ACM Transactions on Programming Languages and Systems (TOPLAS)
Finding computational content in classical proofs
Logical frameworks
Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
Logic: from foundations to applications
The Warshall Algorithm and Dickson's Lemma: Two Examples of Realistic Program Extraction
Journal of Automated Reasoning
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Extracting Constructive Content from Classical Logic via Control-like Reductions
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Extracting Constructive Content from Classical Proofs
Extracting Constructive Content from Classical Proofs
A new method for establishing conservativity of classical systems over their intuitionistic version
Mathematical Structures in Computer Science
Getting results from programs extracted from classical proofs
Theoretical Computer Science
A complexity analysis of functional interpretations
Theoretical Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Light Dialectica Program Extraction from a Classical Fibonacci Proof
Electronic Notes in Theoretical Computer Science (ENTCS)
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We give a Natural Deduction formulation of an adaptation of Gödel's functional (Dialectica) interpretation to the extraction of (more) efficient programs from (classical) proofs. We adapt Jørgensen's formulation of pure Dialectica translation by eliminating his “Contraction Lemma” and allowing free variables in the extracted terms (which is more suitable in a Natural Deduction setting). We also adapt Berger's uniform existential and universal quantifiers to the Dialectica-extraction context. The use of such quantifiers without computational meaning permits the identification and isolation of contraction formulas which would otherwise be redundantly included in the pure-Dialectica extracted terms. In the end we sketch the possible combination of our refinement of Gödel's Dialectica interpretation with its adaptation to the extraction of bounds due to Kohlenbach into a light monotone functional interpretation.