8 research outputs found
A language for multiplicative-additive linear logic
A term calculus for the proofs in multiplicative-additive linear logic is
introduced and motivated as a programming language for channel based
concurrency. The term calculus is proved complete for a semantics in linearly
distributive categories with additives. It is also shown that proof equivalence
is decidable by showing that the cut elimination rewrites supply a confluent
rewriting system modulo equations.Comment: 16 pages without appendices, 30 with appendice
Taylor expansion in linear logic is invertible
Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded
into a differential net, which is its Taylor expansion. We prove that two
different MELL proof-nets have two different Taylor expansions. As a corollary,
we prove a completeness result for MELL: We show that the relational model is
injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the
relational model is exactly axiomatized by cut-elimination