https://github.com/sacerdot/causal2timedformalization

Sources for the formalization in Matita of Causal Reversibility Implies Time Reversibility
https://github.com/sacerdot/causal2timedformalization

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Sources for the formalization in Matita of Causal Reversibility Implies Time Reversibility

• Host: GitHub
• URL: https://github.com/sacerdot/causal2timedformalization
• Owner: sacerdot
• License: gpl-3.0
• Created: 2023-05-17T20:52:46.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-05-21T20:40:44.000Z (over 1 year ago)
• Last Synced: 2024-10-26T22:14:41.316Z (2 months ago)
• Language: Mathematica
• Size: 972 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Causal2TimedFormalization

Sources for the formalization in Matita of the implication between causal reversibility and time reversibility.

The repository contains the formalization of the main theorem presented in the paper ``Causal Reversibility Implies Time Reversibility''

submitted at QEST 2023.

## Structure of the repository

The repository contains the following files:

- formalization.pdf: a PDF file relating the definitions and theorems in the

  paper with those in the formalization

- causal2timed.ma: it caontins all the definitions and proofs in the paper

  require for Theorem 2, which is the main result

  of the paper that is formalized in Matita

- z_axioms.ma: the previous file depends on this one that provides an axiomatization of integer numbers

- z.ma: this file shows a model of the axioms in z_axioms.ma (or, equivalently, an implementation of integer numbers that

  satisfy the axiomatization given in z_axioms and used in the proof)

- complements.ma: it contains some facts not necessary for the main proof; the file is not required by causal2timed.ma

## How to check the proof

The formalization can be checked by Matita version >= 0.99.5, that can be downloaded from [matita](https://github.com/sacerdot/matita).

The easiest way to compile matita is to setup [opam](https://opam.ocaml.org/doc/Install.html) with OCaml version 4.14.1 and then do

```opam pin .''' in the directory where you downloaded matita.

Once installed, it is sufficient to start Matita with ```matita causal2timed.ma''' and then press the ```Execute all''' button to verify

everything in the main file and in the ones included by it.