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Vendor loophp
Package combinator
Short Description A curated list of combinators
License MIT

Keywords combinator educational functional programming combinatory logic

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Informations about the package combinator

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Combinator

Description

This package provides a list of well known Combinators.

A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments. It was introduced in 1920 by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. Combinators which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions - and to remove any mention of variables - particularly in predicate logic.

Requirements

PHP >= 8

Installation

Available combinators

Name	Alias	Composition	Composition using S and K	Haskell	Lambda calculus	Term definition (JS like)	Type	# Arguments
A	Apply	`SK(SK)`	`(S(K))(S(K))`	`$`	`λab.ab`	`a => b => a(b)`	`(a -> b) -> a -> b`	2
B	Bluebird	`S(KS)K`	`S(KS)K`	`.`	`λabc.a(bc)`	`a => b => c => a(b(c))`	`(a -> b) -> (c -> a) -> c -> b`	3
Blackbird	Blackbird	`BBB`	`(S(K(S(KS)K)))(S(KS)K)`	`...`	`λabcd.a(bcd)`	`a => b => c => => d => a(b(c)(d))`	`(c -> d) -> (a -> b -> c) -> a -> b -> d`	4
C	Cardinal	`S(BBS)(KK)`	`((S((S(K(S(KS)K)))S))(KK))`	`flip`	`λabc.acb`	`a => b => c => a(c)(b)`	`(a -> b -> c) -> b -> a -> c`	3
D	Dove	`BB`	`(S(K(S(KS)K)))`		`λabcd.ab(cd)`	`a => b => c => d => a(b)(c(d))`	`(a -> c -> d) -> a -> (b -> c) -> b -> d`	4
E	Eagle	`B(BBB)`	`(S(K((S(K(S(KS)K)))((S(KS))K))))`		`λabcde.ab(cde)`	`a => b => c => d => e => a(b)(c(d)(e))`	`(a -> d -> e) -> a -> (b -> c -> d) -> b -> c -> e`	5
F	Finch	`ETTET`	`((S(K((S((SK)K))(K((S(K(S((SK)K))))K)))))((S(K((S(K(S(KS)K)))((S(KS))K))))((S(K(S((SK)K))))K)))`		`λabc.cba`	`a => b => c => c(b)(a)`	`a -> b -> (b -> a -> c) -> c`	3
G	Goldfinch	`BBC`	`((S(K(S(KS)K)))((S((S(K(S(KS)K)))S))(KK)))`		`λabcd.ad(bc)`	`a => b => c => d => a(d)(b(c))`	`(a -> b -> c) -> (d -> b) -> d -> a -> c`	4
H	Hummingbird	`BW(BC)`	`((S(K((S(K(S((S(K((S((SK)K))((SK)K))))((S(K(S(KS)K)))((S(K(S((SK)K))))K))))))K)))(S(K((S((S(K(S(KS)K)))S))(KK)))))`		`λabc.abcb`	`a => b => c => a(b)(c)(b)`	`(a -> b -> a -> c) -> a -> b -> c`	3
I	Idiot	`SKK`	`((SK)K)`	`id`	`λa.a`	`a => a`	`a -> a`	1
J	Jay	`B(BC)(W(BC(E)))`	`((S(K(S(K((S((S(K(S(KS)K)))S))(KK))))))((S((S(K((S((SK)K))((SK)K))))((S(K(S(KS)K)))((S(K(S((SK)K))))K))))(K((S(K((S((S(K(S(KS)K)))S))(KK))))(S(K((S(K(S(KS)K)))((S(KS))K))))))))`		`λabcd.ab(adc)`	`a => b => c => d => a(b)(a(d)(c))`	`(a -> b -> b) -> a -> b -> a -> b`	4
K	Kestrel	`K`	`K`	`const`	`λab.a`	`a => b => a`	`a -> b -> a`	2
