A Linear Logical Framework

A Linear Logical Framework

syntax Concrete syntax Kinds type type x :A:K {x:A}K A -> K K Types A&B; A & B A B A -o B B oA x :A:B {x:A}B A -> B B M Objects sndM M ̂x :A:M [x^A]M M^N M ^ N x :A:M [x:A]M M N M N The next table gives the relative precedence and associativity of these operators. As in Elf, parentheses are available to override these behaviors. Precedence Oper...

{72 () a Linear Logical Framework

We present the linear type theory ?&> as the formal basis for LLF, a conservative extension of the logical framework LF. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of Mini-ML with mutable references including i...

A Meta Linear Logical Framework

Over the years, logical framework research has produced various type theories designed primarily for the representation of deductive systems. Reasoning about these representations requires expressive special purpose meta logics, that are in general not part of the logical framework. In this work, we describe Lω , a meta logic for the linear logical framework LLF [CP96] and illustrate its use vi...

LINCX: A Linear Logical Framework with First-Class Contexts

Linear logic provides an elegant framework for modelling stateful, imperative and concurrent systems by viewing a context of assumptions as a set of resources. However, mechanizing the meta-theory of such systems remains a challenge, as we need to manage and reason about mixed contexts of linear and intuitionistic assumptions. We present Lincx, a contextual linear logical framework with first-c...

Lincx: A Linear Logical Framework with First-class Context