scholarly journals The execution complexity of logical formulas with restricted quantifiers based on CF-grammars

2021 ◽  
Vol 2131 (2) ◽  
pp. 022131
Author(s):  
K S Korovina ◽  
I Sh Rudova

Abstract The polynomial realized formulas are introduced with quantifiers acting on hierarchy lists described by CF-grammars. Upper estimates of execution complexity are obtained depending from the sort of grammar. These formulas have been applied for formal definition of context-dependent syntax of programming languages and describing dynamic discrete system.

1998 ◽  
Vol 8 (1) ◽  
pp. 1-22 ◽  
Author(s):  
AMR SABRY

Functional programming languages are informally classified into pure and impure languages. The precise meaning of this distinction has been a matter of controversy. We therefore investigate a formal definition of purity. We begin by showing that some proposed definitions which rely on confluence, soundness of the beta axiom, preservation of pure observational equivalences and independence of the order of evaluation, do not withstand close scrutiny. We propose instead a definition based on parameter-passing independence. Intuitively, the definition implies that functions are pure mappings from arguments to results; the operational decision of how to pass the arguments is irrelevant. In the context of Haskell, our definition is consistent with the fact that the traditional call-by-name denotational semantics coincides with the traditional call-by-need implementation. Furthermore, our definition is compatible with the stream-based, continuation-based and monad-based integration of computational effects in Haskell. Finally, we observe that call-by-name reasoning principles are unsound in compilers for monadic Haskell.


1984 ◽  
Vol 13 (173) ◽  
Author(s):  
Brian H. Mayoh

<p>The flood of new programming and specification languages shows no sign of abating, but very few of these languages have a formal definition. The advantages of knowing precisely what is specified in a specification and exactly how a program can behave are obvious, but none of the existing formal definition methods are completely satisfactory.</p><p>Theoreticians have not been idle, but they have concentrated on problems that are not immediately relevant to language designers (algebraic and categoric structuring of definitions, refined notions of concurrency and the like).</p><p>In the belief that the answer to some of the language designers' problems is ''use different formalisms to define fragments of the languages precisely'', we advocate the study of comparative semantics. This paper is a contribution to this study, prompted by the fact that the parallel aspects of ADA seem to require a quite different kind of formal semantics from that used for sequential ADA in ''Formal Definition of ADA'', CII Honeywell Bull, 1981, Paris.</p>


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