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A functional program is a set of functions defined by equations or rules. A functional computation consists of replacing subexpressions by equal (with regard to the function definitions) subexpressions until no more replacements (or reductions) are possible and a value or normal form is obtained. For
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to a value selected from among alternatives imposed by constraints. Each possible value is tried in some order, with the remainder of the program invoked in each case to determine the validity of the binding. Narrowing is an extension of logic programming, in that it performs a similar search, but
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Based on this specification, one can define a function that satisfies this specification by employing logic programming features. Similarly to logic languages, functional logic languages provide search for solutions for existentially quantified variables. In contrast to pure logic languages, they
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r is applicable for reduction if its condition c has been solved. In contrast to purely functional languages where conditions are only evaluated to a
Boolean value, functional logic languages support the solving of conditions by guessing values for the unknowns in the condition. Narrowing as
796:” is used for equational constraints in order to provide a syntactic distinction from defining equations. Similarly, extra variables (i.e., variables not occurring in the left-hand side of the defining equation) are explicitly declared by “
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Since Curry is able to solve equations containing function calls with unknown values, its execution mechanism is based on non-deterministic computations, similarly to logic programming. This mechanism supports also the definition of
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719:” is also useful to specify the behavior of other functions on lists. For instance, the behavior of a function last that yields the last element of a list can be specified as follows: for all lists xs and elements e,
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with non-deterministic search strategies. In contrast to Prolog, which uses backtracking to search for solutions, Curry does not fix a particular search strategy. Hence, there are implementations of Curry, like
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are written as . We can define operations on recursive types by inductive definitions where pattern matching supports the convenient separation of the different cases. For instance, the concatenation operation
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It is nearly a superset of
Haskell but does not support all language extensions of Haskell. In contrast to Haskell, Curry has built-in support for non-deterministic computations involving search.
896:. Functional patterns are enabled by the combined functional and logic features of Curry and support concise definitions of tasks requiring deep pattern matching in hierarchical data structures.
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Narrowing is useful because it allows a function to be treated as a relation: its value can be computed "in both directions". The Curry examples of the previous section illustrate this.
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Due to the absence of side effects, a functional logic program can be executed with different strategies. To evaluate expressions, Curry uses a variant of the
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This article is about the programming language Curry (named in honour of a mathematician and logician). For the mathematician and logician, see
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1399:(Braßel, Fischer, Hanus, Reck, 2010) on modeling lazy non-deterministic (logic) programming (like in Curry) in a purely functional language (
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As noted in the prior section, narrowing can be thought of as reduction on a program term graph, and there are often many different ways (
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Functions on
Booleans can be defined by pattern matching, i.e., by providing several equations for different argument values:
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The principle of replacing equals by equals is still valid provided that the actual arguments have the required form, e.g.:
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show an important feature of Curry: all rules are tried in order to evaluate some operation. Hence, one can define by
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Haskell does not allow such a declaration since the pattern in the left-hand side contains a defined function (
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Sergio, Antoy; Hanus, Michael (2006). "Overlapping Rules and Logic
Variables in Functional Logic Programs".
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560:. For instance, a list of elements, where the type of elements is arbitrary (denoted by the type variable
467:: the value of a computed result does not depend on the order or time of evaluation, due to the absence of
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shown above expresses the fact that the actual argument must match the result of narrowing the expression
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by enumerating their constructors. For instance, the type of
Boolean values consists of the constructors
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832:) to reduce a given term graph. Antoy et al. proved in the 1990s that a particular narrowing strategy,
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There is also another order of evaluation if we replace the arguments of operators from right to left:
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can actually generate values as part of the search rather than just being limited to testing them.
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an operation to insert an element into a list at an indeterminate position so that the operation
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operator, that returns one of its arguments. This operator is defined by the following rules:
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Sergio, Antoy; Hanus, Michael (2006). "Declarative
Programming with Function Patterns".
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1332:- A web-based execution environment for Curry and Haskell with various example programs
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support equation solving over nested functional expressions so that an equation like ys
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Sergio, Antoy; Echahed, Rachid; Hanus, Michael (2007). "A Needed
Narrowing Strategy".
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In this case, both derivations lead to the same result, a property known as
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language. It merges elements of functional and logic programming, including
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discussed in the next section is used to solve this kind of conditions.
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Transforming
Functional Logic Programs into Monadic Functional Programs
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1288:. Lecture Notes in Computer Science. Vol. 4079. pp. 87–101.
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Sergio, Antoy; Hanus, Michael (2010). "Functional Logic
Programming".
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Beyond its application for various programming tasks, the operation “
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456:'double (1+2)' → (1+2)+'(1+2)' → '(1+2)'+3 → '3+3' → 6
450:'double (1+2)' → '(1+2)'+(1+2) → 3+'(1+2)' → '3+3' → 6
439:” to be defined by an infinite set of equations, e.g.,
564:), is either the empty list “” or the non-empty list “
1135:"Curry: A Truly Integrated Functional Logic Language"
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Purely
Functional Lazy Non-deterministic Programming
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1112:"Current release:PAKCS Version 3.6.0 (10/11/23)"
1065:returns any permutation of a given input list.
