Pattern calculus

Pattern calculus bases all computation on pattern matching of a very general kind. Like lambda calculus, it supports a uniform treatment of function evaluation. Also, it allows functions to be passed as arguments and returned as results. In addition, pattern calculus supports uniform access to the internal structure of arguments, be they pairs or lists or trees. Also, it allows patterns to be passed as arguments and returned as results. Uniform access is illustrated by a pattern-matching function that computes the size of an arbitrary data structure. In the notation of the programming language bondi, it is given by the recursive function let rec size = | x y -> (size x) + (size y) | x -> 1 The second, or default case matches the pattern against the argument and returns . This case is used only if the matching failed in the first case. The first, or special case matches against any compound, such as a non-empty list, or pair. Matching binds to the left component and to the right component. Then the body of the case adds the sizes of these components together. Similar techniques yield generic queries for searching and updating. Combining recursion and decomposition in this way yields path polymorphism. The ability to pass patterns as parameters (pattern polymorphism) is illustrated by defining a generic eliminator.…

Pattern calculus bases all computation on pattern matching of a very general kind. Like lambda calculus, it supports a uniform treatment of function evaluation. Also, it allows functions to be passed as arguments and returned as results. In addition, pattern calculus supports uniform access to the internal structure of arguments, be they pairs or lists or trees. Also, it allows patterns to be passed as arguments and returned as results. Uniform access is illustrated by a pattern-matching function that computes the size of an arbitrary data structure. In the notation of the programming language bondi, it is given by the recursive function let rec size = | x y -> (size x) + (size y) | x -> 1 The second, or default case matches the pattern against the argument and returns . This case is used only if the matching failed in the first case. The first, or special case matches against any compound, such as a non-empty list, or pair. Matching binds to the left component and to the right component. Then the body of the case adds the sizes of these components together. Similar techniques yield generic queries for searching and updating. Combining recursion and decomposition in this way yields path polymorphism. The ability to pass patterns as parameters (pattern polymorphism) is illustrated by defining a generic eliminator. Suppose given constructors for creating the leaves of a tree, and for converting numbers into counters. The corresponding eliminators are then elimLeaf = | Leaf y -> y elimCount = | Count y -> y For example, evaluates to as does . These examples can be produced by applying the generic eliminator to the constructors in question. It is defined by elim = | x -> | {y} x y -> y Now evaluates to | {y} Leaf y -> y which is equivalent to . Also is equivalent to . In general, the curly braces contain the bound variables of the pattern, so that is free and is bound in | {y} x y -> y . ==External links== Archive mirror of the links below (which are no longer online) — the original paper, but not most general. bondi programming language research site

Text derived from https://en.wikipedia.org/w/index.php?oldid=1136513868 under CC BY-SA 4.0; modifications have been made.