Semantics Engineering with Redex | Schema Programming Part 24

We end our journey at the bleeding edge of programming language theory. Racket is famous in academia for Redex, a tool for defining, visualizing, and testing language semantics.

What is Redex?

Redex allows you to write down the formal grammar and reduction rules of a language, and then run them. It turns dry mathematical notation into executable code.

Defining a Language (Lambda Calculus)

#lang racket
(require redex)

(define-language L
  (e ::= (lambda (x) e)
         (e e)
         x)
  (x ::= variable-not-otherwise-mentioned))

We just defined the grammar of the pure Lambda calculus!

Defining Reduction Rules

How does the language run? (Beta-reduction)

(define R
  (reduction-relation
   L
   (--> ((lambda (x) e_1) e_2)
        (subst e_1 x e_2)
        "beta")))

Visualization

Redex provides an interactive stepper to watch your language execute term by term.

(traces R (term ((lambda (x) x) (lambda (y) y))))

This pops up a GUI window showing the graph of reduction steps!

Summary

Redex is why many researchers choose Racket. It allows you to prototype not just the syntax of a language (like #lang does), but its deep semantics and correctness.

You have now reached the end of everything. From "Hello World" to "Formal Semantics".