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[Utility & Helpers](/categories/utility) 4. / 5. loophp/church-encoding ActiveLibrary[Utility & Helpers](/categories/utility) loophp/church-encoding ====================== Church encoding in PHP 40[1 issues](https://github.com/loophp/church-encoding/issues)PHPCI passing Since Nov 10Pushed 3mo ago1 watchersCompare [ Source](https://github.com/loophp/church-encoding)[ Packagist](https://packagist.org/packages/loophp/church-encoding)[ RSS](/packages/loophp-church-encoding/feed)WikiDiscussions master Synced 1mo ago READMEChangelogDependenciesVersions (3)Used By (0) [![GitHub stars](https://camo.githubusercontent.com/53f95b59ac3558ac9bb8e71cd6d3a1d0bdee8fcdb97953d997692b911bdc6471/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f73746172732f6c6f6f7068702f6368757263682d656e636f64696e672e7376673f7374796c653d666c61742d737175617265)](https://packagist.org/packages/loophp/church-encoding)[![Sponsor on GitHub](https://camo.githubusercontent.com/f43e1f9ed3dc36b01e8cae156cf5e3fe01245deb7c49aed7ee2dfca00b446166/68747470733a2f2f696d672e736869656c64732e696f2f62616467652f53706f6e736f722d4769744875622d627269676874677265656e2e7376673f7374796c653d666c61742d737175617265)](https://github.com/sponsors/drupol) Church Encoding =============== [](#church-encoding) > A functional programming exercise in PHP demonstrating how data and logic can be represented purely using functions. In mathematics, **Church encoding** is a means of representing data and operators in the Lambda calculus. Church numerals are a representation of natural numbers using Lambda notation. The method is named after [Alonzo Church](https://en.wikipedia.org/wiki/Alonzo_Church), who first encoded data in the Lambda calculus this way. Church encoding is not intended as a practical implementation of primitive data types. Its main purpose is to show that primitive data types are not *necessary*to represent any computation. More information on [Wikipedia](https://en.wikipedia.org/wiki/Church_encoding). History ------- [](#history) This library was created for **personal educational purposes** and made public. It was inspired by the work of [Marcelo Camargo](https://github.com/haskellcamargo). Although available via Composer and [Packagist](https://packagist.org/packages/loophp/church-encoding), this library is primarily useful for **learning and experimentation** rather than production use. Installation ------------ [](#installation) ``` composer require loophp/church-encoding ``` Quick Example ------------- [](#quick-example) ``` use Loophp\ChurchEncoding\Church; // Church numerals $zero = Church::zero(); $one = Church::succ($zero); $two = Church::succ($one); // Church booleans $true = Church::true(); $false = Church::false(); echo $two->toInt(); // 2 ``` Documentation ------------- [](#documentation) ### Church numerals [](#church-numerals) Imagine a programming language that doesn’t support numbers or booleans, only **lambdas**. Could we still represent counting, addition, and multiplication? Yes: that’s the idea behind *Church numerals*. A Church numeral is a function with two parameters: `λf . λx . something` - The first parameter `f` is the *successor function*. - The second parameter `x` represents *zero*. Examples: - `C0 = λf . λx . x` - `C1 = λf . λx . f x` - `C2 = λf . λx . f (f x)` Each numeral applies the successor function `f` as many times as its numeric value. We can count, add, or multiply using these forms — though to “see” the result, we must count the applications of `f` manually. ### Church booleans [](#church-booleans) Booleans can also be represented using functions: - `true = λx . λy . x` - `false = λx . λy . y` These can be used to define logic operators: - `and = λM . λN . M (N true false) false` - `or = λM . λN . M true (N true false)` - `not = λM . M false true` References ---------- [](#references) - *Types and Programming