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Like logic programming, narrowing〔 〕 〔 〕 of algebraic value sets gives a method of reasoning about the values in unsolved or partially solved equations. Where logic programming relies on resolution, the algebra of value sets relies on narrowing rules. Narrowing rules allow the elimination of values from a solution set which are inconsistent with the equations being solved. Unlike logic programming, narrowing of algebraic value sets makes no use of backtracking. Instead all values are contained in value sets, and are considered in parallel. The approach is also similar to the use of constraints〔 〕 in constraint logic programming, but without the logic processing basis. Probabilistic value sets is a natural extension of value sets to deductive probability. The value set construct holds the information required to calculate probabilities of calculated values based on probabilities of initial values. == History == Early programming languages were imperative. These implement functionality by allowing change to be represented. The assignment statement allows a variable to change its value. In mathematics a variable's value may not change. This is fundamental to the mathematical approach. Functional languages based on lambda calculus allow this mathematical approach to programming. Functional languages developed by implementing lazy evaluation, and allowing functions to be passed as parameters. Lazy evaluation is an essential feature of modern functional programming languages such as Haskell. Haskell is the latest in a series of languages based on lambda calculus and let expressions. These languages provide rich functionality through lazy evaluation, and a polymorphic type system using type inference. Functional programming languages also naturally support higher-order functions. Logic programming based on Resolution developed alongside functional programming. Logic programming is a form of relational programming that makes deductions about values. Constraint logic programming extends logic programming, by supporting constraints. Constraint logic programming languages such as ECLiPSe provide the ability to solve complex logic problems. However ECLiPSe is not lazy. Logic programming languages, although they have greater deduction abilities, never gained the power and flexibility of functional languages. Narrowing is a technique that allows logical deduction, with the flexibility of functional languages. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Narrowing of algebraic value sets」の詳細全文を読む スポンサード リンク
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