منابع مشابه
Uniform Heyting arithmetic
We present an extension of Heyting Arithmetic in finite types called Uniform Heyting Arithmetic (HA) that allows for the extraction of optimized programs from constructive and classical proofs. The system HA has two sorts of first-order quantifiers: ordinary quantifiers governed by the usual rules, and uniform quantifiers subject to stronger variable conditions expressing roughly that the quant...
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Deduction Modulo is a formalism that aims at distinguish reasoning from computation in proofs. A theory modulo is formed with a set of axioms and a congruence de ned by rewrite rules: the reasoning part of the theory is given by the axioms, the computational part by the congruence. In deduction modulo, we can in particular build theories without any axiom, called purely computational theories. ...
متن کاملInteractive Learning-Based Realizability for Heyting Arithmetic with EM1
We apply to the semantics of Arithmetic the idea of “finite approximation” used to provide computational interpretations of Herbrand’s Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for ∨, ∃) over a suitable structure N for the language of natural numbers and maps of Gödel’s system T . We introduce a new Realizability semantics we call “Interactive le...
متن کاملURBiVA: Uniform Reduction to Bit-Vector Arithmetic
We describe a system URBiVA for specifying and solving a range of problems by uniformly reducing them to bit-vector arithmetic (bva). A problem description is given in a C-like specification language and this high-level specification is transformed to a bva formula by symbolic execution. The formula is passed to a bva solver and, if it is satisfiable, its models give solutions of the problem. T...
متن کاملInteractive Realizability for second-order Heyting arithmetic with EM1 and SK1
We introduce a classical realizability semantics based on interactive learning for full second-order Heyting Arithmetic with excluded middle and Skolem axioms over Σ1-formulas. Realizers are written in a classical version of Girard’s System F. Since the usual computability semantics does not apply to such a system, we introduce a constructive forcing/computability semantics: though realizers ar...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2005
ISSN: 0168-0072
DOI: 10.1016/j.apal.2004.10.006