Analytical inductive functional programming

Abstract

We describe a new method to induce functional programs from small sets of non-recursive equations representing a subset of their input-output behaviour. Classical attempts to construct functional Lisp programs from input/output-examples are analytical, i.e., a Lisp program belonging to a strongly restricted program class is algorithmically derived from examples. More recent approaches enumerate candidate programs and only test them against the examples until a program which correctly computes the examples is found. Theoretically, large program classes can be induced generate-and-test based, yet this approach suffers from combinatorial explosion. We propose a combination of search and analytical techniques. The method described in this paper is search based in order to avoid strong a-priori restrictions as imposed by the classical analytical approach. Yet candidate programs are computed based on analytical techniques from the examples instead of being generated independently from the examples. A prototypical implementation shows first that programs are inducible which are not in scope of classical purely analytical techniques and second that the induction times are shorter than in recent generate-and-test based methods. © 2009 Springer Berlin Heidelberg.