02-29.rkt

#lang racket

;; Some example λ calculus terms in Racket
;; ID (identity) applied to ID 
;; ((λ (x) x) (λ (x) x))

;; can't run this, y is free--but I can still β reduce it
;;((λ (x) y) (λ (z) y))
;; ⟶β y <-- error, in Racket, because we don't know what y is

;; The Ω combinator -- I can't run this because it is an infinite loop
;; ((λ (x) (x x)) (λ (x) (x x)))

;; In general, anything I write in the λ-calculus can be
;; run in the Racket interpreter. But since Racket isn't
;; using reduction literally (instead it is following
;; the strategy of last class, creating closures), I can't
;; see the reduction textually.

(define (freevars e)
  (match e
    [(? symbol? x) (set x)]
    [`(lambda (,x) ,eb) (set-remove (freevars eb) x)]
    [`(,e0 ,e1) (set-union (freevars e0) (freevars e1))]))