Ki	Kite	`KI`	`(K((SK)K))`		`λab.b`	`a => b => b`	`a -> b -> b`	2
L	Lark	`CBM`	`((S((S(KS))K))(K((S((SK)K))((SK)K))))`		`λab.a(bb)`	`a => b => a(b(b))`		2
M	Mockingbird	`SII`	`((S((SK)K))((SK)K))`		`λa.aa`	`a => a(a)`		1
O	Owl	`SI`	`(S((SK)K))`		`λab.b(ab)`	`a => b => b(a(b))`	`((a -> b) -> a) -> (a -> b) -> b`	2
Omega	Ω	`MM`	`(((S((SK)K))((SK)K))((S((SK)K))((SK)K)))`		`λa.(aa)(aa)`	`a => (a(a))(a(a))`		1
Phoenix					`λabcd.a(bd)(cd)`	`a => b => c => d => a(b(d))(c(d))`	`(a -> b -> c) -> (d -> a) -> (d -> b) -> d -> c`	4
Psi				`on`	`λabcd.a(bc)(bd)`	`a => b => c => d => a(b(c))(b(d))`	`(a -> a -> b) -> (c -> a) -> c -> c -> b`	4
Q	Queer	`CB`	`((S(K(S((S(KS))K))))K)`	`(##)`	`λabc.b(ac)`	`a => b => c => b(a(c))`	`(a -> b) -> (b -> c) -> a -> c`	3
R	Robin	`BBT`	`((S(K(S(KS)K)))((S(K(S((SK)K))))K))`		`λabc.bca`	`a => b => c => b(c)(a)`	`a -> (b -> a -> c) -> b -> c`	3
S	Starling	`S`	`S`	`<*>`	`λabc.ac(bc)`	`a => b => c => a(c)(b(c))`	`(a -> b -> c) -> (a -> b) -> a -> c`	3
S_				`<*>`	`λabc.a(bc)c`	`a => b => c => a(b(c))(c)`	`(a -> b -> c) -> (b -> a) -> b -> c`	3
S2				`<*>`	`λabcd.a((bd)(cd))`	`a => b => c => d => a(b(d))(c(d))`	`(b -> c -> d) -> (a -> b) -> (a -> c) -> a -> d`	4
T	Thrush	`CI`	`((S(K(S((SK)K))))K)`	`(&)`	`λab.ba`	`a => b => b(a)`	`a -> (a -> b) -> b`	2
U	Turing	`LO`	`((S(K(S((SK)K))))((S((SK)K))((SK)K)))`		`λab.b(aab)`	`a => b => b(a(a)(b))`		2
V	Vireo	`BCT`	`((S(K((S((S(K(S(KS)K)))S))(KK))))((S(K(S((SK)K))))K))`		`λabc.cab`	`a => b => c => c(a)(b)`	`a -> b -> (a -> b -> c) -> c`	3
W	Warbler	`C(BMR)`	`((S(K(S((S(K((S((SK)K))((SK)K))))((S(K(S(KS)K)))((S(K(S((SK)K))))K))))))K)`		`λab.abb`	`a => b => a(b)(b)`	`(a -> a -> b) -> a -> b`	2
Y	Y-Fixed point				`λa.(λb(a(bb))(λb(a(bb))))`	`a => (b => b(b))(b => a(c => b(b)(c)))`		1
Z	Z-Fixed point				`λa.M(λb(a(Mb)))`			1

Usage

Simple combinators

Y combinator

Contributing

Feel free to contribute by sending pull requests. We are a usually very responsive team and we will help you going through your pull request from the beginning to the end.

For some reasons, if you can't contribute to the code and willing to help, sponsoring is a good, sound and safe way to show us some gratitude for the hours we invested in this package.

Sponsor me on Github and/or any of the contributors.

Thanks

Authors

Pol Dellaiera

Changelog

See CHANGELOG.md for a changelog based on git commits.

For more detailed changelogs, please check the release changelogs.

All versions of combinator with dependencies

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Package Version

Version 2.0.2 Release 04. Aug 2021
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