Plugging-in Proof Development Environments using Locks in LF

Furio Honsell (1) , Luigi Liquori (2) , Petar Maksimovic (3) , Ivan Scagnetto (1)

1 DIMI - Dipartimento di Matematica e Informatica - Universita Udine
2 KAIROS - Logical Time for Formal Embedded System Design
3 Mathematical Institute of the Serbian Academy of Sciences and Arts

We 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 plugging-in, i.e. gluing together, different Type Theories and proof development environments. The oracle can be invoked either 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, CLLFP , is the canonical version of the system LLFP, presented earlier by the authors. The second system, CLLF P? , features the possibility of invoking the oracle to obtain also a witness satisfying a given constraint. We discuss encodings of Fitch-Prawitz Set theory, call-by-value λ-calculi, systems of Light Linear Logic, and partial functions.

Mots clés: MSCS

Domaines: Informatique et langage [cs.CL]; Logique en informatique [cs.LO]

Furio Honsell, Luigi Liquori, Petar Maksimovic, Ivan Scagnetto. Plugging-in Proof Development Environments using Locks in LF. Mathematical Structures in Computer Science, 2018, 28 (9), pp.1578--1605. ⟨hal-01272647⟩