infix-prefix: a library to convert prefix expressions to infix and vice versa🔗 i

1Warnings🔗 i

• It is not heavily tested.

• Infix to prefix functionality does not count proper precedence and associativity.

• I’m not sure if unary operators are parsed correctly.

2Prefix to infix🔗 i

In order to convert a prefix expressions to infix you need to create a table of operators (by make-ops-table ).

Then you should call the prefix->infix function with an expression to parse and your operators table. From the library, a default operators table is available for addition, subtraction, multiplication and division.

Inner implementation:

• Firstly, expression is converted to a binary tree. That means all forms like (+ 1 2 3) is converted to (+ 1 (+ 2 3)). WARNING: There is a bug, this works correctly for left associative expressions only.

• Then, binary expression are convert to prefix form. This form does not count associativity and precedence, instead it wraps all in parenthesis.

• Finally, groupings are removed according to operators table were they are unnecessary.

3Infix to prefix🔗 i

In order to convert an infix expression to prefix you need to define a special parser with define-infix->prefix-parser . You should supply name and operators that you need to parse.

Then you can call that parser by name and supply an expression.

Inner implementation:

The define-infix->prefix-parser form uses match. It searches for operators inside an expression, splits expression into left and right part, and then calls itself recursively and makes a prefix expression.

4Functions🔗 i