OCaml library : Stdlib.Fun

# Module Stdlib.Fun

    module Fun: Fun

## Combinators

    val id : 'a -> 'a

`id` is the identity function. For any argument `x`, `id x` is `x`.

    val const : 'a -> 'b -> 'a

`const c` is a function that always returns the value `c`. For any argument `x`, `(const c) x` is `c`.

    val compose : ('b -> 'c) -> ('a -> 'b) -> 'a -> 'c

`compose f g` is a function composition of applying `g` then `f`. For any arguments `f`, `g`, and `x`, `compose f g x` is `f (g x)`.

- Since 5.2

    val flip : ('a -> 'b -> 'c) -> 'b -> 'a -> 'c

`flip f` reverses the argument order of the binary function `f`. For any arguments `x` and `y`, `(flip f) x y` is `f y x`.

    val negate : ('a -> bool) -> 'a -> bool

`negate p` is the negation of the predicate function `p`. For any argument `x`, `(negate p) x` is `not (p x)`.

## Exception handling

    val protect : finally:(unit -> unit) -> (unit -> 'a) -> 'a

`protect ~finally work` invokes `work ()` and then `finally ()` before `work ()` returns with its value or an exception. In the latter case the exception is re-raised after `finally ()`. If `finally ()` raises an exception, then the exception `Fun.Finally_raised` is raised instead.

`protect` can be used to enforce local invariants whether `work ()` returns normally or raises an exception. However, it does not protect against unexpected exceptions raised inside `finally ()` such as `Out_of_memory`, `Stack_overflow`, or asynchronous exceptions raised by signal handlers (e.g. `Sys.Break`).

Note: It is a programming error if other kinds of exceptions are raised by `finally`, as any exception raised in `work ()` will be lost in the event of a `Fun.Finally_raised` exception. Therefore, one should make sure to handle those inside the finally.

    exception Finally_raised of exn

`Finally_raised exn` is raised by `protect ~finally work` when `finally` raises an exception `exn`. This exception denotes either an unexpected exception or a programming error. As a general rule, one should not catch a `Finally_raised` exception except as part of a catch-all handler.

## Examples

### Combinators

Combinators provide a lightweight and sometimes more readable way to create anonymous functions, best used as short-lived arguments rather than standalone definitions. The examples below will demonstrate this mainly with the `List` module.

#### id

`List.init` with the index itself

      # List.init 3 Fun.id;;
      - : int list = [0; 1; 2]

Using `List.filter_map` on an `int option list` to filter out `None` elements

      # List.filter_map Fun.id [None; Some 2; Some 3; None; Some 5];;
      - : int list = [2; 3; 5]

Conditionally dispatching functions of type `foo -> foo` or taking them as arguments is another place where `id` may be useful. Consider a primitive logging function which prints a string but gives its user the option to preformat the string before printing, e.g. to insert a time-stamp

      let log ?(preformat : string -> string = Fun.id) message =
        print_endline (preformat message)

Whenever we may build up closures, `id` is often used for the base-case as a no-op. Consider a function which chains a list of unary functions:

      let rec chain = function
        | [] -> Fun.id
        | f :: fs -> fun x -> f (chain fs x)

#### const

`List.init` a list of zeros

      # List.init 3 (Fun.const 0);;
      - : int list = [0; 0; 0]

An allow-all predicate that could be passed to any filtering function e.g. `List.filter` to disable filtration and get back all values

      # List.filter (Fun.const true) [1; 2; 3];;
      - : int list = [1; 2; 3]

Note that applying `const (...)` evaluates the expression `(...)` once, and returns a function that only has the result of this evaluation. To demonstrate this, consider if `(...)` was a call to `Random.bool``()`:

`List.init n (Fun.const (Random.bool()))` for any `n > 0` will have exactly two possible outcomes,

- `[true; true; ...; true]`
- `[false; false; ...; false]`

whereas `List.init n (fun _ -> Random.bool())` will have 2n possible outcomes, because the randomness effect is performed with every element.

For more real-world uses, consider `String.spellcheck` with a constant max distance of 2, instead of the default variable max distance

      let spellcheck known_words word =
        let dict_iter yield = List.iter yield known_words in
        String.spellcheck ~max_dist:(Fun.const 2) dict_iter word

#### flip

Useing `flip` to reverse the comparator passed to `List.sort`, which sorts in the opposite order

      # List.sort (Fun.flip Int.compare) [5; 3; 9; 0; 1; 6; 8];;
      - : int list = [9; 8; 6; 5; 3; 1; 0]

Reversing a list by accumulating a new list using `List.fold_left`, which expects the accumulator to be the first argument of the function passed to it. We pass `List.cons` which has the list as the second argument, so `flip` is useful here

      # List.fold_left (Fun.flip List.cons) [] [1; 2; 3];;
      - : int list = [3; 2; 1]

Interestingly, `flip` can work with functions that aren't binary, by flipping the first two arguments and leaving the rest in order. This is because a function that takes `n+2` arguments is, conceptually, a binary function which returns a function that takes `n` arguments. Given a function `f : a -> b -> c -> d`:

- `flip f` will have type `b -> a -> c -> d`
- `fun x -> flip (f x)` will have type `a -> c -> b -> d`

Using `flip` with non-binary functions like this is discouraged, for its negative impact on readability and reasoning.

#### negate

Mainly used for reversing a predicate in a function which expects one, like `List.find_all` and similar functions

Finding all lists which are not empty using `List.is_empty`

      # List.find_all (Fun.negate List.is_empty) [[0]; [1; 2; 3]; []; [4; 5]];;
      - : int list list = [[0]; [1; 2; 3]; [4; 5]]

From a given list of paths, finding all paths which are not occupied using `Sys.file_exists`

      # List.find_all (Fun.negate Sys.file_exists);;
      - : string list -> string list = <fun>

#### compose

`List.map` on pair elements with a function on the second element

      # List.map (Fun.compose String.length snd) [1, "one"; 2, "two"; 3, "three"];;
      - : int list = [3; 3; 5]

A potential implementation of `Fun.negate`

      let negate f = Fun.compose not f

From the `chain` example, `compose` could have been used in the recursive branch

      let rec chain = function
        | [] -> Fun.id
        | f :: fs -> Fun.compose f (chain fs)

Or even more concisely

      let chain fs = List.fold_right Fun.compose fs Fun.id

From the `spellcheck` example, `compose` and `flip` could be used to condense the function definition so it becomes

      # Fun.compose
          (String.spellcheck ~max_dist:(Fun.const 2))
          (Fun.flip List.iter)
        ;;
      - : string list -> string -> string list = <fun>

As can be seen here, this heavily impacts readability and the ability to reason about the function. Both `String.spellcheck` and `Fun.flip` are not unary, so there is a non-trivial interaction with partial-application in this definition.

Heavy use of these combinators in OCaml is generally discouraged, not only because they can quickly impact readability and reasoning, but also because the produced functions are often in value form, thus subject to the Value Restriction (see the manual section 6.1.2).