Curry - Howard Correspondance
نویسنده
چکیده
These notes are extracted from the rst version of the paper From Computation to Foundations: the-calculus and its webbed modelss. They nearly disappeared in the revised version of that paper, and we make them available separately. 0.1-calculus as a foundation for Programming Theory.-calculus came back to the front of the scene in the sixties with the development of Computer Science, under the impulse of Landin 21] and Backus (cf. 1]) and generated the family of functional languages (Lisp McCarthy 1960], Haskell, Miranda, ML, Caml, ...). In functional languages functions and functionals may be passed as arguments to a program as easily as concrete datas, which is not the case with imperative languages (Fortran, Pascal, C) (the other conceptual diierences between imperative programming (founded by Von Neumann) and functional programming are clearly explained e.g. in the rst pages of 1]). See barendregt's survey 2]: The other main conceptual contribution of-calculus to Programming Theory comes from the fact that its terms can be viewed as proofs as well as programs :-calculus allows the mathematical expression of the Curry Howard Isomorphismm, which is a very deep correspondence between proof theory, i.e. the mathematical analysis of mathematical reasoning, and concrete programming theory. The programming with proofs paradigm is a topic in active progress, and the present developments of the Curry Howard Correspondence generate beautiful and deep exchanges of intuitions and problems between Computer Science , Proof Theory and Mathematics. Because of its signiicance, we devote the next subsection to this correspondence. but for a very slight revision (January 15th, 1999) including the addition of reference 2].
منابع مشابه
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تاریخ انتشار 1997