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Tail recursion modulo cons is a generalization of tail-recursion optimization introduced by David H. D. Warren [9] in the context of compilation of Prolog, seen as an explicitly set once language. It was described (though not named) by Daniel P. Friedman and David S. Wise in 1974 [10] as a LISP compilation technique. As the name suggests, it ...
The significance of tail recursion is that when making a tail-recursive call (or any tail call), the caller's return position need not be saved on the call stack; when the recursive call returns, it will branch directly on the previously saved return position. Therefore, in languages that recognize this property of tail calls, tail recursion ...
Continuation passing style can be used to implement continuations and control flow operators in a functional language that does not feature first-class continuations but does have first-class functions and tail-call optimization. Without tail-call optimization, techniques such as trampolining, i.e. using a loop that iteratively invokes thunk ...
Iterative algorithms can be implemented by means of recursive predicates. Prolog systems typically implement a well-known optimization technique called tail call optimization (TCO) for deterministic predicates exhibiting tail recursion or, more generally, tail calls: A clause's stack frame is discarded before performing a call in a tail ...
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 . g) z.
As with direct recursion, tail call optimization is necessary if the recursion depth is large or unbounded, such as using mutual recursion for multitasking. Note that tail call optimization in general (when the function called is not the same as the original function, as in tail-recursive calls) may be more difficult to implement than the ...
Tail-recursive algorithms can be converted to iteration through a process called tail-recursion elimination or tail-call optimization. Deforestation ( data structure fusion) In languages where it is common for a sequence of transformations to be applied to a list, deforestation attempts to remove the construction of intermediate data structures.
A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n , until reaching the base case ...