Y-Combinator description in Racket

y-combinator-racket.rkt

;; lambda expression do not have any assignments
;; so we will use the form where there is not lambda expressions

((lambda ()
  (define (adder n) (+ n 1))
  (define (mult3 n) (* n 3))
  (mult3 (adder 10))
  ))

;; create make-adder and compose using higher-order functions

((lambda ()
  (define (make-adder a) (lambda (n) (+ n 1)))
  (define (mult3 n) (* n 3))
  (define (compose f g) (lambda (x) (f (g x))))
  ((compose mult3 (make-adder 1)) 10)))


;; tenants correspondence principle
;; introduce binding
;; wrapping a function
;; inlining

;; tenants correspondence principle
((lambda ()
  (define (make-adder a) (lambda (n) (+ n 1)))
  (define (mult3 n) ((lambda () (* n 3))))  ;; update due to Tenants corresponse principle
  (define (compose f g) ((lambda () (lambda (x) (f (g x)))))) ;;update with Tenants correpondence principle
  ((compose mult3 (make-adder 1)) 10)))


;; introduce a binding
;; wrapping a function
((lambda (x) (+ x  1)) 10)

((lambda ()
   (define (make-adder a) (lambda (n1) ((lambda (n) (+ n a)) n1))) ;; wrapping a function
   (define (mult3 n) ((lambda (n) (* n 3)) n))
   (define (compose f g) (
                          (lambda (v)
                            ((lambda () (lambda (x) (f (g x)))))) 1234)) ;; introduce binding
   ((compose mult3 (make-adder 1)) 10)))

;; inlining
((lambda ()
   ;;(define (make-adder) (lambda (a) (lambda (n1) ((lambda (n) (+ n a)) n1)))) ;; wrapping a function
   ;;(define (mult3 n) ((lambda (n) (* n 3)) n))
   (define (compose f g) (
                          (lambda (v)
                            ((lambda () (lambda (x) (f (g x)))))) 1234)) ;; introduce binding
   ((compose
     (lambda (n) (* n 3) n)
     ((lambda (a) (lambda (n1) ((lambda (n) (+ n a)) n1))) 1))
    10)))

;; inlinit compose
((lambda ()
   ;;(define (make-adder) (lambda (a) (lambda (n1) ((lambda (n) (+ n a)) n1)))) ;; wrapping a function
   ;;(define (mult3 n) ((lambda (n) (* n 3)) n))
   ;;(define (compose) (lambda (f g)
   ;;                       (lambda (v)
   ;;                         ((lambda () (lambda (x) (f (g x)))))) 1234)) ;; introduce binding
   (((lambda (f g)
      ((lambda (v)
         ((lambda () (lambda (x) (f (g x)))))) 1234))
     (lambda (n) (* n 10))
     ((lambda (a) (lambda (n1) ((lambda (n) (+ n a)) n1))) 20)) 40)))
       

((lambda ()
   (((lambda (f g)
       ((lambda (v)
          ((lambda () (lambda (x) (f (g x)))))) 1234))
     (lambda (x) (* x 10))
     (lambda (x) (+ x 20))) 40)))

((lambda (a) (lambda (n1) ((lambda (n) (+ n a)) n1))) 10)