LINCX: A Linear Logical Framework with First-Class Contexts

@inproceedings{Georges2017LINCXAL,
  title={LINCX: A Linear Logical Framework with First-Class Contexts},
  author={A{\"i}na Linn Georges and Agata Murawska and Shawn Otis and Brigitte Pientka},
  booktitle={ESOP},
  year={2017}
}
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. 

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References

SHOWING 1-10 OF 47 REFERENCES

A Contextual Logical Framework

A new logical framework with explicit linear contexts and names is presented with the purpose of enabling direct and flexible manipulation of contexts, both for representing systems and meta-properties, and it is proved that the framework admits canonical forms, and that it possesses all desirable meta-theoretic properties.

A linear logical framework

The linear type theory LLF is presented as the formal basis for a conservative extension of the LF logical framework and can be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination.

A concurrent logical framework I: Judgments and properties

The present report, the first of two technical reports describing CLF, presents the frame- work itself and its metatheory, and a novel, algorithmic formulation of the underlying type theory concentrating on canonical forms leads to a simple notion of definitional equality for concurrent computations in which the order of independent steps cannot be distinguished.

Structural Recursion over Contextual Objects

A core programming language is presented that allows structural recursion over open LF objects and contexts and termination of call-byvalue reduction is proven using a reducibility semantics, which establishes consistency and allows the implementation of proofs about LF specifications as well-founded recursive functions using simultaneous pattern matching.

Inductive Beluga: Programming Proofs

beluga is a proof environment which provides a sophisticated infrastructure for implementing formal systems based on the logical framework LF together with a first-order reasoning language for

Reasoning with higher-order abstract syntax in a logical framework

A meta-logic is presented that can be used to reason about judgments coded using HOAS, an extension of a simple intuitionistic logic that admits higher-order quantification over simply typed λ-terms as well as induction and a notion of definition.

Contextual modal type theory

The consequences of relativizing contextual modal logic and its type-theoretic analogue to explicitly specified contexts are investigated.

A hybrid logical framework

This work describes and argues for the usefulness of an extension of LF by features inspired by hybrid logic, which shows how linear logic features can be decomposed into primitive operations manipulating abstract resource labels.

First-class substitutions in contextual type theory

This paper revisits the theory of first-class substitution in contextual type theory (CTT) with a focus on the abstract notion of substitution variables, and describes the implementation of a weak normalization proof for the simply-typed lambda-calculus in Beluga.

Higher-order representation of substructural logics

We present a technique for higher-order representation of substructural logics such as linear or modal logic. We show that such logics can be encoded in the (ordinary) Logical Framework, without any