An extension of lambda-calculus for functional programming

Lambda-Calculus and Functional Programming

ion operator; this is because [x]M is an abbreviation for a term in which M and its subterms do not occur. On the other hand, in the natural reduction for lambda-calculus, replacements inside the scope of an abstraction are extremely natural. Thus, what is now called λβ -reduction satisfies a scheme which weak reduction does not, namely (ξ): if M reduces to N, then λx.M reduces to λx.N. (The sa...

A Consistent Extension of the Lambda-Calculus as a Base for Functional Programming Languages

Church 's lambda-calculus is modified by introducing a new mechanism, the lambda-bar operator # , which neutralizes the effect of one preceding lambda binding. This operator can be used in such a way that renaming of bound variables in any reduction sequence can be avoided, with the effect that efficient interpreters with comparatively simple machine organization can be designed. It is shown th...

An introduction to functional programming through lambda calculus

Lambda Calculus,Conservative Extension and Structural Induction

The issue of whether embedding algebraic theories in higher-order theories such as the simply typed and polymorphic lambda calculi is of interest in programming language design. The establishment of such a conservative extension result permits modularity in the verification of the correctness of datatype and function implementations. In earlier work [Breazu-Tannen & Meyer 1987a], [Breazu-Tannen...

Lambda-calculus Models of Programming Languages

Two aspect of programming languages, recursive definitions and type declarations are analyzed in detail. Church's %-calculus is used as a model of a programming language for purposes of the analysis. The main result on recursion is an analogue to Kleene's first recursion theorem: If A = FA for any %-expressions A and F, then A is an extension of YF in the sense that if E[YF], any expression con...