A Weak Calculus with Explicit Operators for Pattern Matching and Substitution
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Cut rules and explicit substitutions
Mathematical Structures in Computer Science
Pattern matching as cut elimination
Theoretical Computer Science
Resource operators for λ-calculus
Information and Computation
The λ-calculus with constructors: Syntax, confluence and separation
Journal of Functional Programming
Expression reduction systems with patterns
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
A lambda-calculus with constructors
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Expression reduction systems and extensions: an overview
Processes, Terms and Cycles
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
| Hi-index | 0.00 |
We present a typed pattern calculus with explicit pattern matching and explicit substitutions, where both the typing rules and the reduction rules are modeled on the same logical proof system, namely Gentzen sequent calculus for minimal logic. Our calculus is inspired by the Curry-Howard Isomorphism, in the sense that types, both for patterns and terms, correspond to propositions, terms correspond to proofs, and term reduction corresponds to sequent proof normalization performed by cut elimination. The calculus enjoys subject reduction, confluence, preservation of strong normalization w.r.t a system with meta-level substitutions and strong normalization for well-typed terms. As a consequence, it can be seen as an implementation calculus for functional formalisms defined with meta-level operations for pattern matching and substitutions.