HOLL: Program Synthesis for Higher Order Logic Locking

Logic Program Synthesis in a Higher-Order Setting

We describe a system for the synthesis of logic programs from specifications based on higher-order logical descriptions of appropriate refinement operations. The system has been implemented within the proof planning system λClam . The generality of the approach is such that its extension to allow synthesis of higher-order logic programs was straightforward. Some illustrative examples are given....

The Representation of Program Synthesis in Higher Order Logic

In H. Marburger, ed., 14 German Workshop on Artificial Intelligence, Informatik Fachberichte 251, pp. 171–180, c © Springer Verlag, 1990. Systems built for automated program construction aim at the formalization of the programming process in order to produce better software. Their implementations, however, suffer from problems similar to those they are intended to solve. Due to a lack of abstra...

Proving Program Termination in Higher Order Logic∗

We suggest two simple additions to packages that use wellfounded recursion to justify termination of recursive programs: The contraction condition, to be proved in cases when termination conditions are difficult or impossible to extract automatically; user-supplied inductive invariants in cases of nested recursion. We have implemented these additions in Isabelle/HOL and demonstrated their usefu...

Examples for program extraction in Higher-Order Logic

Automatic Program Synthesis in Second-Order Logic

Abetract A resolution-based theorem prover, incorporating a restricted higher-order unification algorithm , has been applied to the automatic synthesis of SN0B0L-4 programs. The set of premisses includes second-order assignment and iteration axioms derived from those of Hoare. Two examples are given of the synthesis of programs that compute elementary functions. Descriptive Terms Higher-order l...