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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 . Most of the frame of the current procedure is no longer needed, and can be replaced by the frame of the tail call, modified as appropriate (similar to ...
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 ...
In Python, non-innermost-local and not-declared-global accessible names are all aliases. Among dynamically-typed languages, Python is moderately type-checked. Implicit conversion is defined for numeric types (as well as booleans), so one may validly multiply a complex number by an integer (for instance) without explicit casting.
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:
Every call in CPS is a tail call, and the continuation is explicitly passed. Using CPS without tail call optimization (TCO) will cause not only the constructed continuation to potentially grow during recursion, but also the call stack. This is usually undesirable, but has been used in interesting ways—see the Chicken Scheme compiler. As CPS ...
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 ...
The Scheme language standard requires implementations to support proper tail recursion, meaning they must allow an unbounded number of active tail calls. [60] [61] Proper tail recursion is not simply an optimization; it is a language feature that assures users that they can use recursion to express a loop and doing so would be safe-for-space. [62]
That is, a statement such as x = expression; (i.e. the assignment of the result of an expression to a variable) clearly calls for the expression to be evaluated and the result placed in x, but what actually is in x is irrelevant until there is a need for its value via a reference to x in some later expression whose evaluation could itself be ...