/* cs342 homework 7
   Dan J. Fraser (1219229) 

Grammar:
    
    question ::= "How much is" number_expression "?"

    number_expression ::= number
    number_expression ::= "the sum of" sum_number_list 
    number_expression ::= "the product of" product_number_list 

    sum_number_list ::= number_expression "and" number_expression
    sum_number_list ::= number_expression "," sum_number_list
    sum_number_list ::= number_expression "," "and" number_expression

    product_number_list ::= number_expression "and" number_expression
    product_number_list ::= number_expression "," product_number_list
    product_number_list ::= number_expression "," "and" number_expression
*/

parse("How":"much":"is":Tokens,question(ParseTree)) :-
   append(B,"?":nil,Tokens),
   not B = nil, 
   number_expression(B,ParseTree).
   
number_expression(B,number(Y)) :- evaluate_number(B,Y).

number_expression(B:nil,number(Y)) :- evaluate_number(B,Y).

number_expression("the":"sum":"of":SumExpr,ParseTree) :-
   sum_number_list(SumExpr,ParseTree).
   
number_expression("the":"product":"of":ProductExpr,ParseTree) :-
   product_number_list(ProductExpr,ParseTree).
   
sum_number_list(SumExpr,sum(T1,T2)) :-
   append(T0,",":List,SumExpr), 
   not T0 = nil,
   number_expression(T0,T1),
   sum_number_list(List,T2).

sum_number_list("and":SumExpr,T1) :-
  number_expression(SumExpr,T1).

sum_number_list(SumExpr,sum(T1,T2)) :-
  append(T0,"and":List,SumExpr), 
  not T0 = nil,
  number_expression(T0,T1),
  number_expression(List,T2).
    
  
product_number_list(ProductExpr,product(T1,T2)) :-
   append(T0,",":List,ProductExpr), 
   not T0 = nil, 
   number_expression(T0,T1),
   product_number_list(List,T2).

product_number_list("and":ProductExpr,T1) :-
  number_expression(ProductExpr,T1).

product_number_list(ProductExpr,product(T1,T2)) :-
  append(T0,"and":List,ProductExpr), 
  not T0 = nil,
  number_expression(T0,T1),
  number_expression(List,T2).