69 resultados para Formal logic
Resumo:
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, 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.
Resumo:
This paper provides a semantics for the UML-RSDS (Reactive System Development Support) subset of UML, using the real-time action logic (RAL) formalism. We show how this semantics can be used to resolve some ambiguities and omissions in UML semantics, and to support reasoning about specifications using the B formal method and tools. We use `semantic profiles' to provide precise semantics for different semantic variation points of UML. We also show how RAL can be used to give a semantics to notations for real-time specification in UML. Unlike other approaches to UML semantics, which concentrate on the class diagram notation, our semantic representation has behaviour as a central element, and can be used to define semantics for use cases, state machines and interactions, in addition to class diagrams.
