DEDALUS-The DEDuctive ALgorithm Ur-Synthesizer*

Program synthesis is the automatic construction of programs to meet given specifications. These specifications constitute a high-level description of the desired program which expresses the purpose of the program, without indicating the method by which that purpose is to be achieved. The specifications are expressed in terms of many constructs which are endemic to the particular subject domain of the desired program (e.g., numbers, sets, lists). Because these constructs are only intended to describe the purpose of the program and need not be computed, they can be of a much higher level than the constructs of any programming . language (e.g., they can include logical quantifiers, set constructors, and other noncomputable operations). The specification language can correspond closely with the concepts a programmer actually uses in thinking about the problem. The techniques we are developing are independent of the choice of a target programming language. The particular language we use in our examples and in our experimental system is a simple LISP-like language containing only basic numerical and list-processing operations, conditional expressions, and recursion. In considering the formation of programs with side effects, we extend the language to include assignments to variables, array elements, and other data-structure components. Our basic approach is to transform the specifications repeatedly according to certain rules; each rule replaces one segment of a program description by another, equivalent, segment. The process continues until a description is obtained that is entirely in terms of the primitive constructs of the target language; this description is the desired program.