%% file:  g1.pl
%% A grammar must specify variables, terminals, and rules.

%% Here is the context-free grammar for addition, multiplication 
%% and exponentiation:
 
%% s -> p + s | p
%% p -> e * p | e
%% e -> v ^ e | v
%% v -> 0 | 1 | 2 | ... | 9

%% Variables are stated as facts.  These facts simply state the names of the variables.

%% In this example, the facts state that s, p, e, and v are variables.
%% These are all in lower case because Prolog thinks of anything beginning
%% in uppercase as one of its own unbound variables.

variable(s).
variable(p).
variable(e).
variable(v).

%% terminal(X) states that X is a terminal.
%% In this case, we are defining terminal using some helpers called
%% digit and operator.

terminal(X) :- digit(X) ; operator(X).

digit(0).
digit(1).
digit(2).
digit(3).
digit(4).
digit(5).
digit(6).
digit(7).
digit(8).
digit(9).
operator(+).
operator(*).
operator(^).

%% Rules are stated as ordered pairs, where the first element is the left-hand-side
%% of a rule and the second argument is the LIST of elements appearing on the right-hand-side
%% of that rule.

rule(s, [p, +, s]).
rule(s, [p]).
rule(p, [e, *, p]).
rule(p, [e]).
rule(e, [v, ^, e]).
rule(e, [v]).
rule(v, [X]) :- digit(X).

member(A, [A | X]).
member(A, [_ | X]) :- member(A, X).