Theorem Provers as Libraries -- An Approach to Formally Verifying Functional Programs

Property-directed verification of functional programs tends to take one of two paths. First, is the traditional testing approach, where properties are expressed in the original programming language and checked with a collection of test data. Alternatively, for those desiring a more rigorous approach, properties can be written and checked with a formal tool; typically, an external proof system. This dissertation details a hybrid approach that captures the best of both worlds: the formality of a proof system paired with the native integration of an embedded, domain specific language (EDSL) for testing. At the heart of this hybridization is the titular concept -- a theorem prover as a library. The verification capabilities of this prover, HaskHOL, are introduced to a Haskell development environment as a GHC compiler plugin. Operating at the compiler level provides for a comparatively simpler integration and allows verification to co-exist with the numerous other passes that stand between source code and program

Going Polymorphic - TH1 Reasoning for Leo-III

While interactive proof assistants for higher-order logic (HOL) commonly admit reasoning within rich type systems, current theorem provers for HOL are mainly based on simply typed lambda-calculi and therefore do not allow such flexibility. In this paper, we present modifications to the higher-order automated theorem prover Leo-III for turning it into a reasoning system for rank-1 polymorphic HOL. To that end, a polymorphic version of HOL and a suitable paramodulation-based calculus are sketched. The implementation is evaluated using a set of polymorphic TPTP THF problems

Generic Theorem Proving Using HOL2P: A Category Theory Inspired Approach

Abstract Integrating formal program verification into mainstream software development has proven to be quite challenging, due to the level of abstract mathematical machinery needed. Although there have been some successes, most existing methods do not adequately support the mechanical verification of generic programs. This thesis seeks to fill this gap by presenting a formalisation and implementation of a category theory inspired approach to generic program specification. Theorems to simplify verification of generic programs are developed along with a formal framework for reasoning. The result is theorem proving support based on type quantification and type operator variables in HOL, HOL2P. This is demonstrated by the verification the Yoenda Lemma

Leo-III Version 1.1 (System description)

Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers. Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use