c# - Shunting-Yard Validate Expression -

we use shunting-yard algorithm evaluate expressions. can validate expression applying algorithm. fails if there missing operands, miss-matched parenthesis, , other things. shunting-yard algorithm has larger supported syntax human readable infix. example,

1 + 2 + 1 2 1 2 + 

are acceptable ways provide '1+2' input shunting-yard algorithm. '+ 1 2' , '1 2 +' not valid infix, standard shunting-yard algorithm can handle them. algorithm not care order, applies operators order of precedence grabbing 'nearest' operands.

we restrict our input valid human readable infix. looking way either modify shunting-yard algorithm fail non-valid infix or provide infix validation prior using shunting-yard.

is aware of published techniques this? must support both basic operator, custom operators, brackets, , functions (with multiple arguments). haven't seen works more basic operators online.

thanks

a nice discussion on shunting yard algorithms http://www.engr.mun.ca/~theo/misc/exp_parsing.htm algorithm presented there uses key idea of operator stack has grammar know should expected next. has 2 main functions e() expects expression , p() expecting either prefix operator, variable, number, brackets , functions. prefix operators bind tighter binary operators want deal of first.

if p stands prefix sequence , b binary operator expression of form

p b p b p 

i.e. either expecting a prefix sequence or binary operator. formally grammar is

e -> p (b p)* 

and p be

p -> -p | variable | constant | etc. 

this translates psudocode

e() {     p()     while next token binary op:          read next op          push onto stack , shunting yard logic          p()     if tokens remain report error     pop remaining operators off stack }  p() {     if next token constant or variable:          add output     else if next token unary minus:           push uminus onto operator stack          p() } 

you can expand handle other unary operators, functions, brackets, suffix operators.