Research in mathematical theory of computation

Research progress in the following areas is reviewed: (1) new version of computer program LCF (logic for computable functions) including a facility to search for proofs automatically; (2) the description of the language PASCAL in terms of both LCF and in first order logic; (3) discussion of LISP semantics in LCF and attempt to prove the correctness of the London compilers in a formal way; (4) design of both special purpose and domain independent proving procedures specifically program correctness in mind; (5) design of languages for describing such proof procedures; and (6) the embedding of ideas in the first order checker

SLR inference: An inference system for fixed-mode logic programs, based on SLR parsing

AbstractDefinite-clause grammars (DCGs) generalize context-free grammars in such a way that Prolog can be used as a parser in the presence of context-sensitive information. Prolog's proof procedure, however, is based on backtracking, which may be a source of inefficiency. Parsers for context-free grammars that use backtracking, for instance, were soon replaced by more efficient methods, such as LR parsers. This suggests incorporating the principles underlying LR parsing into a parser for grammars with context-sensitive information. We present a technique that applies a transformation to the program/grammar by adding leaves to the proof/parse trees and placing the contextual information in such leaves. An inference system is then easily obtained from an LR parser, since only the parts dealing with terminals (which appear at the leaves) must be modified. Although our method is restricted to programs with fixed modes, it may be preferable to DCGs under Prolog for some programs

DECIDABLE PROPERTIES OF MONADIC FUNCTIONAL SCHEMAS

Abstract: We define a class of (monadic) functional schemas which properly includes rIanov * flowchart schemas. We show that the termination, divergence and freedam problems for functional schemas are decidable. Although it is possible to translate a large class of non-free functional schemas into equivalent free functional schemas, we show that this cannot be done in general. We show also that the equivalence problem for free functional schemas is decidable. Most of the results are obtained from well-known results in Focal Languages and Automata Theory. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Advanced Researc