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ESOP'92 Symposium proceedings on 4th European symposium on programming
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NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
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ASIAN '98 Proceedings of the 4th Asian Computing Science Conference on Advances in Computing Science
STACS '87 Proceedings of the 4th Annual Symposium on Theoretical Aspects of Computer Science
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CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
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This paper establishes a Curry-Howard isomorphism for compilation and program execution by showing the following facts. (1) The set of A-normal forms, which is often used as an intermediate language for compilation, corresponds to a subsystem of Kleene's contraction-free variant of Gentzen's intuitionistic sequent calculus. (2) Compiling the lambda terms to the set of A-normal forms corresponds to proof transformation from the natural deduction to the sequent calculus followed by proof normalization. (3) Execution of an A-normal form corresponds to a special proof reduction in the sequent calculus. Different from cut elimination, this process eliminates left rules by converting them to cuts of proofs corresponding to closed values. The evaluation of an entire program is the process of inductively applying this process followed by constructing data structures.