ACM Transactions on Programming Languages and Systems (TOPLAS)
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
Relative complexities of first order calculi
Relative complexities of first order calculi
Basic proof theory
On Transforming Intuitionistic Matrix Proofs into Standard-Sequent Proofs
TABLEAUX '95 Proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
A Uniform Proof Procedure for Classical and Non-Classical Logics
KI '96 Proceedings of the 20th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Intuitionistic Proof Transformations and Their Application to Constructive Program Synthesis
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
Converting Non-Classical Matrix Proofs into Sequent-Style Systems
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
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We present a translation of intuitionistic sequent proofs from a multi-succedent calculus ℒ𝒥 mc into a single-succedent calculus ℒ𝒥. The former gives a basis for automated proof search whereas the latter is better suited for proof presentation and program construction from proofs in a system for constructive program synthesis. Well-known translations from the literature have a severe drawback; they use cuts in order to establish the transformation with the undesired consequence that the resulting program term is not intuitive. We establish a transformation based on permutation of inferences and discuss the relevant properties with respect to proof complexity and program terms. As an important result we show that ℒ𝒥 cannot polynomially simulate ℒ𝒥 mc (both without the cut rule), even in the prepositional fragment.