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Provable isomorphisms of types

Published online by Cambridge University Press:  04 March 2009

Kim B. Bruce ,
Roberto Di Cosmo  and
Giuseppe Longo
Kim B. Bruce
Affiliation:
Dept. of Computer Science, Williams College, Williamstown, MA 01267
Roberto Di Cosmo
Affiliation:
Dip. di Informatica, Università di Pisa, Italy, and LIENS, 45, Rue d'Ulm, Paris, France
Giuseppe Longo
Affiliation:
LIENS (CNRS) – DMI, Ecole Normale Superieure, 45, Rue d'Ulm, Paris, France
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Abstract

A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. Using the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. Using the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having “invertible” proofs between the two terms. Work of Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 2 , Issue 2 , June 1992 , pp. 231 - 247
Copyright
Copyright © Cambridge University Press 1992

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References

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