Curry: An Integrated Functional Logic Language

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Contents 1 Introduction 3 2 Programs 3 2.1 Datatype Declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Type Synonym Declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Function Declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Functions vs. Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.2 Conditional Equations with Boolean Guards . . . . . . . . . . . . . . . . . . 7 2.4 Local Declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Free Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Constraints and Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 Higher-order Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Operational Semantics 12 4 Types 14 4.1 Built-in Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1.1 Boolean Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.1.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.1.4 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.1.5 Floating Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1.6 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1.7 Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1.8 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.9 Tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Type System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Expressions 20 5.1 Arithmetic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.2 List Comprehensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.3 Case Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6 Modules 23 7 Input/Output 27 7.1 Monadic I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.2 Do Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 8 Encapsulated Search 29 8.1 Search Goals and Search Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 8.2 Local Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 8.3 Predefined Search Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 8.4 Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1
9 Interface to External Functions and Constraint Solvers 34 9.1 External Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 9.2 External Constraint Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 10 Literate Programming 36 11 Interactive Programming Environment 36 A Example Programs 38 A.1 Operations on Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 A.2 Higher-Order Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 A.3 Relational Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 A.4 Functional Logic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 A.5 Constraint Solving and Concurrent Programming . . . . . . . . . . . . . . . . . . . . 42 A.6 Concurrent Object-Oriented Programming . . . . . . . . . . . . . . . . . . . . . . . . 44 B Standard Prelude 46 C Syntax of Curry 59 C.1 Lexicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 C.2 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 C.3 Context Free Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 C.4 Infix Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 D Operational Semantics of Curry 64 D.1 Definitional Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 D.2 Computation Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 D.3 Committed Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 D.4 Equational Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 D.5 Higher-Order Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 D.6 Generating Definitional Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 D.7 Encapsulated Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 D.8 Eliminating Local Declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Bibliography 78 Index 82 2
Page 1: Curry An Integrated Functional Logi
Page 5 and 6: and introduces a new n-ary type con
Page 7 and 8: tion 3 with σ(t1 . . . tn) = σ(t
Page 9 and 10: since the variables occurring in pa
Page 11 and 12: tified variable (and, thus, it can
Page 13 and 14: such cases, anonymous functions (λ
Page 15 and 16: ❀ {x=1,y=3} (The empty constraint
Page 17 and 18: 4.1.3 Functions The type t1 -> t2 i
Page 19 and 20: 4.1.8 Strings The type String is an
Page 21 and 22: g :: [a] -> [b] -> ([a],[b]) g x y
Page 23 and 24: In the last translation rule, conca
Page 25 and 26: to the module head. For instance, a
Page 27 and 28: module main where import m1 hiding
Page 29 and 30: take a character (string) and produ
Page 31 and 32: which takes a search goal and produ
Page 33 and 34: instance, if we want to compute the
Page 35 and 36: Intuitively, a function f declared
Page 37 and 38: 10 Literate Programming To encourag
Page 39 and 40: A Example Programs This section con
Page 41 and 42: A.3 Relational Programming Here is
Page 43 and 44: A.5 Constraint Solving and Concurre
Page 45 and 46: A.6 Concurrent Object-Oriented Prog
Page 47 and 48: B Standard Prelude This section con
Page 49 and 50: not :: Bool -> Bool not True = Fals
Page 51 and 52: foldr1 _ [x] = x foldr1 f (x1:x2:xs
Page 53 and 54:
takeWhile _ [] = [] takeWhile p (x:
Page 55 and 56:
enumFromThen n1 n2 = iterate ((n2-n
Page 57 and 58:
putStr [] = done putStr (c:cs) = pu
Page 59 and 60:
owseList (g:gs) = browse g >> putCh
Page 61 and 62:
C.2 Layout Similarly to Haskell, a
Page 63 and 64:
SimplePattern ::= VariableID | _ |
Page 65 and 66:
D Operational Semantics of Curry Th
Page 67 and 68:
Computation step for a single expre
Page 69 and 70:
Eval [e; rule(l | c = r)] ⇒ {id
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to an expression): Eval [ϕ(e1, . .
Page 73 and 74:
Eval [try(g)] ⇒ ⎧ [] if Eval [c
Page 75 and 76:
D.8 Eliminating Local Declarations
Page 77 and 78:
f ′′ x1 . . . xk y1 . . . ym =
Page 79 and 80:
References [1] H. Aït-Kaci. An Ove
Page 81 and 82:
[29] T. Johnsson. Lambda Lifting: T
Page 83 and 84:
Index !!, 49 Dom, 64 VRan, 64 (), 1
Page 85 and 86:
higher-order equation, 6 id, 46 if_
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