Recursive Program Optimization Through Inductive Synthesis Proof Transformation

The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the target, which yields a computationally more efficient algorithm. We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming inductive proofs. We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability and generality

Combining Syntactic and Semantic Bidirectionalization

Matsuda et al. [2007, ICFP] and Voigtlander [2009, POPL] introduced two techniques that given a source-to-view function provide an update propagation function mapping an original source and an updated view back to an updated source, subject to standard consistency conditions. Being fundamentally different in approach, both techniques have their respective strengths and weaknesses. Here we develop a synthesis of the two techniques to good effect. On the intersection of their applicability domains we achieve more than what a simple union of applying the techniques side by side deliver

Transformations of Logic Programs with Goals as Arguments

We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by exploiting this capability when transforming programs, we can improve program efficiency. We propose a set of program transformation rules which extend the familiar unfolding and folding rules and allow us to manipulate clauses with goals which occur as arguments of predicates. In order to prove the correctness of these transformation rules, we formally define the operational semantics of our extended logic programming language. This semantics is a simple variant of LD-resolution. When suitable conditions are satisfied this semantics agrees with LD-resolution and, thus, the programs written in our extended language can be run by ordinary Prolog systems. Our transformation rules are shown to preserve the operational semantics and termination.Comment: 51 pages. Full version of a paper that will appear in Theory and Practice of Logic Programming, Cambridge University Press, U

Functional programming with bananas, lenses, envelopes and barbed wire

We develop a calculus for lazy functional programming based on recursion operators associated with data type definitions. For these operators we derive various algebraic laws that are useful in deriving and manipulating programs. We shall show that all example functions in Bird and Wadler's Introduction to Functional Programming can be expressed using these operators