Functional interpretation and inductive definitions
نویسندگان
چکیده
منابع مشابه
Functional interpretation and inductive definitions
Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.
متن کاملRealizability Interpretation of Generalized Inductive Definitions
Kobayashi, S. and M. Tatsuta, Realizability interpretation of generalized inductive definitions, Theoretical Computer Science 131 (1994) 121-138. Generalized inductive definitions give a way of defining a predicate as the least solution P of the equation P-A [P] where a predicate variable P may occur in a formula A[P] positively. This paper gives a q-realizability interpretation of generalized ...
متن کاملLogic Programming, Functional Programming, and Inductive Definitions
An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that"logic programs"are not about logic but constitute inductive definitions of sets and relations. A skeletal language design based on these considerations is sketched and a prototype implementation discussed.
متن کاملInductive-Inductive Definitions
We present a principle for introducing new types in type theory which generalises strictly positive indexed inductive data types. In this new principle a set A is defined inductively simultaneously with an A-indexed set B, which is also defined inductively. Compared to indexed inductive definitions, the novelty is that the index set A is generated inductively simultaneously with B. In other wor...
متن کاملA Curry-Style Realizability Interpretation for Monotone Inductive Definitions
The logical system AF2μ, an extension of second-order predicate calculus with monotone inductive definitions, is presented. Some properties of this system are shown including that it is a good system for extracting programs from proofs by means of a realizability interpretation in the style of Krivine-Parigot, where the realizers are terms of the Curry-system of λ-calculus and the realizability...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2009
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1254748682