Abstract: "The paper describes a variant of Martin-Löf type theory extended by the principle of type induction, as introduced in the oyster-2 theorem proving system. The system has a procedural meta-language in which a variety of search strategies have been written. Theorem proving in the syste...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Horn, Christian (VerfasserIn), Smaill, Alan (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Edinburgh 1994
Schriftenreihe:	University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 727
Schlagworte:	Bionics and artificial intelligence Computer software Automatic theorem proving Type theory
Zusammenfassung:	Abstract: "The paper describes a variant of Martin-Löf type theory extended by the principle of type induction, as introduced in the oyster-2 theorem proving system. The system has a procedural meta-language in which a variety of search strategies have been written. Theorem proving in the system yields object-level functional programs that implement procedures associated with the theorem that is proved. We demonstrate the application of type induction in proving the existence of a partial decision procedure for a fragment of type theory inside the theory itself. As a result of that proof, we obtain an object-level program that implements such a partial decision procedure, ie given a type theoretic formula x as input, it returns either a proof of x (formally, an element of the type x), or a refutation of x (formally, an element of the type x --> void) or a distinguished value indicating that no decision has been made. Initially an interactive proof of the existence of such a procedure is given, for the fragment of type theory representing classical propositional calculus. That proof turns out to have a very simple structure, the construction of which can easily be automated. Therefore we describe a tactical operator reflect(T) which takes an arbitrary terminating search strategy T as its argument and produces a proof of the existence of a partial decision procedure, the extract term of which simulates the strategy T. Effectively, we compile a meta-level search strategy into an object level functional program. Once we have the object- level procedure, it can be used to avoid execution of the meta-level program altogether where knowledge of its existence is sufficient, or executed in place of the meta-level program."
Beschreibung:	23 S.