How work this DCG Prolog grammar that say if a string is a Roman Number?

Searching on StackOverflow I have found this DCG grammar that say inf a string is a roman number and convert it into a decimal number (in this post: Prolog Roman Numerals (Attribute Grammars)):

roman(N) -->
    group('C','D','M',100, H),
    group('X','L','C',10, T),
    group('I','V','X',1, U),
    {N is H+T+U}.
group(A,B,C, Scale, Value) -->
    (   g3(A, T)
    ;   [A, B], {T = 4}
    ;   [B], g3(A, F), {T is 5+F} % thanks to Daniel for spotting the bug
    ;   [A, C], {T = 9}
    ;   {T = 0}
    ),  {Value is Scale * T}.

g3(C, 1) --> [C].
g3(C, 2) --> [C,C].
g3(C, 3) --> [C,C,C].

This work well but I can't understand how it work.

So I have 3 predicatse:

1) group/5 that take 4 parameters: C, D, M, 100 (where I think that C, D and M represents the multiplicative factor 100.

So what exactly represent H? Is it the sum of the letters that represent the component of finaldecimal number having 100 as multiplicative factor?

In the same way it is definied the version of group/3 predicate for multiplicative factor 10 (X,L,C) and a version of group/3 predicate for multiplicative factor 1 (I,V,X)

So I read the roman/1 predicate in this way: ** An integer number N is a roman number composed by a group of letters that represents the multiplicative factor 100, followed by a group of letters that represents the multiplicative factor 10, followed by the group of letters that represents the multiplicative factor 1.

And have to be TRUE that H+T+U is my original decimal number (where H+T+U is the sum of the letters that represent the component of finaldecimal number having 10 as multiplicative factor + he sum of the letters that represent the component of finaldecimal number having 100 as multiplicative factor + he sum of the letters that represent the component of finaldecimal number having 1 as multiplicative factor)

Is it my reasoning correct or am I missing something?

Now, if my previous reasoning is correct, I have some problem to understand how the group/3 predicate work and what exactly do the g3/2 predicate

Can you help me?

Tnx

Andrea

Solution

Your understanding seems right to me.

group//5 is parametrized with

A the group letter (1 to 3, expressed by g3, like III = 3)
B the midpoint letter (like VI = 6)
C the group letter of successive scale, to be used when subtracting (like IX = 9).

then a group of given scale can have any of these five patterns, giving the numerical value, to be scaled. As I noted in the original post, I like the compactness of this grammar.