Prolog and limitations of backtracking -

this trivial implementation of function returns length of list in prolog

count([], 0). count([_|b], t) :- count(b, u), t u + 1. 

one thing prolog still cannot wrap head around flexibility of using variables parameters.

so example can run count([a, b, c], 3). , true. can run count([a, b], x). , answer x = 2.. oddly (at least me) can run count(x, 3). , @ least 1 result, looks x = [_g4337877, _g4337880, _g4337883] ; before interpreter disappears infinite loop. can run "flexible" count(x, a). , x = [], = 0 ; x = [_g4369400], = 1., incomplete somehow nice.

therefore multifaceted question. can somehow explain prolog not beyond first result when executing count(x, 3).? can somehow make prolog generate number of solutions count(x, a).? there limitation of kind of solutions can generate? specific predicate, prevents me generating solutions possible kinds of queries?

this trivial implementation

depends viewpoint: consider

count(l,c) :- length(l,c). 

shorter , functional. , 1 works use case.

edit

library clp(fd) allows for

:- use_module(library(clpfd)).  count([], 0). count([_|b], t) :- u #>= 0, t #= u + 1, count(b, u).  ?- count(x,3). x = [_g2327, _g2498, _g2669] ; false. 

(further) answering comments

it sarcasm

no, sorry giving impression. attempt give synthetic answer question. every details of implementation of length/2 - indeed longer code - have been weighted give general , efficient building block.

there must general concept

i call (full) prolog such general concept. start, prolog requires solve computational tasks describing relations among predicate arguments. once have described our relations, can query our 'knowledge database', , prolog attempts enumerate all answers, in specific order.

high level concepts unification , depth first search (backtracking) keys in model.

now, think you're looking second order constructs var/1, allow reason about our predicates. such constructs cannot written in (pure) prolog, , growing school of thinking requires avoid them, because rather difficult use. posted alternative using clp(fd), shields in some situation. in question specific context, give simple , elegant solution.

i not trying re-implement length

well, i'm aware of this, since count/2 aliases length/2, why not study reference model ? ( swi-prolog site used have browsable source, seems it's broken right )