Which Algorithm Approach Should I Take to Generate Lambda Expressions in Java?

Question

Good day, I'm trying to find a way to program a lambda expression generator in java with this context-free grammar, and I would want to ask ; what would be the best way to tackle this problem and be able to manipulate them with basic lambda calculus functions such as beta reduction, alpha conversion, etc.?

I tried doing this with Strings, but was advised to discontinue because using strings will limit me to what I can do.

Here's the Context Free Grammar I got over the internet:

 <expr>   ::=  <var>
             | <func> <arg>              # This is an application.
             | lambda <var> . <expr>     # This is an abstraction. 
 <func>   ::=  <var>
             | (lambda <var> . <expr>)    
             | <func> <arg>
 <arg>    ::=  <var>
             | (lambda <var> . <expr>) 
             | (<func> <arg>) 
 <var>    ::= a| b| .... | Z

Answer 1

The simplest approach would be to use a parser generate (perhaps antlr) to make a parser that produces a parse tree. You can then perform your reductions and conversions on the parse tree, rather than on a string, which should make them much simpler.