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The aim of this article is to give the proof-theoretic analysis of various subsystems of Feferman's theory T 1 for explicit mathematics which contain the non-constructive-operator and join. We make use of standard proof-theoretic techniques such as cut-elimination of appropriate semi-formal systems and asymmetrical interpretations in standard structures for… (More)

We characterize the proof-theoretic strength of systems of explicit mathematics with a general principle (MID) asserting the existence of least fixed points for monotone inductive definitions, in terms of certain systems of analysis and set theory. In the case of analysis, these are systems which contain the Σ 1 2-axiom of choice and Π 1 2-comprehension for… (More)

We present a methodology for checking the termination of Prolog programs that can be automated and is scalable. Furthermore, the proposed method can be used to locate errors. It has been successfully implemented as part of a tool that uses static analysis based on formal methods in order to validate Prolog programs. This tool is aimed at supporting the… (More)

In practice, a large part of most Prolog programs is in fact functional , the search facilities of Prolog are only rarely needed. In order to arrive at efficient implementations it is then convenient to make use of the cut operator provided by Prolog. Up to now, this operator has been regarded as an extra–logical control operator that destroys the… (More)

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