| ;; Road to Y Combinator (define inc
(lambda (n)
(+ n 1))) ;; normal length
(define length
(lambda (l)
(cond
((null? l) 0)
(else (inc (length (cdr l))))))) ;; without "define" ;; empty-list-length
(lambda (l)
(cond
((null? l) 0))) ;; execute with empty-list
((lambda (l)
(cond
((null? l) 0))) '())
;; => 0 ;; execute with non-empty-list
((lambda (l)
(cond
((null? l) 0))) '(1 2 3))
;; => #<undef> ;; 1-element-list-length
(lambda (l)
(cond
((null? l) 0)
(else
(inc ((lambda (l)
(cond
((null? l) 0)))(cdr l)))))) ((lambda (l)
(cond
((null? l) 0)
(else
(inc ((lambda (l)
(cond
((null? l) 0)))(cdr l)))))) '())
;; => 0 ((lambda (l)
(cond
((null? l) 0)
(else
(inc ((lambda (l)
(cond
((null? l) 0)))(cdr l)))))) '(a))
;; => 1 ((lambda (l)
(cond
((null? l) 0)
(else
(inc ((lambda (l)
(cond
((null? l) 0)))
(cdr l))))))
'(1 2))
;; => *** ERROR: operation + is not defined between 1 and #<undef> ;;2-elements-list-length
(lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)))
(cdr l))))))
(cdr l)))))) ;; execute 2-elements-list-length
((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)))
(cdr l))))))
(cdr l))))))
'())
;; => 0 ((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)))
(cdr l))))))
(cdr l))))))
'(a))
;; => 1 ((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)))
(cdr l))))))
(cdr l))))))
'(a b))
;; => 2 ((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (l)
(cond
((null? l) 0)))
(cdr l))))))
(cdr l))))))
'(1 2 3))
;; => *** ERROR: operation + is not defined between 1 and #<undef> ;;((lambda (length)
;; (lambda (l)
;; (cond
;; ((null? l) 0)
;; (else (inc (length (cdr l)))))))
;; 'eternity) ;; eternity style empty-list-length (((lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))
'eternity) '())
;; => 0 ;; eternity style 1-element-list-length
(((lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))
((lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))
'eternity))
'(1))
;; => 1 ;; eternity style 2-elements-list-length
(((lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))
((lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))
((lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))
'eternity)))
'(1 2))
;; => 2 ;; without repetitions
((lambda (make-length)
(make-length 'eternity))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l)))))))) ;; execute without-repetitions-eternity-stryle-length
(((lambda (make-length)
(make-length 'eternity))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l))))))))
'())
;; => 0 (((lambda (make-length)
(make-length
(make-length 'eternity)))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l))))))))
'(1))
;; => 1 (((lambda (make-length)
(make-length
(make-length
(make-length 'eternity))))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc (f (cdr l))))))))
'(1 2))
;; => 2 ;;What is recursion like?
;;It is like an infinite tower of applications of make-length to an arbitrary function. ;;Do we readly need an infinite tower?
;;Not really of course. Everytime we use length we only need a finite number. but we never know how many. ;; meke-length to make-length
((lambda (make-length)
(make-length make-length))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc ((f f) (cdr l)))))))) ;; execute make-length to make-length
(((lambda (make-length)
(make-length make-length))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc ((f f) (cdr l))))))))
'())
;; => 0 (((lambda (make-length)
(make-length make-length))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc ((f f) (cdr l))))))))
'(1))
;; => 1 (((lambda (make-length)
(make-length make-length))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc ((f f) (cdr l))))))))
'(1 2))
;; => 2 (((lambda (make-length)
(make-length make-length))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc ((f f) (cdr l))))))))
'(1 2 3 4 5))
;; => 5 ;; without (f f)
(((lambda (make-length)
(make-length make-length))
(lambda (f)
(lambda (l)
(cond
((null? l) 0)
(else (inc
((lambda (x)
((f f) x))
(cdr l))))))))
'(1 2 3 4 5))
;; => 5 ;; move out (f f)
((lambda (f)
(f f))
(lambda (f)
((lambda (g)
(lambda (l)
(cond
((null? l) 0)
(else
(inc (g (cdr l)))))))
(lambda (x)
((f f) x))))) ;; execute move-out-(f f)
(((lambda (f)
(f f))
(lambda (f)
((lambda (g)
(lambda (l)
(cond
((null? l) 0)
(else
(inc (g (cdr l)))))))
(lambda (x)
((f f) x)))))
'(1 2 3 4 5))
;; => 5 ;; extract function's body
;;(lambda (g)
;; (lambda (l)
;; (cond
;; ((null? l) 0)
;; (else (inc (g (cdr l)))))))
(((lambda (le)
((lambda (f)
(f f))
(lambda (f)
(le (lambda (x)
((f f) x))))))
(lambda (g)
(lambda (l)
(cond
((null? l) 0)
(else (inc (g (cdr l))))))))
'(1 2 3 4 5))
;; => 5 ;; named y
(define y
(lambda (le)
((lambda (f)
(f f))
(lambda (f)
(le (lambda (x)
((f f) x))))))) ;; execute y with length
((y (lambda (g)
(lambda (l)
(cond
((null? l) 0)
(else (inc (g (cdr l))))))))
'(1 2 3 4 5)) | 
0 件のコメント:
コメントを投稿