Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
On termination of the direct sum of term-rewriting systems
Information Processing Letters
Information and Computation - Semantics of Data Types
Proofs and types
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Polymorphic rewriting conserves algebraic strong normalization
Selected papers of the 16th international colloquium on Automata, languages, and programming
Handbook of theoretical computer science (vol. B)
Confluence of the lambda calculus with left-linear algebraic rewriting
Information Processing Letters
Handbook of logic in computer science (vol. 2)
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Theoretical Computer Science - Special issue: algebraic development techniques
Parametricity and variants of Girard's J operator
Information Processing Letters
COLOG '88 Proceedings of the International Conference on Computer Logic
Definitions by Rewriting in the Calculus of Constructions
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Inductive definition in type theory
Inductive definition in type theory
Termination of rewriting in the Calculus of Constructions
Journal of Functional Programming
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Building decision procedures in the calculus of inductive constructions
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In this paper, we prove that almost all CIC can be seen as a CAC, and that it can be further extended with non-strictly positive types and inductive-recursive types together with non-free constructors and pattern-matching on defined symbols.