The foundations of the logic of N-tuples

Abstract

This paper (1) points out the inadequacies of the standard mathematical approach to n- tuples, (2) develops an axiomatic base for linear dyadic structures (list structures), (3) uses the axiomatic base to (a) prove a theorem which shows that the system requires an infinite model (Foundedness Theorem), (b) define n-tuples and (c) prove a theorem used in fast pattern matching (Fundamental N-tuple Theorem). Finally, (4) the system is shown to be consistent.

Keywords:

• N-Tuples
• Lists
• Lisp
• Linear Dyadic Structures
• Axiomatic System
• Pattern Matching
• Model
• Consistency

C.R. Categories:

• 5.21
• 5.23

†Newmont mining

‡I.B.M

†Newmont mining

‡I.B.M

Notes

†Newmont mining

‡I.B.M