Abstract
Two type theories, ATT and ATTT, are introduced. ATT is an impredicative type theory closely related to the polymorphic type theory of implicit typing of MacQueen et al. [MPS86]. ATTT is another version of ATT that extends the Girard-Reynolds second order lambda calculus. ATT has notions of intersection, union and singleton types. ATTT has a notion of refinement types as in the type system for ML by Freeman and Pfenning [FP91], plus intersection and union of refinement types and singleton refinement types. We will show how singleton, union and intersection types serve for development of programs without unnecessary codes via a variant of the Curry-Howard isomorphism. More exactly, they give a way to write types as specifications of programs without unnecessary codes which is inevitable in the usual Curry-Howard isomorphism.
In memory of my mother, Yoshie Hayashi
Partly supported by Grant No. 02249209 of the Japanese Ministry of Education.
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Hayashi, S. (1991). Singleton, union and intersection types for program extraction. In: Ito, T., Meyer, A.R. (eds) Theoretical Aspects of Computer Software. TACS 1991. Lecture Notes in Computer Science, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54415-1_71
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DOI: https://doi.org/10.1007/3-540-54415-1_71
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