How to calculate factorial using prolog -

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i have code calculating factorial below : 

fact(1,1). fact(x,r):- x1 x-1, fact(x1,r1), r r1*x.

in mind code shouldn't work right does! reason? think when call fact(3,r), first calculate "x1 x1 -1". goes next rule fact(x1,r1). call goal part again , code execution return goal "fact(x,r)" , continue until reach fact(1,1). means never goes r r1*x part. so, seems thinking wrong.

can tell me step step code execution order in code? thanks

once "reach" fact(1,1), "return" calling recursive iteration , proceed part r r1*x of iteration, r1=1. return again previous level , on. let's @ non-trivial iteration:

fact(3,r) :    x <- 3,    x1 <- 3-1 = 2,    fact(2,r1) :        x' <- 2,       x1' <- 2-1 = 1,       fact(1, r1'), => r1'=1 (matched fact(1,1))        r'<- r1' * x' = 2       r1 = r' = 2    r <- r1*x = 2*3 = 6.

here variable ' denoting variables corresponding fact(2,r) iteration. variables without ' topmost iteration.


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