See also ComposeFunction

An operation on functions, usually denoted by a middot, a circle or juxtaposition.  In the following, let us denote composition by a lowercase 'o'.

 (f o g)(x) = f(g(x))

In HaskellLanguage, we have the predefined function "." which is composition:

 f . g = \x -> f (g x)

Composition can be used extensively to build processing lines out of individual building blocks.  You often see code as the following in Haskell:

 nextmoves breadth = pruneBadMoves breadth . pruneImpossible . genNextMoves
 pruneBadMoves breadth = pruneByValue breadth . estimateMove . pruneByDepth 3
 ...

Some people define InverseFunctionalComposition to avoid these read-last-to-first definitions, e.g.

 f >>> g = \x -> g (f x) -- in Haskell's Control.Category

''...and some people use ForthLanguage or JoyLanguage instead.''

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In SmlLanguage, we have the predefined operator "o" which is composition

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JoyLanguage shows that you can do almost everything with just composition of well-chosen primitives.
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CategoryFunctionalProgramming