Results 241 to 250 of about 173,804,276 (284)

The Calculus of Algebraic Constructions [PDF]

Lecture Notes in Computer Science, 1999
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive recursion, by providing definitions of functions by pattern-matching which capture recursor definitions for arbitrary ...
Frédéric Blanqui
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On the Formalization of the Modal μ-Calculus in the Calculus of Inductive Constructions

Information and Computation, 2001
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Marino Miculan
exaly   +7 more sources

A Gentzen-Style Sequent Calculus of Constructions With Expansion Rules

Theoretical Computer Science, 2000
A Gentzen-style L-formulation of the calculus of constructions is presented and proved equivalent to a natural deduction formulation based on that of [6].
Jonathan P Seldin
exaly   +2 more sources

The Calculus of Constructions

Information and Computation, 1988
This paper presents a calculus which is an impredicative extension of Martin-Löf type theory. It contains as a subsystem the functional system \(F\omega\) developed by J. Y. Girard (1972) in order to extend Gödel's Dialectica interpretation to higher-order arithmetic. It has been shown since then [in \textit{Ch. Paulin}'s thesis (Paris VIII, 1989)] how
Gérard Huet, Thierry Coquand
exaly   +2 more sources

Formalizing Process Algebraic Verifications in the Calculus of Constructions

Formal Aspects of Computing, 1997
This paper reports on the first steps towards the formal verification of correctness proofs of real-life protocols in process algebra. We show that such proofs can be verified, and partly constructed, by a general purpose proof checker.
Jan Friso Groote, Marc Bezem
exaly   +2 more sources

Definitions by Rewriting in the Calculus of Constructions

, 2001
Best student paper (Kleene Award).International audienceThe main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of
Blanqui, Frédéric
exaly   +3 more sources

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Soundness of Coercion in the Calculus of Constructions

Journal of Logic and Computation, 2004
Subtyping in the Calculus of Constructions (CoC) -- or in fact any Pure Type System -- allows \(\beta\)-equality to be represented by \(\leq\) in a judgement \((\Gamma \vdash A\leq B\) or \(\Gamma, \alpha \leq A:K \vdash M:B\)). It becomes useful when \(A\leq B\) is also allowed to hold for some \(\beta\)-distinct \(A\) and \(B\).
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Termination of rewriting in the Calculus of Constructions

Journal of Functional Programming, 2003
We show how to incorporate rewriting into the Calculus of Constructions and we prove that the resulting system is strongly normalizing with respect to beta and rewrite reductions. An important novelty of this paper is the possibility to define rewriting rules over dependently typed function symbols.
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Extensionality in the Calculus of Constructions

2005
This paper presents a method to translate a proof in an extensional version of the Calculus of Constructions into a proof in the Calculus of Inductive Constructions extended with a few axioms. We use a specific equality in order to translate the extensional conversion relation into an intensional system.
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Axiomatization of calculus of constructions

1992
This paper is a companion of [S89, S90b] and it demonstrates that FBO is powerful enough to axiomatize CC-Iike calculi [HHP87, CH88] (where FBO is short for a Framework for Binding Operators [589, S90b], and CC stands for the Calculus of Constructions). More specifically, we introduce an extra universe kind above the original universe type in CC.
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