Proving Theorems with Computers

Proving theorems by reuse

We investigate the improvement of theorem proving by reusing previously computed proofs. We have developed and implemented the PLAGIATOR system which proves theorems by mathematical induction with the aid of a human advisor: If a base or step formula is submitted to the system, it tries to reuse a proof of a previously verified formula. If successful, labour is saved, because the number of requ...

Proving Existential Theorems

Proving Correctness via Free Theorems

Free theorems feature prominently in the field of program transformation for pure functional languages such as Haskell. However, somewhat disappointingly, the semantic properties of so based transformations are often established only very superficially. This paper is intended as a case study showing how to use the existing theoretical foundations and formal methods for improving the situation. ...

Proving Theorems by Program Transformation

In this paper we present an overview of the unfold/fold proof method, a method for proving theorems about programs, based on program transformation. As a metalanguage for specifying programs and program properties we adopt constraint logic programming (CLP), and we present a set of transformation rules (including the familiar unfolding and folding rules) which preserve the semantics of CLP prog...

Proving Behavioural Theorems with Standard First-Order Logic

Behavioural logic is a generalization of first-order logic where the equality predicate is interpreted by a behavioural equality of objects (and not by their identity). We establish simple and general sufficient conditions under which the behavioural validity of some first-order formula with respect to a given first-order specification is equivalent to the standard validity of the same formula ...