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When I write something like map (1+) list in Haskell, what is the internal representation of (1+)? Since it is a partial application of (+), the argument 1 has to be saved somewhere, but I can't get my head around this. Can somebody give me a brief explanation, how currying and partial application is implemented?
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Intuitively, partial function application says "if you fix the first arguments of the function, you get a function of the remaining arguments". For example, if function div(x,y) = x/y, then div with the parameter x fixed at 1 is another function: div1(y) = div(1,y) = 1/y.
Application in JavaScript means that a function is applied to its argument and produces a return value. So partial application also has to do with applying functions to some of their arguments. The function that is applied partially is returned to be used later.
Partial function application refers to calling a multiple parameter function with less than its total number of parameters. This results in a new function taking the remaining number of parameters.
Simple answer. Currying: Lets you call a function, splitting it in multiple calls, providing one argument per-call. Partial Application: Lets you call a function, splitting it in multiple calls, providing multiple arguments per-call.
Partially applied functions (and, indeed, pretty much everything else in the Haskell heap) are represented as closures -- a structure combining a code pointer, and argument slots. Specifically, we call values that are not in a fully evaluated form thunks.
See this earlier question on boxed data and the GHC manual on how thunks are represented.
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