Welcome to the λLab!

This is a wiki for collaborative scientific work at the interface of Mathematics, Logic and Computer science, especially around the notions of computation and deduction.

Purpose

The λLab is a collective and open lab book centered around the Curry-Howard-Lambek correspondence, organised as a wiki. This short definition contains four principles.

The λLab is a lab book

Just as its big brother the nLab, the λLab is a lab book, i.e. a place to collect and keep track of everyday scientific work. In particular (but not exclusively), it can be

• a place for synthesising more ore less “well-known” material and “cleaning up” its presentation,
• a detailed record of pertinent references on the topics it covers,
• a laboratory for ongoing and future research.

As a consequence, the λLab is not an encyclopedy:

• Its content is work-in-progress. Don't expect it to be polished, complete material.
• Its content has variable statuses. Next to the (seemingly) encyclopedic material, there will be exploratory work, possibly lengthy digressions, etc.

The λLab is a collective project

Making this work collectively allows to join the efforts of everyone who is willing to make one. The selfish motivation for this is that the contributors will benefit from each others' work. The selfless motivation is that science is usually better when it is produced as a group.

This has three consequences.

• The content should be of common interest among the λLab community. The exploratory nature of the λLab does not mean that it is the place for personal notes.
• The style should be as neutral and understandable as possible. Literary experiments should be avoided.
• Discussion is part of the work and of the content. Each page on the λLab comes with a Talk page where the contributors are supposed to discuss the way they organise the material, and where hopefully new ideas and connections will appear.

The λLab is an open project

Making this work openly allows to benefit from the contributions of any passer-by (and incidentally, allows passers-by to benefit from it).

This means that you should feel free to contribute, even in a minimalistic way. On the other hand, the nLab motto is also valid here: “Be bold. If you find your eyebrows raised by some entry, don’t turn away to be the next one not to work on it.”

You are only requested to comply with the general spirit of the λLab, and with a few guidelines listed here. If you have any question, feel free to ask in the appropriate Talk page or in the Coffee room.

The λLab is driven by the Curry-Howard-Lambek correspondence

What (loosely) connects the material in the λLab is the interplay between

• the study of computation in Mathematics and Computer science,
• the formalisations of deduction in (mathematical) Logic,
• the various notions of semantics of the above in mathematical structures.

The (more or less formal) idea that these three are connected is the Curry-Howard-Lambek correspondence. A perspective oriented by this correspondence should be the general “bias” of the λLab. This implies that:

• This is an orientation, not a golden rule. Any contribution connected to this “backbone” is a priori welcome (remember: be bold!).
• Any other orientation is coincidental. At first, the contributors may come from some specific communities and the λLab may grow in an according direction. Any contribution balancing such a phenomenon is more than welcome.
• The λLab is not the nLab. There is no need to duplicate material from the nLab here (unless it is patent that the λLab is more appropriate). More importantly, similar material should probably be presented differently on the λLab and on the nLab.

Also, we mention Mathematics and Computer science but insights from and applications to other disciplines enter the scope of the λLab.

Technical matters

Viewing and editing the λLab

To correctly view the mathematical formulas in the λLab, you are advised to use a web browser that supports MathML. This is currently the case of all major browsers.

(Math rendering on the λLab is currently the result of a combination of MediaWiki's Math extension, runned server-side and therefore cacheable and faster, and of the KaTeX library, runned client-side but offering some essential additional features. The former is set up to render only MathML, the latter renders both HTML and MathML. You can force MathML rendering using some browser add-ons, e.g. Native MathML.)

Everybody is welcome if they want to contribute to the λLab. Contributors are only requested to take note of the writing guidelines and technical advice provided in the How to contribute page.

If you face difficulties while viewing or editing the λLab, please report it:

• here if you think you found a bug,
• here if you would like to request a technical improvement or a new feature,
• in the Coffee room if you are unsure, or in any other case.

Making use of the material from the λLab

The λLab is an open and public scientific project. Therefore:

• You are free to use and distribute the content from the λLab, provided you acknowledge the source and distribute it under similar terms. Formally, the material is distributed under the terms of CreativeCommons Attribution-ShareAlike 4.0 International license.
• The contributors should be aware that their contributions will be distributed under these terms.