Curry: An Integrated Functional Logic Language

collect [g] = [g]
collect (g1:g2:gs) = concat (map solveAll (g1:g2:gs))
(concat concatenates a list of lists to a single list). For instance, if append is the list concatenation,
then the expression
solveAll \l -> append l [1] =:= [0,1]
reduces to [\l->l=:=[0]].
The value computed for the search variable in a search goal can be easily accessed by applying
it to a free variable. For instance, the evaluation of the applicative expression
(solveAll \l->append l [1] =:= [0,1]) =:= [g] & g x
binds the variable g to the search goal [\l->l=:=[0]] and the variable x to the value [0] (due to
solving the constraint x=:=[0]). Based on this idea, there is a predefined function
findall :: (a->Success) -> [a]
which takes a search goal and collects all solutions (computed by a depth-first search like solveAll)
for the search variable into a list.
Due to the laziness of the language, search goals with infinitely many solutions cause no problems
if one is interested only in finitely many solutions. For instance, a function which computes only
the first solution w.r.t. a depth-first search strategy can be defined by
first g = head (findall g)
Note that first is a partial function, i.e., it is undefined if g has no solution.
8.2 Local Variables
Some care is necessary if free variables occur in the search goal, like in the goal
\l2 -> append l1 l2 =:= [0,1]
Here, only the variable l2 is abstracted in the search goal but l1 is free. Since non-deterministic
bindings cannot be performed during encapsulated search, free variables are never bound inside encapsulated
search. Thus, if it is necessary to bind a free variable in order to proceed an encapsulated
search operation, the computation suspends. For instance, the expression
first \l2 -> append l1 l2 =:= [0,1]
cannot be evaluated and will be suspended until the variable l1 is bound by another part of the
computation. Thus, the constraint
s =:= (first \l2->append l1 l2 =:= [0,1]) & l1 =:= [0]
can be evaluated since the free variable l1 in the search goal is bound to [0], i.e., this constraint
reduces to the answer
{l1=[0], s=[1]}
In some cases it is reasonable to have unbound variables in search goals, but these variables should
be treated as local, i.e., they might have different bindings in different branches of the search. For
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