(Prolog) Parsing Lisp s-expressions Into Prolog Terms

Question

I have written a parser in Prolog that takes a tokenized list and should return an expression where the variable is unified with the value of the evaluated equation:

Tokens = ['(', is, v('X',3),'(', +, 1, 2, ')', ')' ]
Expr = (3 is 1 + 2)

At present, my parser is returning the following:

Expr [is, _G32432, '(', +, 1, 2, ')'|_G19343]

Does anyone have an idea for how I can fix this parser? I have included the code below:

%Definite Clause Grammar (DCG) for Lisp s-expressions
expression(N) --> atom(N).
expression(N) --> integer(N).
expression(N) --> variable(N).
expression(N) --> list(N).
list(N) --> ['('], sequence(N), [')'].
sequence(_) --> [].
sequence([H|T]) --> expression(H), sequence(T).
%atom(_) --> [].
atom(N) --> [N],{atom(N)}.
%variable(_) --> [].
variable(N) --> [v(_,N)],{var(N)}.
%integer(_) --> [].
integer(N) --> [N],{integer(N)}.    

evaluate(String, Expr):-
tokenize(String, Tokens),
expression(Expr,Tokens,[]),
write('Expression: '), write_term(Expr, [ignore_ops(true)]).

EDIT: Below is my working version of the parser:

expression(N) --> atom(N).    %an atom is a type of expression
expression(N) --> integer(N). %an integer is a type of expression
expression(N) --> variable(N). %a variable is a type of expression
expression(M) --> list(N),{M=..N}.  
list(N) --> ['('], sequence(N), [')'].   %a sequence within parens is a type of list
sequence([]) --> [].                 %a sequence can be empty
sequence([H|T]) --> expression(H), sequence(T).  %a sequence can be composed of an expression
% sequence([]) --> []. %and a sequence atom(_) --> [].
atom(N) --> [N],{atom(N),N \= '(', N \= ')'}. %parens are not atoms, but all other Prolog atoms 
% If N is a variable and it is within the v(Label,X) data structure,
% then it is a var in this grammar
variable(N) --> [v(_,N)],{var(N)}.
%variable(_) --> [].
%integer(_) --> [].
integer(N) --> [N],{integer(N)}.

Answer 1

One of your input tokens is [1]. Notice that it will never match your rule [2] since N is an integer and not a variable (also, 'X' is an atom and not a variable).

[1]   v('X',3)
[2]   variable(N) --> [v(_,N)],{var(N)}.

Changing [2] to [3] fixes this problem.

[3]   variable(N) --> [N], {var(N)}.

PS: Also make sure you close the resulting expression in the base case for sequence//1 by replacing the corresponding line with [4].

[4]   sequence([]) --> [].