LINCX: A Linear Logical Framework with First-Class Contexts [chapter]

Aina Linn Georges, Agata Murawska, Shawn Otis, Brigitte Pientka
2017 Lecture Notes in Computer Science  
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-class mixed contexts. Lincx allows us to model (linear) abstract syntax trees as syntactic structures
more » ... at may depend on intuitionistic and linear assumptions. It can also serve as a foundation for reasoning about such structures. Lincx extends the linear logical framework LLF with firstclass (linear) contexts and an equational theory of context joins that can otherwise be very tedious and intricate to develop. This work may be also viewed as a generalization of contextual LF that supports both intuitionistic and linear variables, functions, and assumptions. We describe a decidable type-theoretic foundation for Lincx that only characterizes canonical forms and show that our equational theory of context joins is associative and commutative. Finally, we outline how Lincx may serve as a practical foundation for mechanizing the metatheory of stateful systems.
doi:10.1007/978-3-662-54434-1_20 fatcat:ecrq5g3ejza77dycjdgir7ewr4