Power of Brute-Force Search in Strongly-Typed Inductive Functional Programming Automation

Abstract

A successful case of applying brute-force search to functional programming automation is presented and compared with a conventional genetic programming method. From the information of the type and the property that should be satisfied, this algorithm is able to find automatically the shortest Haskell program using the set of function components (or library) configured beforehand, and there is no need to design the library every time one requests a new functional program. According to the presented experiments, programs consisted of several function applications can be found within some seconds even if we always use the library designed for general use. In addition, the proposed algorithm can efficiently tell the number of possible functions of given size that are consistent with the given type, and thus can be a tool to evaluate other methods like genetic programming by providing the information of thebaseline performance.1. construct a set of functions whose return type matches the requested type, and 2. for the type of each argument of each function in the set, if ever, do the same thing recursively.Without the type constraint, repeating that process until small number of depth causes the number of programs explode. However, as we shall see in Section 5, with type constraints the number of matching functions consisted of several functions is sometimes surprisingly small. Its analogy with the cases where doing search for future moves in playing deterministic board games like chess is interesting: because the number of interesting moves is limited by each situation, brute force search without highly heuristic approach like genetic programming can work well.

Functional genetic programming and exhaustive program search with combinator expressions

“…The effort required to generate combinator-expression solutions to the even-parity prob-lem on N inputs, and to find implementations of a stack and queue compares favorably with the works of Yu [39], Kirshenbaum [15], Agapitos and Lucas [1], Wong and Leung [37], Koza [17], Langdon [18], and Katayama [14].…”

“…Genetic programming is not always the best way to automatically generate programssometimes, particularly in the case of small programs, an exhaustive enumeration of every correctly typed expression is more efficient than evolution [14]. Although, in principle, exhaustive enumeration of all valid programs can be applied to any program representation, the simple structure of combinator expressions makes them well suited for this task, and the algorithms we have developed for genetic programming can be easily adapted for this purpose.…”

“…Like Katayama [14], to specify a problem, we parse the built-in values and the fitness function, and infer their types from code in a programming language, rather than coding them directly into the system. We specify the built-in values and fitness function in a subset of Standard ML that we call Mini-ML.…”

“…• We show that generating combinator expressions is efficient compared to the works of Yu [39], Kirshenbaum [15], Agapitos and Lucas [1], Wong and Leung [37], Koza [17], Langdon [18], and Katayama [14] on several problems: even parity on N inputs, and devising representations and implementations for stacks and queues;…”

“…] Typed, functional program representations are well suited for genetic programming and other methods of program search [24,39,14,25]. A strong type system can eliminate a very large number of ill-formed programs from the search space, and the expressiveness of functional programming languages makes it possible to represent complex programs concisely.…”