some Improvements To Turner's Algorithm For Bracket Abstraction, Martin W. Bunder
Faculty of Engineering and Information Sciences - Papers: Part A
A computer handles A-terms more easily if these are translated into combinatory terms. This translation process is called bracket abstraction. The simplest abstraction algorithm-the (fab) algorithm of Curry (see Curry and Feys [6])-is lengthy to implement and produces combinatory terms that increase rapidly in length as the number of variables to be abstracted increases.