. The Coq and ProPre systems show the automated termination of a recursive function by first constructing a tree associated with the specification of the function which satisfies a notion of terminal property and then verifying that this construction process is formally correct. However, those two steps strongly depend on inductive principles and hence Coq and ProPre can only deal with the termination proofs that are inductive. There are however many functions for which the termination proofs are non-inductive. In this article, we attempt to extend the class of functions whose proofs can be done automatically `a la Coq and ProPre to a larger class including functions whose termination proofs are not inductive. We do this by extending the terminal property notion and replacing the verification step above by one that searches for a decreasing measure which can be used to establish the termination of the function. 1 Introduction Termination is an important property in the verification ...

We investigate an automated program synthesis system based on the paradigm of programming by proofs. To automatically extract a -term that computes a recursive function given by a set of equations the system must nd a formal proof of the totality of the given function. Because of the particular logical framework, usually such approaches make it dicult to use techniques such as those in rewriting theory. We overcome this diculty for the automated system that we consider by exploiting product types. As a consequence, this would enable the incorporation of termination techniques used in other areas while still extracting programs.

This document describes the Hume programming language. Hume (Higher-order Unified Meta-Environment) is a strongly typed, functionally-based language with an integrated tool set for developing, proving and assessing concurrent, resource-limited systems, such as embedded or safetycritical systems. It aims to extend the frontiers of language design for such systems, introducing new levels of abstraction and provability

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