Gluing together Proof Environments: Canonical extensions of LF Type Theories featuring Locks

Abstract

International audienceWe present two extensions of the LF Constructive Type Theory featuring monadic locks. A lock is a monadic type construct that captures the effect of an external call to an oracle. Such calls are the basic tool for gluing together diverse Type Theories and proof development environments. The oracle can either be invoked in order to check that a constraint holds or to provide a suitable witness. The systems are presented in the canonical style developed by the CMU School. The first system, CLLF_P , is the canonical version of the system LLF_P , presented earlier by the authors. The second system, CLLF_P? , features the possibility of invoking the oracle to obtain a witness satisfying a given constraint. We discuss encodings of Fitch-Prawitz Set theory, call-by-value λ-calculi, and systems of Light Linear Logic. Finally, we show how to use Fitch-Prawitz Set Theory to define a type system that types precisely the strongly normalizing terms

Plugging-in proof development environments usingLocksinLF

“…In this paper, we use a Curry-style syntax of terms because it is more suitable for implementations in that it simplifies the notation. While, as remarked in Honsell et al (2015), the typeful syntaxà la Church allows for a more direct comparison with non-canonical systems. Indeed, there is a correspondence between the two systems.…”

“…This work is an extended version of Honsell et al (2015) and is part of an ongoing research programme, (Honsell et al 2012;Honsell 2013;Honsell et al 2014, aiming to define a simple Universal Meta-language for Logics, extending the constructive type theory LF, that can support the effects of plugging-in and integrating different proof development environments.…”