Abstract
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.
This work was partly supported by the Japanese Ministry of Education Grant-in-Aid for Scientific Research on Priority Area no. 275 “Advanced databases,” and by the Parallel and Distributed Processing Research Consortium, Japan.
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Ohori, A. (1999). A Curry-Howard Isomorphism for Compilation and Program Execution. In: Girard, JY. (eds) Typed Lambda Calculi and Applications. TLCA 1999. Lecture Notes in Computer Science, vol 1581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48959-2_20
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