Proofs as processes

Functions as proofs as processes

This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the π-calculus closely related to linear logic. Decompositions of intuitionistic and classical logics into this system provide type-preserving translations of the λand λμ-calculus, both for call-by-name and call-by-value evaluation strategies. ...

Towards Proofs as Successful Executions of Processes

We further the understanding of the relationship between process calculi and non-commutative logic. This work focuses on, a first-order extension of the proof calculus BV featuring a de Morgan dual pair of nominal quantifiers, called BV1. An embedding of π-calculus process as predicates in BV1 is defined, and a procedure is provided for extracting successful executions from proofs of embedded p...

Compositional Proofs for Networks of Processes

In this version misprints and inaccuracies in the Introduction and section 2 have been corrected. INTRODUCTION Over the last decade much attention was devoted to compositional methods for speci-cation and veriication of concurrent systems (See for example BKP], dR], AL], MP2]). This approach seems to ooer a convenient alternative to the global one, in which only the complete system is available...

Proofs as Games

Proofs as Polynomials

Girard’s Geometry of Interaction (GoI) develops a mathematical framework for modelling the dynamics of cut-elimination. In previous work we introduced a typed version of GoI, called Multiobject GoI (MGoI) for multiplicative linear logic [22]. This was later extended to cover the exponentials by the first author [23]. Our development of MGoI depends on a new theory of partial traces, as well as ...