Linear type systems (allow exchange, but neither weakening nor contraction): Every variable is used exactly once. Affine type systems (allow exchange and weakening, but not contraction): …

A linear type system is to a linear logic as a \normal" type system, like the simply-typed -calculus, is to an intuitionistic logic. The overall ff is that every variable must be used exactly once.

Jul 10, 2024 · Linear type theory is the linear logic-version of type theory. In the definition of (Seely 89, prop. 1.5), following , this is the internal language of/has categorical semantics in …

In type theory, we elevate the concept of proof to a primary concept. In constructive logic this is important because proofs give rise to computation under reduction, as discussed in the …

A simple form of linear types (specifically MLL, the fragment of linear logic without the additive/‘choice’ operators ⊕ and &) can be encoded as a programming language in which …

Specifically, programming languages can use linear types to get the “best of both worlds” between memory-safe, garbage-collected languages like Java and “memory-unsafe” …

We call a type system that enforces this property linear, after Girard’s linear logic [Gir87]. Even though our ultimate goal is in the runtime system, we start with functional expressions. We say …

Mar 24, 2023 · Linear types, also known as linear logic or linear type systems, are a concept in programming language theory and type systems that enforces the constraint that each …

I Determine whether type or context can be used in linear setting I un(˝) if and only if ˝= un ˇ. I lin(˝) if and only if ˝= un ˇor ˝= lin ˇ. I q() if and only if for all ( x:˝) 2, we have q(˝). 23/30

Hype for Types Linear Logic and Linear Type Systems February 15, 20227/23 Introduction to Linear Logic In linear logic, we have neither weakening nor contraction.