Combinatory foundation of functional programming

Authors:
Corrado Böhm
Affiliations:
-
Venue:
LFP '82 Proceedings of the 1982 ACM symposium on LISP and functional programming
Year:
1982

Citing 5
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Abstract

A proposal is described for embedding FP and a part of FFP into a system C(IN)V of Combinatory Logic generated by the 6-tuple of combinators (A,B,C*,O,L,D) under the operation of application. At the same time C(IN)V is viewed as an algebraic extension of elementary arithmetic, including addition multiplication and exponentiation, leading to a non commutative semi-ring with an infinity of zero (infinite)-like elements. Two interesting submonoids have been selected: Lº able to represent the set of FP-Sequences and L+ able to represent the set of FP-Constructions. All basic objects forming operators like Composition, Apply To All Condition and Insert Right are then efficiently expressed inside C(IN)V. The same is done for some operators belonging to FFP as Lifting and the APPLY of LISP establishing a basis for a future reduction (operational) semantics of FP.