Create a program which parses and evaluates arithmetic expressions.

Requirements

 An abstract-syntax tree (AST) for the expression must be created from parsing the input. 
 The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.) 
 The expression will be a string or list of symbols like "(1+3)*7". 
 The four symbols + - * / must be supported as binary operators with conventional precedence rules. 
 Precedence-control parentheses must also be supported.


Note

For those who don't remember, mathematical precedence is as follows:

 Parentheses
 Multiplication/Division (left to right)
 Addition/Subtraction (left to right)


C.f
 
 24 game Player.
 Parsing/RPN calculator algorithm.
 Parsing/RPN to infix conversion.


USING: accessors kernel locals math math.parser peg.ebnf ;
IN: rosetta.arith
 
TUPLE: operator left right ;
TUPLE: add < operator ;   C: <add> add
TUPLE: sub < operator ;   C: <sub> sub
TUPLE: mul < operator ;   C: <mul> mul
TUPLE: div < operator ;   C: <div> div
 
EBNF: expr-ast
spaces   = [\n\t ]*
digit    = [0-9]
number   = (digit)+                         => [[ string>number ]]
 
value    =   spaces number:n                => [[ n ]]
           | spaces "(" exp:e spaces ")"    => [[ e ]]
 
fac      =   fac:a spaces "*" value:b       => [[ a b <mul> ]]
           | fac:a spaces "/" value:b       => [[ a b <div> ]]
           | value
 
exp      =   exp:a spaces "+" fac:b         => [[ a b <add> ]]
           | exp:a spaces "-" fac:b         => [[ a b <sub> ]]
           | fac
 
main     = exp:e spaces !(.)                => [[ e ]]
;EBNF
 
GENERIC: eval-ast ( ast -- result )
 
M: number eval-ast ;
 
: recursive-eval ( ast -- left-result right-result )
    [ left>> eval-ast ] [ right>> eval-ast ] bi ;
 
M: add eval-ast recursive-eval + ;
M: sub eval-ast recursive-eval - ;
M: mul eval-ast recursive-eval * ;
M: div eval-ast recursive-eval / ;
 
: evaluate ( string -- result )
    expr-ast eval-ast ;