# A Framework for the Formalisation of Pi Calculus Type Systems in Isabelle/HOL

@inproceedings{Gay2001AFF, title={A Framework for the Formalisation of Pi Calculus Type Systems in Isabelle/HOL}, author={Simon J. Gay}, booktitle={TPHOLs}, year={2001} }

We present a formalisation, in the theorem proving system Isabelle/HOL, of a linear type system for the pi calculus, including a proof of runtime safety of typed processes. The use of a uniform encoding of pi calculus syntax in a meta language, the development of a general theory of type environments, and the structured formalisation of the main proofs, facilitate the adaptation of the Isabelle theories and proof scripts to variations on the language and other type systems.

## 16 Citations

### A First-Order Syntax for the Pi-Calculus in Isabelle/HOL using Permutations

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2001

### {\pi} with leftovers: a mechanisation in Agda

- Computer Science
- 2020

This work presents the first full mechanisation in Agda of a π-calculus with linear, graded and shared types, all under the same unified framework, and shows that the type system is stable under substitution and prove subject reduction.

### Proof-relevant π-calculus

- Computer Science
- 2015

This work presents a formalisation in Agda that explores the theory of concurrent transitions, residuation, and causal equivalence of traces, which has not previously been formalised for the π-calculus.

### Higher-Order Abstract Syntax with Induction in Isabelle/HOL: Formalizing the pi-Calculus and Mechanizing the Theory of Contexts

- Computer ScienceFoSSaCS
- 2001

This paper presents a formalization of the π-calculus in Isabelle/HOL, using well-formedness predicates which both eliminate exotic terms and yield structural induction, which is used to derive the Theory of Contexts fully within the mechanization.

### π with leftovers: a mechanisation in Agda

- Computer ScienceFORTE
- 2021

This work presents the first full mechanisation in Agda of a {\pi}-calculus with linear, graded and shared types, all under the same unified framework, and shows that the type system is stable under substitution and prove subject reduction.

### An extensible approach to session polymorphism †

- Computer ScienceMathematical Structures in Computer Science
- 2015

This work provides a polymorphic session typing system for the π calculus, and demonstrates the utility of session-type-level functions in combination with polymorphicsession typing.

### Proof-relevant π-calculus: a constructive account of concurrency and causality

- Computer ScienceMathematical Structures in Computer Science
- 2017

This work presents a formalisation in Agda of the theory of concurrent transitions, residuation and causal equivalence of traces for the π-calculus, and proofs of the ‘diamond lemma’ for the residuals of concurrent transitioning and a formal definition of equivalences of traces up to permutation of transitions.

### A fully adequate shallow embedding of the π-calculus in Isabelle/HOL with mechanized syntax analysis

- Computer ScienceJournal of Functional Programming
- 2003

The work at hand demonstrates how exotic terms can be eliminated by means of a two-level well-formedness predicate, further preparing the ground for an implementation of structural induction in terms of rule induction, and hence providing fully-fledged syntax analysis.

### HOπ in Coq

- Computer ScienceCPP
- 2018

Strong context bisimilarity is formalized and proved to be compatible, i.e., closed under every context, using Howe’s method, based on several proof schemes developed in a previous paper.

### A Coq Library for Verification of Concurrent Programs

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2008