implement a simple C like language in Prolog?

Question

I'm new to prolog, so this's quite a challenge to me. I'm supposed to implement a simple C like language in Prolog.

the ultimate goal is to be able to execute something like this:
?- run([begin,a,:=,10,while,a,>,5,begin,write,a,a,:=,a,-,1,end,end]).

and get: 
10 
9
8
7
6 
yes

However, I'm stuck at the first step. This is what I have achieved so far. out of local stack!

statement(Vars,_Vars) --> assign(Vars,_Vars).
statement(Vars,Vars2) --> statement(Vars,Vars1), statement(Vars1,Vars2). 

assign(Vars,_Vars) --> default_assign(Vars,_Vars).
assign(Vars,_Vars) --> simple_assign(Vars,_Vars).

% a //default value 0
default_assign(Vars,_Vars) --> 
    var_name(Var_Name),
    {update_vars([Var_Name,0],Vars,_Vars)}.

% a = 0
simple_assign(Vars,_Vars) --> 
    var_name(Var_Name),[=],var_value(Var_Value),
    {update_vars([Var_Name,Var_Value],Vars,_Vars)}.

% a = b
simple_assign(Vars,_Vars) --> 
    var_name(Var_Name1),[=],var_name(Var_Name2),
    {
    update_vars([Var_Name1,Var_Value],Vars,_Vars)
    }.

var_name(Var_Name) --> [Var_Name],{\+number(Var_Name2)}.    
var_value(Var_Value) -->[Var_Value],{number(Var_Value)}.

% found match, update
update_vars(Var,Vars,_Vars):-
    member(Var,Vars),
    update(Var,Vars,_Vars),
    _Vars\==[].
% no match, append
update_vars(Var,Vars,_Vars):-
    \+member(Var,Vars),
    append(Var,Vars,_Vars).

update([Name,Value],[],[]).
update([Name,Value],[[Name,Old_Value]|T1],[[Name,Value]|T2]):-
    update([Name,Value],T1,T2).
update([Name,Value],[[Name1,Value1]|T1],[[Name1,Value1]|T2]):-
    [Name,Value]\=[Name1,Value1],
    update([Name,Value],T1,T2).

append([Name,Value],[],[[Name,Value]]).
append([Name,Value],[H|T1],[H|T2]):-
    append([Name,Value],T1,T2).

Here's my logic. First I want to be able to consume the list(that's how I interpret it - -!), so the grammar structure is really really important. And I'm also thinking about using a variable list 'Vars' in forms of [[Name,Value],[a,1],[b,2]...], and an updated version - '_Vars'. So I can pass it to other statements like while loop and write.

statement(Vars,Vars2) --> statement(Vars,Vars1), statement(Vars1,Vars2).
% this seems wrong...

But... It looks like the logic is wrong from the beginning. :\ below is the simplified version. I would really appreciate it if you can help me out here. And I really hope I won't take this with me in Christmas. T.T

statement --> assign.
statement --> statement, statement.

assign --> simple_assign.
assign --> default_assign.

default_assign --> 
    var_name(Var_Name).
simple_assign --> 
    var_name,[=],var_value.

var_name --> 
    [Var_Name],{\+number(Var_Name)}.    
var_value -->
    [Var_Value],{number(Var_Value)}.

Answer 1

This is how I would go about it:

1. transform the source code into a abstract syntax tree

   begin 
     a := 1
     while a < 5
     begin
       a := a + 1;
     end
   end
   

   becomes

   statements([
       assign(a, number(1)),
       while(greater(variable(a), number(5))), 
             statements([
                 assign(a, plus(variable(a), number(1)))
                        ])
            )
              ])
   

2. build an interpreter for it.

   There are various interpreters. The easiest one is the vanilla interpreter. Here is one I would begin with:

   interpret(number(N), State, N, State).
   interpret(assign(Variable, Statement), State, Value, NewState) :- 
       interpret(Statement, State, Value, NewState1), 
       assignVariable(Variable, Value, NewState1, NewState).
   

Answer 2

Your code seems appropriate, just some typo around, resulting in singletons, that probably harm the soundness of your attempt.

There are + 2 singletons in simple_assign (Var_Name2 and Var_Value), and + Var_Name2 is singleton in var_name

I guess you're not using and IDE with proper syntax highlighting...

edit singletons apart, I must say that User' answer is more useful than mine (+1). Attempting to provide a modifiable environment while parsing doesn't work. Here is how I tested, with a somewhat different version of your grammar:

test :-
    phrase(statement(S), [begin,a,:=,10,while,a,>,5,begin,write,a,a,:=,a,-,1,end,end]),
    eval(S, [], _).

% grammar

statement(Var := Expr) --> var(Var), [:=], expr(Expr).
statement(write(E)) --> [write], expr(E).
statement(while(C, S)) --> [while], condition(C), statement(S).
statement(S) --> [begin], statements(S), [end].

statements([S|R]) --> statement(S), statements(R).
statements([]) --> [].

condition(L > R) --> expr(L), [>], expr(R).

expr(L - R) --> (var(L) ; num(L)), [-], expr(R).
expr(E) --> (var(E) ; num(E)).

var(var(V)) --> [V], {atom(V)}.
num(num(N)) --> [N], {number(N)}.

% evaluation

eval([S|R], Vs, Us) :- eval(S, Vs, V1), eval(R, V1, Us).
eval([], Vs, Vs).

eval(V := E, Vs, Us) :-
    exprv(E, Vs, Ve),
    ( select(V := _, Vs, R) -> Us = [V := Ve | R] ; Us = [V := Ve | Vs] ).
eval(write(E), Vs, Vs) :- exprv(E, Vs, Ve), writeln(Ve).
eval(while(C, S), Vs, Ts) :-
    satisfied(C, Vs) -> eval(S, Vs, Us), eval(while(C, S), Us, Ts) ; Vs = Ts.

% no side effect here

exprv(L-E, Vs, Ve) :- exprv(L, Vs, Vl), exprv(E, Vs, R), Ve is Vl - R.
exprv(num(N), _, N).
exprv(var(V), Vs, Vv) :- memberchk(var(V) := Vv, Vs).

satisfied(L > R, Vs) :- exprv(L, Vs, Vl), exprv(R, Vs, Vr), Vl > Vr.