How to do a parser in Prolog? - parsing

Question

I would like to do a parser in prolog. This one should be able to parse something like this:
a = 3 + (6 * 11);
For now I only have this grammar done. It's working but I would like to improve it in order to have id such as (a..z)+ and digit such as (0..9)+.
parse(-ParseTree, +Program, []):-
parsor(+Program, []).
parsor --> [].
parsor --> assign.
assign --> id, [=], expr, [;].
id --> [a] | [b].
expr --> term, (add_sub, expr ; []).
term --> factor, (mul_div, term ; []).
factor --> digit | (['('], expr, [')'] ; []).
add_sub --> [+] | [-].
mul_div --> [*] | [/].
digit --> [0] | [1] | [2] | [3] | [4] | [5] | [6] | [7] | [8] | [9].
Secondly, I would like to store something in the ParseTree variable in order to print the ParseTree like this:
PARSE TREE:
assignment
ident(a)
assign_op
expression
term
factor
int(1)
mult_op
term
factor
int(2)
add_op
expression
term
factor
left_paren
expression
term
factor
int(3)
sub_op
...
And this is the function I'm going use to print the ParseTree:
output_result(OutputFile,ParseTree):-
open(OutputFile,write,OutputStream),
write(OutputStream,'PARSE TREE:'),
nl(OutputStream),
writeln_term(OutputStream,0,ParseTree),
close(OutputStream).
writeln_term(Stream,Tabs,int(X)):-
write_tabs(Stream,Tabs),
writeln(Stream,int(X)).
writeln_term(Stream,Tabs,ident(X)):-
write_tabs(Stream,Tabs),
writeln(Stream,ident(X)).
writeln_term(Stream,Tabs,Term):-
functor(Term,_Functor,0), !,
write_tabs(Stream,Tabs),
writeln(Stream,Term).
writeln_term(Stream,Tabs1,Term):-
functor(Term,Functor,Arity),
write_tabs(Stream,Tabs1),
writeln(Stream,Functor),
Tabs2 is Tabs1 + 1,
writeln_args(Stream,Tabs2,Term,1,Arity).
writeln_args(Stream,Tabs,Term,N,N):-
arg(N,Term,Arg),
writeln_term(Stream,Tabs,Arg).
writeln_args(Stream,Tabs,Term,N1,M):-
arg(N1,Term,Arg),
writeln_term(Stream,Tabs,Arg),
N2 is N1 + 1,
writeln_args(Stream,Tabs,Term,N2,M).
write_tabs(_,0).
write_tabs(Stream,Num1):-
write(Stream,'\t'),
Num2 is Num1 - 1,
write_tabs(Stream,Num2).
writeln(Stream,Term):-
write(Stream,Term),
nl(Stream).
write_list(_Stream,[]).
write_list(Stream,[Ident = Value|Vars]):-
write(Stream,Ident),
write(Stream,' = '),
format(Stream,'~1f',Value),
nl(Stream),
write_list(Stream,Vars).
I hope someone will be able to help me. Thank you !

Answer 1

Here's an enhancement of your parser as written which can get you started. It's an elaboration of the notions that #CapelliC indicated.
parser([]) --> [].
parser(Tree) --> assign(Tree).
assign([assignment, ident(X), '=', Exp]) --> id(X), [=], expr(Exp), [;].
id(X) --> [X], { atom(X) }.
expr([expression, Term]) --> term(Term).
expr([expression, Term, Op, Exp]) --> term(Term), add_sub(Op), expr(Exp).
term([term, F]) --> factor(F).
term([term, F, Op, Term]) --> factor(F), mul_div(Op), term(Term).
factor([factor, int(N)]) --> num(N).
factor([factor, Exp]) --> ['('], expr(Exp), [')'].
add_sub(Op) --> [Op], { memberchk(Op, ['+', '-']) }.
mul_div(Op) --> [Op], { memberchk(Op, ['*', '/']) }.
num(N) --> [N], { number(N) }.
I might have a couple of niggles in here, but the key elements I've added to your code are:
Replaced digit with num which accepts any Prolog term N for which number(N) is true
Used atom(X) to identify a valid identifier
Added an argument to hold the result of parsing the given expression item
As an example:
| ?- phrase(parser(Tree), [a, =, 3, +, '(', 6, *, 11, ')', ;]).
Tree = [assignment,ident(a),=,[expression,[term,[factor,int(3)]],+,[expression,[term,[factor,[expression,[term,[factor,int(6)],*,[term,[factor,int(11)]]]]]]]]] ? ;
This may not be an ideal representation of the parse tree. It may need some adjustment per your needs, which you can do by modifying what I've shown a little. And then you can write a predicate which formats the parse tree as you like.
You could also consider, instead of a list structure, an embedded Prolog term structure as follows:
parser([]) --> [].
parser(Tree) --> assign(Tree).
assign(assignment(ident(X), '=', Exp)) --> id(X), [=], expr(Exp), [;].
id(X) --> [X], { atom(X) }.
expr(expression(Term)) --> term(Term).
expr(expression(Term, Op, Exp)) --> term(Term), add_sub(Op), expr(Exp).
term(term(F)) --> factor(F).
term(term(F, Op, Term)) --> factor(F), mul_div(Op), term(Term).
factor(factor(int(N))) --> num(N).
factor(factor(Exp)) --> ['('], expr(Exp), [')'].
add_sub(Op) --> [Op], { memberchk(Op, ['+', '-']) }.
mul_div(Op) --> [Op], { memberchk(Op, ['*', '/']) }.
num(N) --> [N], { number(N) }.
Which results in something like this:
| ?- phrase(parser(T), [a, =, 3, +, '(', 6, *, 11, ')', ;]).
T = assignment(ident(a),=,expression(term(factor(int(3))),+,expression(term(factor(expression(term(factor(int(6)),*,term(factor(int(11)))))))))) ? ;

Answer 2

A recursive rule for id//0, made a bit more generic:
id --> [First], {char_type(First,lower)}, id ; [].
Building the tree could be done 'by hand', augmenting each non terminal with the proper term, like
...
assign(assign(Id, Expr)) --> id(Id), [=], expr(Expr), [;].
...
id//0 could become id//1
id(id([First|Rest])) --> [First], {memberchk(First, [a,b])}, id(Rest) ; [], {Rest=[]}.
If you're going to code such parsers frequently, a rewrite rule can be easily implemented...