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Collection of forms and higher order functions that assist function composition and definition of functions in a point-free style

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==========

[Documentation](http://pkg-build.racket-lang.org/doc/point-free/index.html)

Collection of forms and higher order functions that assist function composition and definition of functions in a point-free style. Point-free functions are functions that don't name their arguments, they're created purely by composing other functions. For example:

```racket
(define number->symbol (compose string->symbol number->string))
```

Racket functions have symmetry between output and input values. This means that functions can accept multiple values and return multiple output values. This makes point-free functions more difficult to define, because regular function composition can be unwieldy. Contrast this to a language like Haskell, where functions can only accept and return one value.

There are two ways to compose two functions of one input and one output `f` and `g`. You can chain the output of `g` to the input of `f` with standard function composition, as in `(compose f g)`. However, you can also make a function that accepts two values, gives one to `f` and one to `g`, and returns both outputs as two values. Basically, functions can be composed in *series* or in *parallel*.

This package defines several convenient ways of composing functions to make point-free logic clean and simple to express. Composing functions in parallel can be done with the `join` function:

```racket
(define add1-sub1 (join add1 sub1))
(add1-sub1 10 10) ;; evaluates to (values 11 9)
```

The function `join*` takes a function and joins it with itself repeatedly

```racket
(define add1-each (join* add1))
(add1-each 1 2 3) ;; evaluates to (values 2 3 4)
```

On its own this function is rarely useful, but it can be combined elegantly with `compose`. Here's a point-free function that finds the hypotenuse of a right triangle (with `sqr` being a function that squares a number)

```racket
(define pythagoras (compose sqrt + (join* sqr)))
(pythagoras 3 4) ;; evaluates to 5
(pythagoras 5 12) ;; evaluates to 13
```

Another included primitive composition function is `thrush`, which is the reverse of `compose` - the first function given to `thrush` gets inputs first, then gives its output to the second, which gives its output to the third, etc.:

```racket
(define symbol-length-even?
  (thrush symbol->string
          string-length
          even?))
(symbol-length-even? 'foo) ;; #f
(symbol-length-even? 'barbaz) ;; #t
```

Some functions that combine these primitive composition operators together are included, including `wind*`, which takes three functions and essentially "wraps" the first function - all inputs to it are transformed with the second function, and all outputs from the first are transformed with the third:

```racket
(define pythagoras (wind* + sqr sqrt))
(pythagoras 3 4) ;; evaluates to 5
(pythagoras 5 12) ;; evaluates to 13
```

Variations on this function are also provided, as well as a more general `wind` function that can transform different inputs and outputs to the wound function with different transformer functions.

A few macros for defining point-free functions with these composition operators are also included:

```racket
(define/compose first-even?
  even? first)
(define/thrush symbol-length-even?
  symbol->string string->number even?)
(define/wind* pythagoras
  + sqr sqrt)

(first-even? '(2 3 4)) ;; #t
(symbol-length-even? 'foo) ;; #f
(pythagoras 3 4) ;; 5
```

This package also supplies a way to compose functions that know how many arguments they have. The `arg-count` form takes an expression that produces a function and an identifier, and binds that identifier to contain the number of arguments given to the produced function in the expression:

```racket
(define num-args-received
  (arg-count n (const n)))
(num-args-received 'foo 'bar 'baz) ;; evaluates to 3
```

A definition form is also included:

```racket
(define/arg-count num-args-received n
  (const n))
```

Combining this with syntax extensions for defining anonymous functions such as [`fancy-app`](https://github.com/samth/fancy-app) yields very succinct function definitions:

```racket
(define/arg-count average n
  (compose (/ _ n) +))
(average 8 10 12) ;; evaluates to 10
```

To install, run `raco pkg install point-free`. Then to use in a module, `(require point-free)`.

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