https://github.com/andreasabel/ipl

Agda formalization of Intuitionistic Propositional Logic
https://github.com/andreasabel/ipl

Last synced: 5 months ago
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Agda formalization of Intuitionistic Propositional Logic

• Host: GitHub
• URL: https://github.com/andreasabel/ipl
• Owner: andreasabel
• License: unlicense
• Created: 2018-05-16T07:35:12.000Z (about 8 years ago)
• Default Branch: master
• Last Pushed: 2025-11-14T19:44:21.000Z (7 months ago)
• Last Synced: 2025-11-14T21:25:40.407Z (7 months ago)
• Language: TeX
• Size: 2.99 MB
• Stars: 22
• Watchers: 3
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# ipl [![Build Status](https://travis-ci.org/andreasabel/ipl.svg?branch=master)](https://travis-ci.org/andreasabel/ipl)

Agda formalization of Intuitionistic Propositional Logic (IPL)

[Agda HTML listing](https://andreasabel.github.io/ipl/html/Everything.html).

## Normalization by Evaluation for IPL, Call-By-Push-Value, and Polarized Lambda Calculus (without soundness)

The simple Normalization by Evaluation (NbE) algorithm

that produces from every IPL (CBPV, resp.) derivation a normal derivation.

Version published 2019-02-16 on arXiv:

* Article [Normalization by Evaluation for Call-by-Push-Value and Polarized Lambda-Calculus](https://arxiv.org/abs/1902.06097)

* Formalization of Section 2, [NbE of IPL using a Cover Monad](https://andreasabel.github.io/ipl/html/NfModelMonad.html)

* Formalization of (a variant of) Section 3, [NbE for Call-by-Push-Value](https://andreasabel.github.io/ipl/html-cbpv/NfCBPV.html)

* Partial formalization of Section 4, [Syntax and Semantics of Polarized Lambda-Calculus](https://andreasabel.github.io/ipl/html-focusing/Polarized.html)

Version presented 2018-07-19 at the

[Initial Types Club](https://github.com/InitialTypes/Club):

* [PDF Handout](https://andreasabel.github.io/ipl/nbeSum.pdf)

* [Agda HTML listing](https://andreasabel.github.io/ipl/html/NfModelCaseTree.html)

## Soundness

Soundness of NbE means that the computational behavior (functional

interpretation) of IPL proofs is preserved by normalization.

We implement sound-by-construction NbE using Kripke predicates.

* [Agda HTML listing](https://andreasabel.github.io/ipl/html/NbeModel.html).