An Introduction to Functional Programming Through Lambda Calculus Greg Michaelson
Publisher: Addison-Wesley

A Simply Typed Lambda-Calculus for Forward Automatic Differentiation. Abstract: We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite lambda-terms that are lambda_{letrec}-expressible in the sense that they arise as infinite unfoldings of terms in lambda_{letrec}, the lambda-calculus with letrec. It makes many things considerably easier on programmers. On the road to maximally implementing the Lambda Calculus -- everything is not yet a function in Javascript -- we still have not attained its full power. In this post I would like to give a down-to-earth introduction to the subject of the paper and to explain the problem it is attempting to solve. We provide two characterizations, using concepts we introduce for infinite lambda-terms: regularity, strong regularity, and binding-capturing chains. So, not only LISP does not implement automated eta-conversion, but there is every reason to believe that no programming language would ever be capable of doing this. But before I get to it, I'd like to talk a little about the connection between generic programming and functional programming, give a short intro to functional programming; and then show some examples in C++ and D that involve pattern matching and type lists. Programming is that it's easy to define and implement. You can describe typeless lambda calculus with just a few formulas in operational semantics. I am proud to announce that my first computer science paper has been accepted to MFPS XXVIII! I am working on design and implementation of a functional programming language with support for automatic differentiation. Even without introducing the index variable i, we still introduce the concept of succeeding elements and therefore of a successor function:.