Abstract
This paper presents an interactive, tactic-driven, proof development system, a Theorem Prover calledTheo. Both the meta and the object levels of our theorem prover are logics presented in Typol. Typol is the programming language that implements Natural Semantics, a semantics developed at Inria and pioneered by G. Plotkin under the name Structural Operational Semantics. So Theo is written in Typol and helps the user to build proofs in an object logic also written in Typol. Tactics and tacticals are written in Typol. Other important features of Theo are the form chosen for representing proofs, and the way proofs are performed. The internal form of the proofs is very compact, expressed with combinators, that can be related to the λ-calculus used in Automath and its descendants. Meanwhile, Theo performs proofs by a pure calculus on proofs, using a resolution rule. Proofs may be incomplete and may contain logical variables. Theo is developed under the Centaur system, as well as Typol. This system provides a modern graphic man-machine interface that Theo uses, for the user's advantage.
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