Curry: An Integrated Functional Logic Language

4.1.8 Strings
The type String is an abbreviation for [Char], i.e., strings are considered as lists of characters.
String constants are enclosed in double quotes. Thus, the string constant "Hello" is identical to
the character list [’H’,’e’,’l’,’l’,’o’]. A term can be converted into a string by the function
show :: a -> String
For instance, the result of (show 42) is the character list [’4’,’2’].
4.1.9 Tuples
If t1, t2, . . . , tn are types and n ≥ 2, then (t1,t2,...,tn) denotes the type of all n-tuples. The
elements of type (t1,t2,...,tn) are (x1,x2,...,xn) where xi is an element of type ti (i = 1, . . . , n).
Thus, for each n, the tuple-building operation (,. . .,) (with n − 1 commas) can be considered as
an n-ary constructor introduced by the pseudo-declaration
data (a1,a2, . . . ,an) = (,. . .,) a1 a2...an
where (x1,x2,...,xn) is equivalent to the constructor application “(,. . .,) x1 x2...xn”.
The unit type () has only a single element () and can be considered as defined by
data () = ()
Thus, the unit type can also be interpreted as the type of 0-tuples.
4.2 Type System
Curry is a strongly typed language with a Hindley/Milner-like polymorphic type system [13]. 8 Each
variable, constructor and operation has a unique type, where only the types of constructors have
to be declared by datatype declarations (see Section 2.1). The types of functions can be declared
(see Section 2.3) but can also be omitted. In the latter case they will be reconstructed by a type
inference mechanism.
Note that Curry is an explicitly typed language, i.e., each function has a type. The type can only
be omitted if the type inferencer is able to reconstruct it and to insert the missing type declaration.
In particular, the type inferencer can reconstruct only those types which are visible in the module
(cf. Section 6). Each type inferencer of a Curry implementation must be able to insert the types of
the parameters and the free variables (cf. Section 2.5) for each rule. The automatic inference of the
types of the defined functions might require further restrictions depending on the type inference
method. Therefore, the following definition of a well-typed Curry program assumes that the types
of all defined functions are given (either by the programmer or by the type inferencer). A Curry
implementation must accept a well-typed program if all types are explicitly provided but should
also support the inference of function types according to [13].
A type expression is either a type variable, a basic type like Bool, Success, Int, Float, Char
(or any other type constructor of arity 0), or a type constructor application of the form (T τ1 . . . τn)
8 The extension of the type system to Haskell’s type classes is not included in the kernel language but may be
considered in a future version.
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