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43-456: KRC ( Kent Recursive Calculator ) is a lazy functional language developed by David Turner from November 1979 to October 1981 based on SASL , with pattern matching , guards and ZF expressions (now more usually called list comprehensions ). Two implementations of KRC were written: David Turner's original one in BCPL running on EMAS , and Simon J. Croft's later one in C under Unix , and KRC

86-466: A stream ) of Fibonacci numbers . The calculation of the n -th Fibonacci number would be merely the extraction of that element from the infinite list, forcing the evaluation of only the first n members of the list. Take for example this trivial program in Haskell : In the function numberFromInfiniteList , the value of infinity is an infinite range, but until an actual value (or more specifically,

129-429: A computation and performing it later is slower than performing it immediately. This can be alleviated through strictness analysis . Lazy evaluation can also introduce memory leaks due to unevaluated expressions. Some programming languages delay evaluation of expressions by default, and some others provide functions or special syntax to delay evaluation. In Miranda and Haskell , evaluation of function arguments

172-552: A method to evaluate them when the value is needed. The body of this method must contain the code required to perform this evaluation. Since the introduction of lambda expressions in Java SE8, Java has supported a compact notation for this. The following example generic interface provides a framework for lazy evaluation: The Lazy interface with its eval() method is equivalent to the Supplier interface with its get() method in

215-453: A polynomial number with call-by-need. Call-by-need embodies two optimizations - never repeat work (similar to call-by-value), and never perform unnecessary work (similar to call-by-name). Lazy evaluation can also lead to reduction in memory footprint , since values are created when needed. In practice, lazy evaluation may cause significant performance issues compared to eager evaluation. For example, on modern computer architectures, delaying

258-455: A reference to x in some later expression whose evaluation could itself be deferred, though eventually the rapidly growing tree of dependencies would be pruned to produce some symbol rather than another for the outside world to see. Lazy evaluation allows control structures to be defined normally, and not as primitives or compile-time techniques. For example, one can define if-then-else and short-circuit evaluation operators: These have

301-414: A single piece of state, like condition codes, then the logic required to update that state sequentially may become a performance bottleneck. The problem is particularly acute on some processors designed with pipelining (since 1990) or with out-of-order execution . Such a processor may require additional control circuitry to detect hidden side effects and stall the pipeline if the next instruction depends on

344-399: A specific value at a certain index) is needed, the list is not evaluated, and even then, it is only evaluated as needed (that is, until the desired index.) Provided the programmer is careful, the program completes normally. However, certain calculations may result in the program attempting to evaluate an infinite number of elements; for example, requesting the length of the list or trying to sum

387-408: A third. In computer windowing systems , the painting of information to the screen is driven by expose events which drive the display code at the last possible moment. By doing this, windowing systems avoid computing unnecessary display content updates. Another example of laziness in modern computer systems is copy-on-write page allocation or demand paging , where memory is allocated only when

430-469: A value immediately and then pass it on, which is useful if a constructor field should generally be lazy. However, neither of these techniques implements recursive strictness—for that, a function called deepSeq was invented. Also, pattern matching in Haskell 98 is strict by default, so the ~ qualifier has to be used to make it lazy. In Java , lazy evaluation can be done by using objects that have

473-487: A value stored in that memory is changed. Laziness can be useful for high performance scenarios. An example is the Unix mmap function, which provides demand driven loading of pages from disk, so that only those pages actually touched are loaded into memory, and unneeded memory is not allocated. MATLAB implements copy on edit , where arrays which are copied have their actual memory storage replicated only when their content

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516-522: Is false there will be no attempt at evaluating the Expression . Conversely, in an eager language the above definition for ifThenElse a b c would evaluate (a), (b), and (c) regardless of the value of (a). This is not the desired behavior, as (b) or (c) may have side effects , take a long time to compute, or throw errors. It is usually possible to introduce user-defined lazy control structures in eager languages as functions, though they may depart from

559-446: Is already available. If so, the stored result is simply returned. If not, the function is evaluated, and another entry is added to the lookup table for reuse. Lazy evaluation is difficult to combine with imperative features such as exception handling and input/output , because the order of operations becomes indeterminate. The opposite of lazy evaluation is eager evaluation , sometimes known as strict evaluation. Eager evaluation

602-499: Is an optimisation implemented in some compilers called strictness analysis , which, in some cases, allows the compiler to infer that a value will always be used. In such cases, this may render the programmer's choice of whether to force that particular value or not, irrelevant, because strictness analysis will force strict evaluation . In Haskell, marking constructor fields strict means that their values will always be demanded immediately. The seq function can also be used to demand

