Formal proof of correctness of long division algorithm as appearing in PLCC Chapter 2, modelled within an Imp variant

This project consists of the following files (excluding README.md, LICENSE and .gitignore):

• _CoqProject - used for generating the Makefile to build this project
• Maps.v - total maps
• Imp.v - the Imp programming language (variant)
• Hoare.v - proof rules for reasoning about Imp programs
• LongDivision.v - the long division algorithm in Imp and its proof of correctness

Fire up your terminal, change directory to your local copy of this repo and run coq_makefile -f _CoqProject -o Makefile, then open any vernacular file from this repo in your CoqIDE and select Compile > Make.

N.B. The terminal workaround is necessary for generating the correct Makefile due to coq/coq#10736.

In the end of Chapter 2 of Program Logics for Certified Compilers (PLCC), the reader is advised to work through the steps of the proof involving the correctness of the long division algorithm shown here (or consult a detailed proof referenced by the book). You are advised not to peek at the contents of this repo until you have at least made an attempt at proving it yourself, though it is not mandatory to do so.

The long division algorithm is taken from a free excerpt of PLCC while the toy programming language used in this repo is a variant of Imp in Software Foundations, an excellent resource for learning Coq.

A signification portion of work in this repo is adapted from the Software Foundations series, whose license terms are reproduced verbatim below as per the license terms:

Copyright (c) 2019

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