Information and Computation - Semantics of Data Types
Linear programming with two variables per inequality in poly-log time
SIAM Journal on Computing
Handbook of theoretical computer science (vol. B)
An algorithm for testing conversion in type theory
Logical frameworks
Confluence of the lambda calculus with left-linear algebraic rewriting
Information Processing Letters
Handbook of logic in computer science (vol. 2)
Proving the correctness of reactive systems using sized types
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Theoretical Computer Science - Special volume on computer algebra
Type inference with constrained types
Theory and Practice of Object Systems - Special issue on foundations of object-oriented languages
Higher-Order and Symbolic Computation
Dependent Types for Program Termination Verification
Higher-Order and Symbolic Computation
A General Type Inference Framework for Hindley/Milner Style Systems
FLOPS '01 Proceedings of the 5th International Symposium on Functional and Logic Programming
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
COLOG '88 Proceedings of the International Conference on Computer Logic
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Dependent types in practical programming
Dependent types in practical programming
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
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
Inductive types in the Calculus of Algebraic Constructions
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Rewriting modulo in deduction modulo
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Practical inference for type-based termination in a polymorphic setting
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Type-based termination of generic programs
Science of Computer Programming
Implementing a normalizer using sized heterogeneous types
Journal of Functional Programming
On the relation between sized-types based termination and semantic labelling
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
CIC∧: type-based termination of recursive definitions in the calculus of inductive constructions
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Semi-continuous sized types and termination
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Towards generic programming with sized types
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Implementing a normalizer using sized heterogeneous types
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
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Since Val Tannen's pioneering work on the combination of simply-typed λ-calculus and first-order rewriting [11], many authors have contributed to this subject by extending it to richer typed λ-calculi and rewriting paradigms, culminating in the Calculus of Algebraic Constructions. These works provide theoretical foundations for type-theoretic proof assistants where functions and predicates are defined by oriented higher-order equations. This kind of definitions subsumes usual inductive definitions, is easier to write and provides more automation. On the other hand, checking that such user-defined rewrite rules, when combined with β-reduction, are strongly normalizing and confluent, and preserve the decidability of type-checking, is more difficult. Most termination criteria rely on the term structure. In a previous work, we extended to dependent types and higher-order rewriting, the notion of “sized types” studied by several authors in the simpler framework of ML-like languages, and proved that it preserves strong normalization. The main contribution of the present paper is twofold. First, we prove that, in the Calculus of Algebraic Constructions with size annotations, the problems of type inference and type-checking are decidable, provided that the sets of constraints generated by size annotations are satisfiable and admit most general solutions. Second, we prove the latter properties for a size algebra rich enough for capturing usual induction-based definitions and much more.