645-560: Is changed, possibly leading to an out of memory error when updating an element afterwards instead of during the copy operation. The number of beta reductions to reduce a lambda term with call-by-need is no larger than the number needed by call-by-value or call-by-name reduction. And with certain programs the number of steps may be much smaller, for example a specific family of lambda terms using Church numerals take an infinite amount of steps with call-by-value (i.e. never complete), an exponential number of steps with call-by-name, but only

688-586: Is commonly used to produce side effects, to update a system's state. By contrast, declarative programming is commonly used to report on the state of system, without side effects. Functional programming aims to minimize or eliminate side effects. The lack of side effects makes it easier to do formal verification of a program. The functional language Haskell eliminates side effects such as I/O and other stateful computations by replacing them with monadic actions. Functional languages such as Standard ML , Scheme and Scala do not restrict side effects, but it

731-413: Is customary for programmers to avoid them. Effect systems extend types to keep track of effects, permitting concise notation for functions with effects, while maintaining information about the extent and nature of side effects. In particular, functions without effects correspond to pure functions. Assembly language programmers must be aware of hidden side effects—instructions that modify parts of

774-681: Is delayed by default. In many other languages, evaluation can be delayed by explicitly suspending the computation using special syntax (as with Scheme's " delay " and " force " and OCaml 's " lazy " and " Lazy.force ") or, more generally, by wrapping the expression in a thunk . The object representing such an explicitly delayed evaluation is called a lazy future . Raku uses lazy evaluation of lists, so one can assign infinite lists to variables and use them as arguments to functions, but unlike Haskell and Miranda, Raku does not use lazy evaluation of arithmetic operators and functions by default. In lazy programming languages such as Haskell, although

817-416: Is idempotent if multiple applications of the subroutine have the same effect on the system state as a single application, in other words if the function from the system state space to itself associated with the subroutine is idempotent in the mathematical sense . For instance, consider the following Python program: setx is idempotent because the second application of setx to 3 has the same effect on

860-405: Is not evaluated as soon as it gets bound to a variable, but when the evaluator is forced to produce the expression's value. 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

903-459: Is often combined with memoization , as described in Jon Bentley 's Writing Efficient Programs . After a function's value is computed for that parameter or set of parameters, the result is stored in a lookup table that is indexed by the values of those parameters; the next time the function is called, the table is consulted to determine whether the result for that combination of parameter values

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946-418: Is said to have a side effect if it has any observable effect other than its primary effect of reading the value of its arguments and returning a value to the invoker of the operation. Example side effects include modifying a non-local variable , a static local variable or a mutable argument passed by reference ; raising errors or exceptions; performing I/O ; or calling other functions with side-effects. In

989-405: Is similar to constructing a new instance of an anonymous class that implements Lazy<Integer> with an eval method returning 1 . Each iteration of the loop links a to a new object created by evaluating the lambda expression inside the loop. Each of these objects holds a reference to another lazy object, b , and has an eval method that calls b.eval() twice and returns

1032-467: Is that generated object will always take the same amount of memory. From version 2.2 forward, Python manifests lazy evaluation by implementing iterators (lazy sequences) unlike tuple or list sequences. For instance (Python 2): In the .NET framework, it is possible to do lazy evaluation using the class System . Lazy < T > . The class can be easily exploited in F# using the lazy keyword, while

1075-427: Is the evaluation strategy employed in most programming languages . Lazy evaluation was introduced for lambda calculus by Christopher Wadsworth. For programming languages, it was independently introduced by Peter Henderson and James H. Morris and by Daniel P. Friedman and David S. Wise. Delayed evaluation is used particularly in functional programming languages. When using delayed evaluation, an expression

1118-473: The force method will force the evaluation. There are also specialized collections like Microsoft . FSharp . Collections . Seq that provide built-in support for lazy evaluation. In C# and VB.NET, the class System . Lazy < T > is directly used. Or with a more practical example: Another way is to use the yield keyword: Side effect (computer science) In computer science , an operation, function or expression

1161-501: The java.util.function library. Each class that implements the Lazy interface must provide an eval method, and instances of the class may carry whatever values the method needs to accomplish lazy evaluation. For example, consider the following code to lazily compute and print 2 : In the above, the variable a initially refers to a lazy integer object created by the lambda expression () -> 1 . Evaluating this lambda expression

1204-433: The range() function returns a generator which computes elements of the list on demand. Elements are only generated when they are needed (e.g., when print(r[3]) is evaluated in the following example), so this is an example of lazy or deferred evaluation: In Python 2.x is possible to use a function called xrange() which returns an object that generates the numbers in the range on demand. The advantage of xrange

