Generic Environments in Coq

TL;DR

This paper presents a flexible library for environments in Coq, enabling abstract, reusable environment definitions with proven properties and an implementation using lists, facilitating formal reasoning in proof development.

Contribution

It introduces a generic environment library in Coq, parameterized by variable modules, with formal properties and a list-based implementation.

Findings

Provides a reusable environment abstraction in Coq.

Defines standard and advanced environment operations.

Ensures all operations satisfy formal properties.

Abstract

We introduce a library which provides an abstract data type of environments, as a functor parameterized by a module defining variables, and a function which builds environments for such variables with any Type of type. Usual operations over environments are defined, along with an extensive set of basic and more advanced properties. Moreover, we give an implementation using lists satisfying all the required properties.