# Parsing arithmetic expressions with Parsec

TweetParsec provides Text.Parsec.Expr module to parse *expressions*. `buildExpressionParser`

creates an expression parser from the given operator table.

For example, let’s assume that we want to parse a simple arithmetic expression such as `1+2*3-4/2`

. Here `*`

and `/`

has higher precedence than `+`

, `-`

and all operators are left-associative. We can represent the grammar in BNF Converter notation.

```
EAdd. Exp ::= Exp "+" Exp1 ;
ESub. Exp ::= Exp "-" Exp1 ;
EMul. Exp1 ::= Exp1 "*" Exp2 ;
EDiv. Exp1 ::= Exp1 "/" Exp2 ;
EInt. Exp2 ::= Integer ;
coercions Exp 2 ;
```

Here’s our AST for the arithmetic expression.

```
data Exp = EAdd Exp Exp
| ESub Exp Exp
| EMul Exp Exp
| EDiv Exp Exp
| EInt Integer
```

We can build an expression parser, `expr`

as in the following. We specify operators with their precedences and associativities in the operator table. Operators with higher precedence come first in the operator table. So `*`

and `/`

has higher precedence than `+`

and `-`

in this example.

```
term = parens expr
<|> EInt <$> natural
table = [ [binary "*" EMul AssocLeft, binary "/" EDiv AssocLeft ]
, [binary "+" EAdd AssocLeft, binary "-" ESub AssocLeft ]
]
binary name fun assoc = Infix (do { reservedOp name; return fun }) assoc
expr :: Parser Exp
expr = buildExpressionParser table term
```

`Text.Parsec.Expr`

can handle prefix and postfix operators too. We can use the following helper functions to specify these operators.

```
prefix name fun = Prefix (do { reservedOp name; return fun })
postfix name fun = Postfix (do { reservedOp name; return fun })
```

See the calculator example for the complete code.