# Quark: Common combinators for Elixir
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# Table of Contents
- [Quick Start](#quick-start)
- [Summary](#summary)
- [Includes](#includes)
- [Functional Overview](#functional-overview)
- [Curry](#curry)
- [Functions](#functions)
- [Macros](#macros-defcurry-and-defcurryp)
- [Partial](#partial)
- [Macros](##macros-defpartial-and-defpartialp)
- [Pointfree](#pointfree)
- [Compose](#compose)
- [Common Combinators](#common-combinators)
- [Classics](#classics)
- [SKI System](#ski-system)
- [BCKW System](#bckw-system)
- [Fixed Point](#fixed-point)
- [Sequence](#sequence)
# Quick Start
```elixir
def deps do
[{:quark, "~> 2.3"}]
end
defmodule MyModule do
use Quark
# ...
end
```
# Summary
[Elixir](http://elixir-lang.org) is a functional programming language,
but it lacks some of the common built-in constructs that many other functional
languages provide. This is not all-together surprising, as Elixir has a strong
focus on handling the complexities of concurrency and fault-tolerance, rather than
deeper functional composition of functions for reuse.
## Includes
- A series of classic combinators (SKI, BCKW, and fixed-points), along with friendlier aliases
- Fully-curried and partially applied functions
- Macros for defining curried and partially applied functions
- Composition helpers
- Composition operator: `<|>`
- A plethora of common functional programming primitives, including:
- `id`
- `flip`
- `const`
- `pred`
- `succ`
- `fix`
- `self_apply`
# Functional Overview
## Curry
### Functions
`curry` creates a 0-arity function that curries an existing function. `uncurry` applies arguments to curried functions, or if passed a function creates a function on pairs.
### Macros: `defcurry` and `defcurryp`
Why define the function before currying it? `defcurry` and `defcurryp` return
fully-curried 0-arity functions.
```elixir
defmodule Foo do
import Quark.Curry
defcurry div(a, b), do: a / b
defcurryp minus(a, b), do: a - b
end
# Regular
div(10, 2)
# => 5
# Curried
div.(10).(5)
# => 2
# Partially applied
div_ten = div.(10)
div_ten.(2)
# => 5
```
## Partial
:crown: We think that this is really the crowning jewel of `Quark`.
`defpartial` and `defpartialp` create all arities possible for the defined
function, bare, partially applied, and fully curried.
This does use up the full arity-space for that function name, however.
### Macros: `defpartial` and `defpartialp`
```elixir
defmodule Foo do
import Quark.Partial
defpartial one(), do: 1
defpartial minus(a, b, c), do: a - b - c
defpartialp plus(a, b, c), do: a + b + c
end
# Normal zero-arity
one
# => 1
# Normal n-arity
minus(4, 2, 1)
# => 1
# Partially-applied first two arguments
minus(100, 5).(10)
# => 85
# Partially-applied first argument
minus(100).(10).(50)
# => 40
# Fully-curried
minus.(10).(2).(1)
# => 7
```
## Pointfree
Allows defining functions as straight function composition (ie: no need to state the argument).
Provides a clean, composable named functions. Also doubles as an aliasing device.
```elixir
defmodule Contrived do
import Quark.Pointfree
defx sum_plus_one, do: Enum.sum() |> fn x -> x + 1 end.()
end
Contrived.sum_plus_one([1,2,3])
#=> 7
```
## Compose
Compose functions to do convenient partial applications.
Versions for composing left-to-right and right-to-left are provided
The operator `<|>` is done "the math way" (right-to-left).
The operator `<~>` is done "the flow way" (left-to-right).
Versions on lists also available.
```elixir
import Quark.Compose
# Regular Composition
sum_plus_one = fn x -> x + 1 end <|> &Enum.sum/1
sum_plus_one.([1,2,3])
#=> 7
add_one = &(&1 + 1)
piped = fn x -> x |> Enum.sum |> add_one.() end
composed = add_one <|> &Enum.sum/1
piped.([1,2,3]) == composed.([1,2,3])
#=> true
sum_plus_one = (&Enum.sum/1) <~> fn x -> x + 1 end
sum_plus_one.([1,2,3])
#=> 7
# Reverse Composition (same direction as pipe)
x200 = (&(&1 * 2)) <~> (&(&1 * 10)) <~> (&(&1 * 10))
x200.(5)
#=> 1000
add_one = &(&1 + 1)
piped = fn x -> x |> Enum.sum() |> add_one.() end
composed = (&Enum.sum/1) <~> add_one
piped.([1,2,3]) == composed.([1,2,3])
#=> true
```
## Common Combinators
A number of basic, general functions, including `id`, `flip`, `const`, `pred`, `succ`, `fix`, and `self_apply`.
## Classics
### SKI System
The SKI system combinators. `s` and `k` alone can be combined to express any
algorithm, but not usually with much efficiency.
We've aliased the names at the top-level (`Quark`), so you can use `const`
rather than having to remember what `k` means.
```elixir
1 |> i()
#=> 1
"identity combinator" |> i()
#=> "identity combinator"
Enum.reduce([1,2,3], [42], &k/2)
#=> 3
```
### BCKW System
The classic `b`, `c`, `k`, and `w` combinators. A similar "full system" as SKI,
but with some some different functionality out of the box.
As usual, we've aliased the names at the top-level (`Quark`).
```elixir
c(&div/2).(1, 2)
#=> 2
reverse_concat = c(&Enum.concat/2)
reverse_concat.([1,2,3], [4,5,6])
#=> [4,5,6,1,2,3]
repeat = w(&Enum.concat/2)
repeat.([1,2])
#=> [1,2,1,2]
```
### Fixed Point
Several fixed point combinators, for helping with recursion. Several formulations are provided,
but if in doubt, use `fix`. Fix is going to be kept as an alias to the most efficient
formulation at any given time, and thus reasonably future-proof.
```elixir
fac = fn fac ->
fn
0 -> 0
1 -> 1
n -> n * fac.(n - 1)
end
end
factorial = y(fac)
factorial.(9)
#=> 362880
```
### Sequence
Really here for `pred` and `succ` on integers, by why stop there?
This works with any ordered collection via the `Quark.Sequence` protocol.
```elixir
succ 10
#=> 11
42 |> origin() |> pred() |> pred()
#=> -2
```
