• source :: 7 lines of code, 3 minutes: Implement a programming language

Notes

Lambda calculushas three fundamental operations: variable references, anonymous functions and function calls.

$\lambda v . e$ is comperable to =(v) > e in JavaScript. $(f e)$ is a function call.

If we wanted to define a lambda calculus interpreter, it would be trivial to express that:

eval  : Expression * Environment -> Value
apply : Value * Value -> Value

Environment = Variable -> Value
Value       = Closure
Closure     = Lambda * Environment

It also has a trivial implementation in Racket

#lang racket

; bring in the match library:
(require racket/match)

; eval matches on the type of expression:
(define (eval exp env)
  (match exp
    [`(,f ,e)        (apply (eval f env) (eval e env))]
    [`(λ ,v . ,e)   `(closure ,exp ,env)]
    [(? symbol?)     (cadr (assq exp env))]))

; apply destructures the function with a match too:
(define (apply f x)
  (match f
    [`(closure (λ ,v . ,body) ,env)
     (eval body (cons `(,v ,x) env))]))

; read in, parse and evaluate:
(display (eval (read) '()))    (newline)

The rest of this post has a longer interpreter and some worthwhile links.