Basic simple type theory
Permutability of proofs in intuitionistic sequent calculi
Theoretical Computer Science - Special issue: Gentzen
Fully Automatic Adaptation of Software Components Based on Semantic Specifications
AMAST '02 Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology
Cut Formulae and Logic Programming
ELP '93 Proceedings of the 4th International Workshop on Extensions of Logic Programming
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Foundations for a tool for the automatic adaptation of software components based on semantic specifications
Finite combinatory logic with intersection types
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Complete completion using types and weights
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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For use in earlier approaches to automated module interface adaptation, we seek a restricted form of program synthesis. Given some typing assumptions and a desired result type, we wish to automatically build a number of program fragments of this chosen typing, using functions and values available in the given typing environment. We call this problem term enumeration. To solve the problem, we use the Curry-Howard correspondence (propositions-as-types, proofs-as-programs) to transform it into a proof enumeration problem for an intuitionistic logic calculus. We formally study proof enumeration and counting in this calculus. We prove that proof counting is solvable and give an algorithm to solve it. This in turn yields a proof enumeration algorithm.