# Clojure: Partial Function (Currying)

`partial`

is for creating a new function with a pre-filled argument(s) of a given function.

`partial`

is a function that decompose a function by pre-fill `n` count its parameters. It returns a function g. When g is called with no arguments, it is equivalent to calling ƒ with `n` args. When g is given args, they are feed to ƒ starting with the unfilled args.

Let's use math notation here.

Suppose you have a function ƒ that takes 3 args. You have:

ƒ[x, y, z]

when you call

partial[ƒ,a]

it returns a function, let's call it g.

When g is invoked

g[]

is equivalent to

ƒ[a]

All together, it's this:

(partial[ƒ,a])[] = ƒ[a]

if g is given args, it is feed to ƒ, starting with ƒ's second arg. That is,

(partial[ƒ,a])[] = ƒ[a] (partial[ƒ,a])[b] = ƒ[a,b] (partial[ƒ,a])[b,c] = ƒ[a,b,c]

If `partial`

is given more args, it consumes more args from ƒ.

(partial[ƒ,a,b])[] = ƒ[a,b] (partial[ƒ,a,b])[x1] = ƒ[a,b,x1] (partial[ƒ,a,b])[x1,x2] = ƒ[a,b,x1,x2]

Let's use Clojure for example.

Suppose your function f[a,b,c] takes 3 args.

(defn f "join one or more strings" [& args] (apply str args)) (f "a" "b" "c") ; ⇒ "a b c" ;; define g. To be partial of f, feeding it 3 as first arg (def g (partial f "3")) (g) ; ⇒ "3" (g "4") ; ⇒ "34"

## Function Composition

`(comp)`

`(comp f)`

`(comp f g)`

`(comp f g & fs)`

Takes a set of functions and returns a fn that is the composition of those fns. The returned fn takes a variable number of args, applies the rightmost of fns to the args, the next fn (right-to-left) to the result, etc.

;; example of compose (defn f1 "append 1 to string x" [x] (str x "1")) (defn f2 "append 2 to string x" [x] (str x "2")) (defn f3 "append 3 to string x" [x] (str x "3")) (f1 "a") ; "a1" (def g (comp f3 f2 f1 )) (g "x") ; "x123" (g "a" "x") ;; 1. Unhandled clojure.lang.ArityException ;; Wrong number of args (2) passed to: user/f1 ;; because f1 only takes 1 arg

## Apply

`(apply f args)`

`(apply f x args)`

`(apply f x y args)`

`(apply f x y z args)`

`(apply f a b c d & args)`

Applies fn f to the argument list formed by prepending intervening arguments to args.

;; example of apply ;; apply just takes all of its args, and feed to the function as multiple args, like unwrap the bracket (apply str ["a" "b"]) ; "ab" (apply str "1" ["a" "b"]) ; "1ab" (apply str "1" "2" ["a" "b"]) ; "12ab" ;; here's what str does ;; str takes 1 or more args of string, and return a joined string (str "a" "b") ; "ab" ;; can be just 1 arg (str "a" ) ; "a" ;; if arg is not a string, it's converted to string (str "a" ["a" "b"]) ; "a[\"a\" \"b\"]" (str "a" 1) ; "a1"

## Misc

`(trampoline `

call `f` `args`) `f` with `args`. If it returns a function, call it again (with no args). Repeat until it returns a value that is not a function, return that value. clojure.core/trampoline

`(constantly `

→ Returns a function that takes any number of arguments and returns `x`)`x`. clojure.core/constantly

`(complement `

→ Takes a fn `f`)`f` and returns a fn that takes the same arguments as `f`, has the same effects, if any, and returns the opposite truth value. clojure.core/complement

`(memoize `

→ Returns a memoized version of a referentially transparent function. The memoized version of the function keeps a cache of the mapping from arguments to results and, when calls with the same arguments are repeated often, has higher performance at the expense of higher memory use.
clojure.core/memoize`f`)