package combic

Combic: A Lightweight OCaml Library for Combinatory Logic

Combic is a minimalistic OCaml library that provides a simple implementation of combinatory logic lambdas with their associated bird names. It offers a straightforward way to incorporate combinators into your projects without the need for external dependencies.

Introduction

Combinatory logic is a branch of mathematical logic that describes computation using combinators, which are higher-order functions that rely solely on function application to achieve desired results. Combic makes these combinators readily available in OCaml, allowing you to leverage their power in a concise and elegant manner.

Installation

To use Combic in your OCaml project, you can install it via OPAM:

opam install combic

(* Return first argument, ignoring second *)
let first = kestrel 1 2 (* Returns 1 *)

(* Return second argument, ignoring first *)
let second = penguin 1 2 (* Returns 2 *)

(* Passes a single value to both arguments of a binary function *)
let double = warbler ( * ) 2 (* Returns 4 *)

(* Flip the arguments of a binary function *)
let concatenated = cardinal String.concat ["a"; "b"] "," (* Returns "a,b" *)

(* Function composition *)
let inc_and_double = bluebird ( * ) (( + ) 1) 3 (* Returns 8 *)

Combinators

Combic provides the following combinators with their associated bird names:

• identity (i): Returns the first argument, ignoring the second.

• kestrel (k): Returns the first argument, ignoring the second.

• penguin (pi): Returns the second argument, ignoring the first.

• warbler (w): Passes a single value to both arguments of a binary function.

• cardinal (c): Flips the arguments of a binary function.

• bluebird (b): Function composition.

• blackbird (b1): Composition where the second function takes two arguments.

• blunting (b2): Composition where the second function takes three arguments.

• becard (b3): Composition with three functions.

• starling (s): Composition with three functions (different order).

• violetstarling (sigma): Composition with three functions (different order).

• dove (d): Composition with three functions (different order).

• zebradove (delta): Composition with three functions (different order).

• phoenix (fi): Composition with three functions (different order).

• dickcissel (d1): Composition with four functions.

• dovekie (d2): Composition with four functions (different order).

• eagle (e): Composition with four functions (different order).

• goldeneagle (epsilon): Composition with four functions (different order).

• pheasant (fi1): Composition with four functions (different order).

• baldeagle (ehat): Composition with five functions.

Each combinator is a higher-order function that takes one or more functions as arguments and returns a new function. The combinators can be used to compose, flip, or apply functions in various ways, enabling more concise and expressive code.

For example, warbler takes a binary function and a value, and returns a new function that applies the original function to the given value twice. cardinal flips the arguments of a binary function, allowing you to partially apply the arguments in a different order.

The composition combinators, like bluebird, blackbird, blunting, and others, enable you to compose multiple functions together, creating a new function that applies the functions in a specific order.

These combinators provide a powerful and elegant way to manipulate and combine functions in OCaml, promoting code reuse and enhancing the expressiveness of your code.

Contributing

Contributions to Combic are welcome. If you find any issues or have suggestions for improvements, please open an issue or submit a pull request on the GitHub repository.

License

This project is under an MIT License... do what you want with it.