Languages* ([TAPL](https://www.cis.upenn.edu/~bcpierce/tapl/)) - *Structure and Interpretation of Computer Programs* ([SICP](https://en.wikipedia.org/wiki/Structure_and_Interpretation_of_Computer_Programs)) - Lectures by [Robert “Corky” Cartwright](https://www.cs.rice.edu/~cork/) - Gabriel Lebec: [Part 1](https://www.youtube.com/watch?v=3VQ382QG-y4) and [Part 2](https://www.youtube.com/watch?v=pAnLQ9jwN-E) - Package [loophp/combinator](https://github.com/loophp/combinator) - [Lambda calculus on Wikipedia](https://en.wikipedia.org/wiki/Lambda_calculus) - [Church encoding on Wikipedia](https://en.wikipedia.org/wiki/Church_encoding) - [Programming with Less Than Nothing](https://joshmoody.org/blog/programming-with-less-than-nothing/) Code Quality, Tests and Benchmarks ---------------------------------- [](#code-quality-tests-and-benchmarks) Every change triggers automated tests via [GitHub Actions](https://github.com/loophp/church-encoding/actions). - Tests are written with [PHPSpec](http://www.phpspec.net/) (`composer phpspec`) - Static analysis via [PHPStan](https://github.com/phpstan/phpstan) and [Psalm](https://github.com/vimeo/psalm) - Mutation testing with [Infection](https://github.com/infection/infection) (`composer infection`) - Pre-commit checks with [GrumPHP](https://github.com/phpro/grumphp) (`composer grumphp`) Contributing ------------ [](#contributing) Contributions are welcome! Send a pull request on GitHub. If you prefer to support my open-source work financially, you can sponsor me on [GitHub](https://github.com/sponsors/drupol) or [PayPal](https://www.paypal.me/drupol). Project Status -------------- [](#project-status) This project is **feature-complete** and stable. It is maintained for educational purposes and may receive occasional compatibility updates. Changelog --------- [](#changelog) See [CHANGELOG.md](https://github.com/loophp/church-encoding/blob/master/CHANGELOG.md) for the commit-based changelog. For detailed release notes, visit [the release page](https://github.com/loophp/church-encoding/releases). ### Health Score 20 — LowBetter than 14% of packages Maintenance48 Moderate activity, may be stable Popularity4 Limited adoption so far Community10 Small or concentrated contributor base Maturity16 Early-stage or recently created project Bus Factor1 Top contributor holds 54.6% of commits — single point of failure How is this calculated?**Maintenance (25%)** — Last commit recency, latest release date, and issue-to-star ratio. Uses a 2-year decay window. **Popularity (30%)** — Total and monthly downloads, GitHub stars, and forks. Logarithmic scaling prevents top-heavy scores. **Community (15%)** — Contributors, dependents, forks, watchers, and maintainers. Measures real ecosystem engagement. **Maturity (30%)** — Project age, version count, PHP version support, and release stability. ### Community Maintainers ![](https://avatars.githubusercontent.com/u/252042?v=4)[Pol Dellaiera](/maintainers/drupol)[@drupol](https://github.com/drupol) --- Top Contributors [![drupol](https://avatars.githubusercontent.com/u/252042?v=4)](https://github.com/drupol "drupol (53 commits)")[![dependabot[bot]](https://avatars.githubusercontent.com/in/29110?v=4)](https://github.com/dependabot[bot] "dependabot[bot] (32 commits)")[![renovate[bot]](https://avatars.githubusercontent.com/in/2740?v=4)](https://github.com/renovate[bot] "renovate[bot] (12 commits)") --- Tags church-encodingeducationalfunctional-programminglearning ### Embed Badge ![Health badge](/badges/loophp-church-encoding/health.svg) ``` [![Health](https://phpackages.com/badges/loophp-church-encoding/health.svg)](https://phpackages.com/packages/loophp-church-encoding) ``` ### Alternatives [joaopaulolndev/filament-edit-env Package to edit env file 322.5k](/packages/joaopaulolndev-filament-edit-env) PHPackages © 2026 [Directory](/)[Categories](/categories)[Trending](/trending)[Changelog](/changelog)[Analyze](/analyze)