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The maps to symbol, ↦, is a rightward arrow protruding from a vertical bar. It is used in mathematics and in computer science to denote functions.In Z notation, a specification language used in software development, [1] this symbol is called the maplet arrow and the expression x ↦ y is called a maplet.
Immediately invoked function expressions may be written in a number of different ways. [3] A common convention is to enclose the function expression – and optionally its invocation operator – with the grouping operator, [4] in parentheses, to tell the parser explicitly to expect an expression.
An inclusion map may also be referred to as an inclusion function, an insertion, [1] or a canonical injection. A "hooked arrow" ( U+ 21AA ↪ RIGHTWARDS ARROW WITH HOOK ) [ 2 ] is sometimes used in place of the function arrow above to denote an inclusion map; thus: ι : A ↪ B . {\displaystyle \iota :A\hookrightarrow B.}
For example, when writing :, the intent is that and are types, while the arrow is a type constructor, specifically, the function type or arrow type. Similarly, the Cartesian product X × Y {\displaystyle X\times Y} of types is constructed by the product type constructor × {\displaystyle \times } .
The anonymous function here is the multiplication of the two arguments. The result of a fold need not be one value. Instead, both map and filter can be created using fold. In map, the value that is accumulated is a new list, containing the results of applying a function to each element of the original list.
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Therefore, compilers will attempt to transform the first form into the second; this type of optimization is known as map fusion and is the functional analog of loop fusion. [2] Map functions can be and often are defined in terms of a fold such as foldr, which means one can do a map-fold fusion: foldr f z . map g is equivalent to foldr (f .
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