Three Tactic Theorem Proving

Abstract. We describe the key features of the proof description language of Declare, an experimental theorem prover for higher order logic. We take a somewhat radical approach to proof description: proofs are not described with tactics but by using just three expressive outlining constructs. The language is \declarative" because each step speci es its logical consequences, i.e. the constants and formulae that are introduced, independently of the justi cation of that step. Logical constants and facts are lexically scoped in a style reminiscent of structured programming. The style is also heavily \inferential", because Declarerelies on an automated prover to eliminate much of the detail normally made explicit in tactic proofs. Declare has been partly inspired by Mizar, but provides better automation. The proof language has been designed to take advantage of this, allowing proof steps to be both large and controlled. We assess the costs and bene ts of this approach, and describe...

• Type: Conference
• Year: 1999
• Where: TPHOL
• Authors: Don Syme
• Keywords: Automated Reasoning, Proof Description, Proof Description Language, Theorem Prover, TPHOL 1999