1247-474: The default is to evaluate expressions only when they are demanded, it is possible in some cases to make code more eager—or conversely, to make it more lazy again after it has been made more eager. This can be done by explicitly coding something which forces evaluation (which may make the code more eager) or avoiding such code (which may make the code more lazy). Strict evaluation usually implies eagerness, but they are technically different concepts. However, there

1290-481: The elements of the list with a fold operation would result in the program either failing to terminate or running out of memory . As another example, the list of all Fibonacci numbers can be written in the programming language Haskell as: In Haskell syntax, " : " prepends an element to a list, tail returns a list without its first element, and zipWith uses a specified function (in this case addition) to combine corresponding elements of two lists to produce

1333-448: The language's syntax for eager evaluation: Often the involved code bodies need to be wrapped in a function value, so that they are executed only when called. Delayed evaluation has the advantage of being able to create calculable infinite lists without infinite loops or size matters interfering in computation. The actual values are only computed when needed. For example, one could create a function that creates an infinite list (often called

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1376-456: The original ran in time exponential in the number of iterations, the memoized version runs in linear time : Java's lambda expressions are just syntactic sugar . Anything that can be written with a lambda expression can be rewritten as a call to construct an instance of an anonymous inner class implementing the interface, and any use of an anonymous inner class can be rewritten using a named inner class, and any named inner class can be moved to

1419-429: The outermost nesting level. In JavaScript , lazy evaluation can be simulated by using a generator . For example, the stream of all Fibonacci numbers can be written, using memoization , as: In Python 2.x the range() function computes a list of integers. The entire list is stored in memory when the first assignment statement is evaluated, so this is an example of eager or immediate evaluation: In Python 3.x

1462-447: The presence of side effects, a program's behaviour may depend on history; that is, the order of evaluation matters. Understanding and debugging a function with side effects requires knowledge about the context and its possible histories. Side effects play an important role in the design and analysis of programming languages . The degree to which side effects are used depends on the programming paradigm. For example, imperative programming

1505-399: The processor state which are not mentioned in the instruction's mnemonic. A classic example of a hidden side effect is an arithmetic instruction that implicitly modifies condition codes (a hidden side effect) while it explicitly modifies a register (the intended effect). One potential drawback of an instruction set with hidden side effects is that, if many instructions have side effects on

1548-435: The program has constructed a linked list of 11 objects and that all of the actual additions involved in computing the result are done in response to the call to a.eval() on the final line of code. This call recursively traverses the list to perform the necessary additions. We can build a Java class that memoizes a lazy object as follows: This allows the previous example to be rewritten to be far more efficient. Where

1591-435: The results of those effects. Absence of side effects is a necessary, but not sufficient, condition for referential transparency. Referential transparency means that an expression (such as a function call) can be replaced with its value. This requires that the expression is pure , that is to say the expression must be deterministic (always give the same value for the same input) and side-effect free. Side effects caused by

1634-505: The same value as the first application to -3. One common demonstration of side effect behavior is that of the assignment operator in C . The assignment a = b is an expression that evaluates to the same value as the expression b , with the side effect of storing the R-value of b into the L-value of a . This allows multiple assignment: Because the operator right associates , this

1677-403: The sum. The variable b is needed here to meet Java's requirement that variables referenced from within a lambda expression be effectively final. This is an inefficient program because this implementation of lazy integers does not memoize the result of previous calls to eval . It also involves considerable autoboxing and unboxing . What may not be obvious is that, at the end of the loop,

1720-414: The system state as the first application: x was already set to 3 after the first application, and it is still set to 3 after the second application. A pure function is idempotent if it is idempotent in the mathematical sense . For instance, consider the following Python program: abs is idempotent because the second application of abs to the return value of the first application to -3 returns

1763-449: The time taken for an operation to execute are usually ignored when discussing side effects and referential transparency. There are some cases, such as with hardware timing or testing, where operations are inserted specifically for their temporal side effects e.g. sleep(5000) or for (int i = 0; i < 10000; ++i) {} . These instructions do not change state other than taking an amount of time to complete. A subroutine with side effects

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1806-419: The usual semantics, i.e., ifThenElse a b c evaluates (a), then if and only if (a) evaluates to true does it evaluate (b), otherwise it evaluates (c). That is, exactly one of (b) or (c) will be evaluated. Similarly, for EasilyComputed || LotsOfWork , if the easy part gives True the lots of work expression could be avoided. Finally, when evaluating SafeToTry && Expression , if SafeToTry

1849-496: Was the main language used for teaching functional programming at the University of Kent at Canterbury (UK) from 1982 to 1985. The direct successor to KRC is Miranda , which includes a polymorphic type discipline based on that of Milner's ML . This programming-language -related article is a stub . You can help Misplaced Pages by expanding it . Lazy evaluation The benefits of lazy evaluation include: Lazy evaluation

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