817:Narrowing is a mechanism whereby a variable is
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1338:- A collection of software packages for Curry
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614:” is usually written as and finite lists x1
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23:. For the computer science technique, see
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120:Learn how and when to remove this message
1103:
923:Thus, the evaluation of the expression
549:not '(not False)' → 'not True' → False
2285:Nondeterministic programming languages
2270:Functional logic programming languages
1353:A major Curry implementation, targets
1344:- The Münster Curry Compiler, targets
175:Ludwig Maximilian University of Munich
56:Please improve this article by adding
2280:Programming languages created in 1995
478:do, Curry supports the definition of
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2275:Haskell programming language family
1375:, and supports fair parallel search
388:language, an implementation of the
160:Michael Hanus, Sergio Antoy, et al.
2265:Experimental programming languages
2213:Category:Mathematical philosophers
474:As many functional languages like
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1393:(Fischer, Kiselyov, Shan, 2009),
892:). Such a pattern is also called
69:"Curry" programming language
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187:Complutense University of Madrid
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920:x ? y = x x ? y = y
2300:Software using the BSD license
2295:Academic programming languages
490:that are declared as follows:
435:if we interpret the operator “
191:Technical University of Madrid
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58:secondary or tertiary sources
907:non-deterministic operations
390:functional logic programming
2123:Curry–Howard correspondence
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2223:Category:Mathematicians
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1133:Hanus, Michael (ed.).
398:constraint programming
45:relies excessively on
2143:Programming languages
1506:York Haskell Compiler
1222:10.1145/347476.347484
179:University of Münster
150:, non-strict, modular
2290:Literate programming
2202:Open-source software
2111:computer programming
2021:Open-source software
1092:breadth-first search
558:recursive data types
480:algebraic data types
231:/ (10 November 2023)
16:Programming language
1216:(4). ACM: 776–822.
938:The rules defining
848:Functional patterns
556:can be obtained by
197:First appeared
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2233:Category:Logicians
1976:Simon Peyton Jones
1921:Lennart Augustsson
1876:Real World Haskell
1541:Concurrent Haskell
1379:Curry Mailing List
1294:10.1007/11799573_9
1261:10.1007/11680093_2
1210:Journal of the ACM
1114:. 10 November 2023
1088:depth-first search
894:functional pattern
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792:Here, the symbol “
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65:Find sources:
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43:This article
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21:Haskell Curry
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1981:David Roundy
1961:Simon Marlow
1926:Richard Bird
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2106:mathematics
1991:Audrey Tang
1971:Erik Meijer
1946:John Hughes
1603:TidalCycles
1440:programming
1193:2 September
1118:14 November
1013:defined by
931:as well as
572:and a list
319:/curry-lang
313:.informatik
225:3.6.0
2249:Categories
1941:Paul Hudak
1678:QuickCheck
1098:References
1069:Strategies
925:0 ? 1
830:strategies
610:The type “
461:confluence
144:functional
80:newspapers
47:references
2102:Namesakes
1886:Community
1847:SQream DB
1796:git-annex
1727:wxHaskell
1656:Libraries
1230:0004-5411
913:, called
813:Narrowing
351:target),
343:target),
315:.uni-kiel
166:Developer
110:July 2019
2128:Currying
1986:Joe Stoy
1634:Bluespec
1523:Dialects
1461:features
1447:Software
1369:Curry2Go
1238:47275506
1188:MVPS.net
1170:14578759
927:returns
425:double 1
297:3-clause
262:Platform
255:inferred
139:Paradigm
25:Currying
2192:Italics
2165:Haskell
2012:Italics
1840:Paradox
1802:Haddock
1778:Cardano
1752:Servant
1722:Fudgets
1547:Cryptol
1438:Haskell
1401:Haskell
1364:Haskell
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476:Haskell
445:1+2 = 3
441:1+1 = 2
394:Haskell
370:Haskell
359:target)
357:Haskell
302:Website
290:License
205: (
94:scholar
1916:Arvind
1895:Eponym
1833:Pandoc
1828:LOLITA
1790:Ganeti
1733:xmonad
1672:Parsec
1588:Orwell
1355:Prolog
1300:
1267:
1236:
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1045:insert
998:insert
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842:Prolog
612:List a
374:Prolog
341:Prolog
328:Major
309:.pages
267:x86-64
251:strong
247:static
96:
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2152:Brook
1815:House
1808:HaXml
1784:Darcs
1764:Yesod
1703:Stack
1697:Cabal
1639:(BSV)
1580:Ωmega
1573:Idris
1553:Curry
1495:Gofer
1360:KiCS2
1351:PAKCS
1234:S2CID
1166:S2CID
1084:KiCS2
819:bound
775:where
659:->
656:->
535:False
529:False
510:False
488:False
384:is a
382:Curry
353:KiCS2
337:PAKCS
307:curry
283:Linux
148:logic
133:Curry
101:JSTOR
87:books
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1758:Snap
1628:Atom
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1298:ISBN
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321:.org
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