Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
PX: a computational logic
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Program derivation by proof transformation
Program derivation by proof transformation
Extraction of Structured Programs from Specification Proofs
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Moving proofs-as-programs into practice
ASE '97 Proceedings of the 12th international conference on Automated software engineering (formerly: KBSE)
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In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting "correct" programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors (see, for example, [9], [5] and [12]), but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.