Theoretical Computer Science
A logical analysis of modules in logic programming
Journal of Logic Programming
A Purely Logical Account of Sequentiality in Proof Search
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Optimal Reduction of Functional Expressions
PLILP '98/ALP '98 Proceedings of the 10th International Symposium on Principles of Declarative 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
Non-commutativity and MELL in the Calculus of Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Intersection types for explicit substitutions
Information and Computation
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
An Algorithmic Interpretation of a Deep Inference System
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Journal of Functional Programming
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
A local system for intuitionistic logic
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
The theory of calculi with explicit substitutions revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Focusing and polarization in intuitionistic logic
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
| Hi-index | 0.00 |
We present a system for propositional implicative intuitionistic logic in the calculus of structures, which is a generalisation of the sequent calculus to the deep inference methodology. We show that it is sound and complete with respect to the usual sequent calculus, and consider a restricted system for a smaller class of formulas. Then, we encode lambda-terms with explicit substitutions in these formulas and exhibit a correspondence between proof search in this system and reduction in a lambda-calculus with explicit substitutions. Finally, we present a further restriction to allow a correspondence with the standard lambda-calculus, and show that we can prove results on lambda-calculi by proving results on derivations in the proof systems.