Evaluation strategy

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In computer science, an evaluation strategy is a set of (usually deterministic) rules for determining the evaluation of expressions in a programming language. Emphasis is typically placed on functions or operators — an evaluation strategy defines when and in what order the arguments to a function are evaluated, when they are substituted into the function, and what form that substitution takes. The lambda calculus, a formal system for the study of functions, has often been used to model evaluation strategies, where they are usually called reduction strategies. Evaluation strategies divide into two basic groups, strict and non-strict, based on how arguments to a function are handled. A language may combine several evaluation strategies; for example, C++ combines call-by-value with call-by-reference. Most languages that are predominantly strict use some form of non-strict evaluation for boolean expressions and if-statements.

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[edit] Strict evaluation

In strict evaluation, the arguments to a function are always evaluated completely before the function is applied.

Under Church encoding, eager evaluation of operators maps to strict evaluation of functions; for this reason, strict evaluation is sometimes called "eager". Most existing programming languages use strict evaluation for functions.

[edit] Applicative order

Applicative order (or leftmost innermost) evaluation refers to an evaluation strategy in which the arguments of a function are evaluated from left to right in a post-order traversal of reducible expressions (redexes). Unlike call-by-value, applicative order evaluation reduces terms within a function body as much as possible before the function is applied.

[edit] Call by value

Call-by-value evaluation is the most common evaluation strategy, used in languages as far-ranging as C and Scheme. In call-by-value, the argument expression is evaluated, and the resulting value is bound to the corresponding variable in the function (usually by capture-avoiding substitution or by copying the value into a new memory region). If the function or procedure is able to assign values to its parameters, only the local copy is assigned -- that is, anything passed into a function call is unchanged in the caller's scope when the function returns.

Call-by-value is not a single evaluation strategy, but rather the family of evaluation strategies in which a function's argument is evaluated before being passed to the function. While many programming languages that use call-by-value evaluate function arguments left-to-right, some (such as O'Caml) evaluate functions and their arguments right-to-left.

[edit] Call by reference

In call-by-reference evaluation, a function is passed an implicit reference to its argument rather than the argument value itself. If the function is able to modify such a parameter, then any changes it makes will be visible to the caller as well. If the argument expression is an L-value, its address is used. Otherwise, a temporary object is constructed by the caller and a reference to this object is passed; the object is then discarded when the function returns.

Some languages contain a notion of references as first-class values. ML, for example, has the "ref" constructor; references in C++ may also be created explicitly. In these languages, "call-by-reference" may be used to mean passing a reference value as an argument to a function.

In languages (such as C) that contain unrestricted pointers instead of or in addition to references, call-by-address is a variant of call-by-reference where the reference is an unrestricted pointer.

[edit] Call by copy-restore

Call-by-copy-restore, call-by-value-result or call-by-value-return (as termed in the Fortran community) is a special case of call-by-reference where the provided reference is unique to the caller. If a parameter to a function call is a reference that might be accessible by another thread of execution, its contents are copied to a new reference that is not; when the function call returns, the updated contents of this new reference are copied back to the original reference ("restored").

The semantics of call-by-value-return also differ from those of call-by-reference where two or more function arguments alias one another; that is, point to the same variable in the caller's environment. Under call-by-reference, writing to one will affect the other; call-by-value-return avoids this by giving the function distinct copies, but leaves the result in the caller's environment undefined (depending on which of the aliased arguments is copied back first).

When the reference is passed to the callee uninitialized, this evaluation strategy may be called call-by-result.

[edit] Partial evaluation

Main article: partial evaluation

In partial evaluation, evaluation may continue into the body of a function that has not been applied. Any sub-expressions that do not contain unbound variables are evaluated, and function applications whose argument values are known may be reduced. In the presence of side-effects, complete partial evaluation may produce unintended results; for this reason, systems that support partial evaluation tend to do so only for "pure" expressions (expressions without side-effects) within functions.

[edit] Non-strict evaluation

In non-strict evaluation, arguments to a function are not evaluated unless they are actually used in the evaluation of the function body.

Under Church encoding, lazy evaluation of operators maps to non-strict evaluation of functions; for this reason, non-strict evaluation is sometimes referred to as "lazy".[citation needed] Boolean expressions in many languages use lazy evaluation; in this context it is often called short circuiting. Conditional expressions also usually use lazy evaluation, albeit for different reasons.

[edit] Normal order

Normal-order (or leftmost outermost) evaluation is the evaluation strategy where the outermost redex is always reduced, applying functions before evaluating function arguments. It differs from call-by-name in that call-by-name does not evaluate inside the body of an unapplied function.

[edit] Call by name

In call-by-name evaluation, the arguments to functions are not evaluated at all — rather, function arguments are substituted directly into the function body using capture-avoiding substitution. If the argument is not used in the evaluation of the function, it is never evaluated; if the argument is used several times, it is re-evaluated each time. (See Jensen's Device.)

Call-by-name evaluation can be preferable over call-by-value evaluation because call-by-name evaluation always yields a value when a value exists, whereas call-by-value may not terminate if the function's argument is a non-terminating computation that is not needed to evaluate the function. Opponents of call-by-name claim that it is significantly slower when the function argument is used, and that in practice this is almost always the case.

Call-by-name evaluation is rarely implemented directly, but frequently used in considering theoretical properties of programs and programming languages. Real-world languages with call-by-name semantics tend to be implemented using call-by-need evaluation. Call-by-name is the default evaluation in ALGOL.

[edit] Call by need

Call-by-need is a memoized version of call-by-name where, if the function argument is evaluated, that value is stored for subsequent uses. In a "pure" (effect-free) setting, this produces the same results as call-by-name; when the function argument is used two or more times, call-by-need is almost always faster.

Because evaluation of expressions may happen arbitrarily far into a computation, languages using call-by-need generally do not support computational effects (such as mutation) except through the use of monads. This eliminates any unexpected behavior from variables whose values change prior to their delayed evaluation.

Haskell is perhaps the most well-known language that uses call-by-need evaluation.

[edit] Call by macro expansion

Call-by-macro-expansion is similar to call-by-name, but uses textual substitution rather than capture-avoiding substitution. With uncautious use, macro substitution may result in variable capture and lead to undesired behavior. Hygienic macros avoid this problem by checking for and replacing shadowed variables that are not parameters.

[edit] Nondeterministic strategies

[edit] Full β-reduction

Under full β-reduction, any function application may be reduced (substituting the function's argument into the function using capture-avoiding substitution) at any time. This may be done even within the body of an unapplied function.

[edit] Call by future

Call-by-future (or parallel call-by-name) is like call-by-need, except that the function's argument may be evaluated in parallel with the function body (rather than only if used). The two threads of execution synchronize when the argument is needed in the evaluation of the function body; if the argument is never used, the argument thread may be killed.

[edit] Optimistic evaluation

Optimistic evaluation is another variant of call-by-need in which the function's argument is partially evaluated for some amount of time (which may be adjusted at runtime), after which evaluation is aborted and the function is applied using call-by-need. This approach avoids some of the runtime expense of call-by-need, while still retaining the desired termination characteristics.

[edit] See also

[edit] References

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