Proof-search in type-theoretic languages: an introduction
Identifieur interne : 001F70 ( Istex/Checkpoint ); précédent : 001F69; suivant : 001F71Proof-search in type-theoretic languages: an introduction
Auteurs : Didier Galmiche [France] ; David J. Pym [Royaume-Uni]Source :
- Theoretical Computer Science [ 0304-3975 ] ; 2000.
English descriptors
- Teeft :
- Academic press, Algebraic, Algorithm, Answer substitution, Atomic positions, Automat, Avron, Axiom, Basic idea, Boolean constraints, Cade, Cade workshop, Calculus, Cambridge university press, Category theory, Cient, Classical logic, Classical search, Classical sequent calculus, Comput, Computational, Computer, Computer science, Conf, Consequence relation, Consequence relations, Constructive program synthesis, Constructive type theory, Deductive systems, Dependent types, Electronic notes, Encoding, Erent, Formula tree, Framework, Function space, Functional programming, Functorial models, Galmiche, Girard, Herbrand, Herbrand models, Herbrand structure, Hereditary harrop formulae, Inductive, Inference rules, Interactive, Interactive theorem provers, Internal logic, Internal structure, Internat, Intuitionistic, Intuitionistic logic, Intuitionistic logics, Intuitionistic propositional logic, Intuitionistic provability, Judgement, July, Kripke, Kripke models, Lambda calculus, Lecture notes, Linear logic, Linear logic programming, Logic, Logic comput, Logic programming, Logic programming language, Logical framework, Logical frameworks, Logical systems, Matrix, Minimal logic, Modal logics, Natural deduction, Natural deduction systems, Normal proofs, Nuprl, Operational semantics, Other logics, Oxford university press, Parigot, Petri nets, Pfenning, Predicate, Predicate logic, Proc, Program synthesis, Programming, Programming language, Proof nets, Proof nets construction, Proof search, Proof system, Proof systems, Proof theory, Proof transformations, Proofsearch, Propositional, Propositional intuitionistic logic, Provability, Provable, Prover, Provers, Pure appl, Representation mechanism, Resolution calculus, Saratoga springs, Satisfaction relation, Search procedure, Search space, Semantics, Sequent, Sequent calculi, Sequent calculus, Sequents, Single publication, Springer, Structural rules, Substructural, Substructural logics, Symbolic logic, Tableau, Theorem provers, Theoret, Theoretical computer science, Typable terms, Type system, Type systems, Type theories, Type theory, Uniform proofs, Wallen.
Abstract
Abstract: We introduce the main concepts and problems in the theory of proof-search in type-theoretic languages and survey some specific, connected topics. We do not claim to cover all of the theoretical and implementation issues in the study of proof-search in type-theoretic languages; rather, we present some key ideas and problems, starting from well-motivated points of departure such as a definition of a type-theoretic language or the relationship between languages and proof-objects. The strong connections between different proof-search methods in logics, type theories and logical frameworks, together with their impact on programming and implementation issues, are central in this context.
Url:
DOI: 10.1016/S0304-3975(99)00169-3
Affiliations:
- France, Royaume-Uni
- Angleterre, Grand Est, Grand Londres, Lorraine (région)
- Londres, Vandœuvre-lès-Nancy
- Université Henri Poincaré, Université de Londres
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<front><div type="abstract" xml:lang="en">Abstract: We introduce the main concepts and problems in the theory of proof-search in type-theoretic languages and survey some specific, connected topics. We do not claim to cover all of the theoretical and implementation issues in the study of proof-search in type-theoretic languages; rather, we present some key ideas and problems, starting from well-motivated points of departure such as a definition of a type-theoretic language or the relationship between languages and proof-objects. The strong connections between different proof-search methods in logics, type theories and logical frameworks, together with their impact on programming and implementation issues, are central in this context.</div>
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