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**A generic graphic framework for combining inference tools and editing proofs and formulae.**
*(English)*
Zbl 0836.68106

Summary: A running system for combining inference tools, editing and checking proofs in different logics is presented. It is based on a formalism similar to and developed from the Calculus of Constructions (Coquand and Huet). The system named \(\text{GLEF}_{\text{ATINF}}\), is a key component of the inference laboratory ATINF (ATelier d’INFérence) developed at LIFIA-IMAG since 1985.

Its stabilities are independent of the logic and the calculus used. It is therefore possible to present and combine proofs coming from any theorem prover. The user may entirely define the graphic presentation of proofs, formulae, …he wishes.

Some other original features are: proofs can be viewed and browsed in different ways, (parts of) proofs can be memorized and reused, the size of inference steps for proof presentation can be fixed arbitrarily, regularities in proofs can be handled in a natural manner, equational and non equational proofs are treated in a homogeneous way, …The principles of the underlying formalism and the several languages used are presented. The system has been implemented on Macintosh (and will soon be ported on SUN workstation).

The system should also allow easy integration of theorem provers with symbolic computation systems (integration of MATHEMATICA is planned for a near future). Several running examples in classical and non-classical logics give a clear idea of the capabilities of the system. In particular, we consider a proof obtained by the well known resolution- based theorem prover OTTER (McCune, 1990). \(\text{GLEF}_{\text{ATINF}}\) helped to discover its regularities and shows evidence of them to the user. Finally, the main lines of current and future work are given.

Its stabilities are independent of the logic and the calculus used. It is therefore possible to present and combine proofs coming from any theorem prover. The user may entirely define the graphic presentation of proofs, formulae, …he wishes.

Some other original features are: proofs can be viewed and browsed in different ways, (parts of) proofs can be memorized and reused, the size of inference steps for proof presentation can be fixed arbitrarily, regularities in proofs can be handled in a natural manner, equational and non equational proofs are treated in a homogeneous way, …The principles of the underlying formalism and the several languages used are presented. The system has been implemented on Macintosh (and will soon be ported on SUN workstation).

The system should also allow easy integration of theorem provers with symbolic computation systems (integration of MATHEMATICA is planned for a near future). Several running examples in classical and non-classical logics give a clear idea of the capabilities of the system. In particular, we consider a proof obtained by the well known resolution- based theorem prover OTTER (McCune, 1990). \(\text{GLEF}_{\text{ATINF}}\) helped to discover its regularities and shows evidence of them to the user. Finally, the main lines of current and future work are given.

### MSC:

68T15 | Theorem proving (deduction, resolution, etc.) (MSC2010) |

03B35 | Mechanization of proofs and logical operations |