ion of the Specification Borrowing a saying of Einstein's, I maintain that specifications should be as abstract as possible, but not more abstract. I see three limitations to the degree of abstraction. First, a specification as an adequate formalization of the requirements cannot be more abstract than the requirements themselves. If a specific algorithm is required, this algorithm must be specified. This argument applies as well to non-functional requirements constraining possible implementations. Some constraints can appear as comments in specifications, e.g. the requirement that a specific language should be used for the implementation. Other constraints, however, must be concretely specified, e.g. the requirement that the future software system has to adhere to the data structures of a given interface. The second limitation to abstraction arises when we make formal specifications executable. Even if the degree of abstraction of the data structures and the algorithms stays the same,...

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This paper presents an overview and a survey of logic program synthesis. Logic program synthesis is interpreted here in a broad way; it is concerned with the following question: given a specification, how do we get a logic program satisfying the specification? Logic programming provides a uniquely nice and uniform framework for program synthesis since the specification, the synthesis process and the resulting program can all be expressed in logic. Three main approaches to logic program synthesis by formal methods are described: constructive synthesis, deductive synthesis and inductive synthesis. Related issues such as correctness and verification as well as synthesis by informal methods are briefly presented. Our presentation is made coherent by employing a unified framework of terminology and notation, and by using the same running example for all the approaches covered. This paper thus intends to provide an assessment of existing work and a framework for future research in logic program synthesis.

We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a verification proof. The approach is a two-level one: At the object level, we prove program verification conjectures in a sorted, first-order theory. The conjectures are of the form 8args \Gamma\Gamma\Gamma\Gamma! : prog(args \Gamma\Gamma\Gamma\Gamma! ) $ spec(args \Gamma\Gamma\Gamma\Gamma! ). At the meta-level, we plan the object-level verification with an unspecified program definition. The definition is represented with a (second-order) meta-level variable, which becomes instantiated in the course of the planning.

We present a method for proving properties of definite logic programs. This method is called unfold/fold proof method because it is based on the unfold/fold transformation rules...

We develop two applications of middle-out reasoning in inductive proofs: Logic program synthesis and the selection of induction schemes. Middle-out reasoning as part of proof planning was first suggested by Bundy et al [Bundy et al 90a]. Middle-out reasoning uses variables to represent unknown terms and formulae. Unification instantiates the variables in the subsequent planning, while proof planning provides the necessary search control. Middle-out reasoning is used for synthesis by planning the verification of an unknown logic program: The program body is represented with a meta-variable. The planning results both in an instantiation of the program body and a plan for the verification of that program. If the plan executes successfully, the synthesized program is partially correct and complete. Middle-out reasoning is also used to select induction schemes. Finding an appropriate induction scheme during synthesis is difficult, because the recursion of the program, which is un...

We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a verification proof. The approach is a two-level one: At the object level, we prove program verification conjectures in a sorted, first-order theory. The conjectures are of the form 8args \Gamma\Gamma\Gamma\Gamma! : prog(args \Gamma\Gamma\Gamma\Gamma! ) $ spec(args \Gamma\Gamma\Gamma\Gamma! ). At the meta-level, we plan the object-level verification with an unspecified program definition. The definition is represented with a (second-order) meta-level variable, which becomes instantiated in the course of the planning. This technique is an application of the CL A M proof planning system [Bundy et al 90c]. CL A M is currently powerful enough to plan verification proofs for given programs. We show that, if CL A M's use of middle-out reasoning is extended, it will also be able to synthesize programs. 1 Introduction The aim of t...

In this position paper, we give a critical analysis of the deductive and inductive approaches to program synthesis, and of the current research in these fields. From the shortcomings of these approaches and works, we identify future research directions for these fields, as well as a need for cooperation and cross-fertilization between them.

. We show how logical frameworks can provide a basis for logic program synthesis. With them, we may use first-order logic as a foundation to formalize and derive rules that constitute program development calculi. Derived rules may be in turn applied to synthesize logic programs using higher-order resolution during proof that programs meet their specifications. We illustrate this using Paulson's Isabelle system to derive and use a simple synthesis calculus based on equivalence preserving transformations. 1 Introduction Background In 1969 Dana Scott developed his Logic for Computable Functions and with it a model of functional program computation. Motivated by this model, Robin Milner developed the theorem prover LCF whose logic PP used Scott's theory to reason about program correctness. The LCF project [13] established a paradigm of formalizing a programming logic on a machine and using it to formalize different theories of functional programs (e.g., strict and lazy evaluation) and the...

This paper generalizes an algebraic method for the design of a correct compiler to tackle specification and verification of an optimized compiler. The main optimization issues of concern here include the use of existing contents of registers where possible and the identification of common expressions. A register table is introduced in the compiling specification predicates to map each register to an expression whose value is held by it. We define different kinds of predicates to specify compilation of programs, expressions and Boolean tests. A set of theorems relating to these predicates, acting as a correct compiling specification, are presented and an example proof within the refinement algebra of the programming language is given. Based on these theorems, a prototype compiler in Prolog is produced.