Reductions for Synthesis Procedures

Abstract

Abstract. A synthesis procedure acts as a compiler for declarative specifications. It accepts a formula describing a relation between inputs and outputs, and generates a function implementing this relation. This paper presents the first synthesis procedures for 1) algebraic data types and 2) arrays. Our procedures are reductions that lift a synthesis procedure for the elements into synthesis procedures for containers storing these elements. We introduce a framework to describe synthesis procedures as systematic applications of inference rules. We show that, by interpreting both synthesis problems and programs as relations, we can derive and modularly prove widely applicable transformation rules, simplifying both the presentation and the correctness argument.

Synthesis modulo recursive functions

“…In this section, we briefly describe the formal reasoning behind these constructive steps and provide some illustrative examples. Whereas an earlier (purely theoretical) version of the framework was presented in [15], the new framework supports the notion of path condition, and is the first time we report on the practical realization of this framework.…”

“…We have shown in previous work how to design a set of rules to ensure completeness of synthesis for a well-specified class of formulas, e.g. integer linear arithmetic relations [23] or simple term algebras [15]. In the interest of remaining selfcontained, we shortly describe some generic rules.…”

“…In this paper we do not use synthesis rules for linear integer arithmetic. Instead, we here use synthesis procedure rules for algebraic data types [15,46], which were not reported in an implemented system before. This gives us building blocks for synthesis of recursion-free code.…”

“…A notable degree of automation in our synthesizer comes from synthesis procedures [15,23,24], which compile specification fragments expressed in decidable logics. The present work is, in fact, the first implementation of the synthesis procedure for algebraic data types we previously developed [46].…”

Developing Verified Software Using Leon

“…This functionality was originally aimed at being fully automated [10]. Synthesis in Leon is based on a custom deductive synthesis framework incorporating, for example, syntax-driven rules, rules supporting synthesis procedures [7,[14][15][16], and a form of counterexampleguided synthesis [10]. Subsequently we have worked on interfaces to perform this synthesis interactively, which allows the developer both to explore different alternatives if the solution is not unique, and to guide synthesis using manual steps.…”