Abstract:
These notes are extracted from the rst version of the paper iFrom Computation to Foundations: the -calculus and its webbed modelsj. 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 dioeerences 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 P...
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