Type inference in intuitionistic linear logic

We study the type checking and type inference problems for intuitionistic linear logic: given a System F typed λ-term, (i) for an alleged linear logic type, determine whether there exists a corresponding typing derivation in linear logic (type checking) (ii) provide a concise description of all possible corresponding linear logic typings (type inference). We solve these problems using a novel algorithmic type system for linear logic whose typing rules carry arithmetic side conditions describing essentially the nesting depth of (proof-net) boxes. By understanding these side conditions as unknowns we then reduce type inference to solving a system of arithmetic constraints. We show that these constraint systems fall into a tractable class hence leading to an efficient (polynomial-time) solution. There are two important restrictions: first, our source language is typed System F rather than untyped lambda calculus; this is necessary because type inference for System F is known to be und...

• Type: Journal
• Year: 2010
• Where: PPDP
• Authors: Patrick Baillot, Martin Hofmann
• Keywords: Linear Logic, PPDP 2010, Programming Languages, Type Inference, Type Systems