[mercury-users] no clauses for predicate, mistaken higher-order predicate call

[Terrence Brannon]

Please help me obliterate this final error.

[localhost:mercury/primality/divisors] metaperl% mmc -E --infer-all divisors.m
divisors.m:005: Error: no clauses for predicate `divisors:main/2'.
divisors.m:010: Inferred :- pred --->(pred((io:state), (io:state)), (pred)).
[localhost:mercury/primality/divisors] metaperl% 

==== program follows

:- module divisors.
:- interface.
:- import_module io.

:- pred main(io__state::di, io__state::uo) is det.

:- implementation.
:- import_module std_util, int, list.

main ---> prime(12).



%  Abelson and Sussman, SICP, Section 1.2.6

%  Since ancient times, mathematicians have been fascinated by problems
%  concerning prime numbers, and many people have worked on the problem
%  of determining ways to test if numbers are prime. One way to test if
%  a number is prime is to find the number's divisors. The following
%  program finds the smallest integral divisor (greater than 1) of a
%  given number n. It does this in a straightforward way, by testing n
%  for divisibility by successive integers starting with 2.

% (define (smallest-divisor n)
%   (find-divisor n 2))
% (define (find-divisor n test-divisor)
%   (cond ((> (square test-divisor) n) n)
%         ((divides? test-divisor n) test-divisor)
%         (else (find-divisor n (+ test-divisor 1)))))
% (define (divides? a b)
%   (= (remainder b a) 0))

:- func smallest_divisor(int) = int.
smallest_divisor(N) = find_divisor(N,2).


:- func find_divisor(int, int) = int.
find_divisor(N,TestDivisor) = Ans :-
 (
 TestDivisor*TestDivisor > N ->  Ans = N
  ;			  
 divides(TestDivisor,N)      ->  Ans = TestDivisor
  ;
 Ans = find_divisor(N,(1 + TestDivisor))
 )
 .

:- pred divides(int, int).
:- mode divides(in , in ) is semidet.
divides(A,B) :- rem(B,A) = 0.

% We can test whether a number is prime as follows: n is prime if and only if n is its own smallest divisor.

% (define (prime? n)
%   (= n (smallest-divisor n)))

:- pred prime(int). 
:- mode prime(in) is semidet.

prime(N) :- N = smallest_divisor(N).


% The end test for find-divisor is based on the fact that if n is not
% prime it must have a divisor less than or equal to n. This means
% that the algorithm need only test divisors between 1 and
% n. Consequently, the number of steps required to identify n as prime
% will have order of growth (n).


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