Prolog : coin change -

i new prolog, trying solve classic coin change problem.

change(m,p,n,d) formula m>=0 , m = p+5*n+10*d here approach

change(m,p,n,d) :-      m p+5*n+10*d,      p m - (5*n+10*10). 

couple of test-cases

  change(100,10,8,5).   true   change(x,10,8,5).   x = 100. 

however, if try

 change(100,p,8,5). 

it gives me "arguments not sufficiently instantiated" instead of p = 10. casuing ?

edit : fix code using between predicate between(0,m,p),between(0,m,n),between(0,m,d),m p+5*n+10*d.

use clpfd!

:- use_module(library(clpfd)). 

all need express change/4 one equation:

change(money,pennies,nickels,dimes) :-    money #= pennies + nickels*5 + dimes*10. 

let's run ground query given op!

?- change(100,10,8,5). true. 

next up, 4 queries having one variable:

 ?- change(money,10,8,5). money = 100.  ?- change(100,pennies,8,5). pennies = 10.  ?- change(100,10,nickels,5). nickels = 8.  ?- change(100,10,8,dimes). dimes = 5. 

---

as using clpfd, can ask more general queries, 1 three variables:

?- change(100,pennies,nickels,dimes). 100 #= pennies + 5*nickels + 10*dimes. 

note not (yet) enumerate possible combinations... takes 2 steps:

1. state "all counts non-negative" using ins/2:

    ?- [pennies,nickels,dimes] ins 0..sup,    change(100,pennies,nickels,dimes). 100 #= pennies + 5*nickels + 10*dimes, pennies in 0..100, nickels in 0..20, dimes   in 0..10. 

2. use enumeration predicate labeling/2:

    ?- zs = [pennies,nickels,dimes],    zs ins 0..sup,    change(100,pennies,nickels,dimes),    labeling([],zs).   pennies = 0  , nickels = 0, dimes = 10 ; pennies = 0  , nickels = 2, dimes = 9 ; pennies = 0  , nickels = 4, dimes = 8 % next 115 answers omitted sake of brevity ; pennies = 90 , nickels = 2, dimes = 0 ; pennies = 95 , nickels = 1, dimes = 0 ; pennies = 100, nickels = 0, dimes = 0 ; false.