Curry: An Integrated Functional Logic Language

type RecF a = a -> RecF a -- recursive definitions not allowed
type Place = [Addr] -- mutually recursive definitions not allowed
type Addr = [Place]
However, recursive definitions with an intervening datatype are allowed, since recursive datatype
definitions are also allowed. For instance, the following definitions are valid:
type Place = [Addr]
data Addr = Tag [Place]
2.3 Function Declarations
A function is defined by a type declaration (which can be omitted) followed by a list of defining
equations. A type declaration for an n-ary function has the form
f :: τ1 -> τ2 -> · · · -> τn -> τ
where τ1, . . . , τn, τ are type expressions and τ is not a functional type. The simplest form of a
defining equation (or rule) for an n-ary function f (n ≥ 0) is
f t1 . . . tn = e
where t1, . . . , tn are data terms and the right-hand side e is an expression. The left-hand side
f t1 . . . tn must not contain multiple occurrences of a variable. Functions can also be defined by
conditional equations which have the form
f t1 . . . tn | c = e
where the condition c is a constraint (cf. Section 2.6). In order to apply a conditional equation, its
condition must be solved.
Note that one can define functions with a non-determinate behavior by providing several rules
with overlapping left-hand sides or free variables (i.e., variables which do not occur in the left-hand
side) in the conditions or right-hand sides of rules. For instance, the following non-deterministic
function inserts an element at an arbitrary position in a list:
insert x [] = [x]
insert x (y:ys) = x : y : ys
insert x (y:ys) = y : insert x ys
Such non-deterministic functions can be given a perfect declarative semantics [18] and their implementation
causes no overhead in Curry since techniques for handling non-determinism are already
contained in the logic programming part (see also [4]). However, deterministic functions are advantageous
since they provide for more efficient implementations (like the dynamic cut [34]). If one is
interested only in defining deterministic functions, this can be ensured by the following restrictions:
1. Each variable occurring in the right-hand side of a rule must also occur in the corresponding
left-hand side.
2. If f t1 . . . tn | c = e and f t ′ 1 . . . t′ n | c ′ = e ′ are rules defining f and σ is a substitu-
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