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If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations. Tail calls can be implemented without adding a new stack frame to the call stack.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
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 ...
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
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 ...
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 ...
A simple tail recursive parser can be written much like a recursive descent parser. The typical algorithm for parsing a grammar like this using an abstract syntax tree is: Parse the next level of the grammar and get its output tree, designate it the first tree, F; While there is terminating token, T, that can be put as the parent of this node:
Hazard symbols; List of mathematical constants (typically letters and compound symbols) Glossary of mathematical symbols; List of physical constants (typically letters and compound symbols) List of common physics notations (typically letters used as variable names in equations) Rod of Asclepius / Caduceus as a symbol of medicine