;;  -----------------------------------------------------------------------
;; |                                                                       |
;; |   FILE           :   map-nlist.rkt                                    |
;; |   AUTHOR         :   Eugene Wallingford                               |
;; |   CREATION DATE  :   2024/02/20                                       |
;; |                                                                       |
;; |   DESCRIPTION    :   Solutions to the two warm-up exercises in        |
;; |                      Session 11.  We revisit structural recursion,    |
;; |                      mutual recursion, and program derivation.        |
;; |                                                                       |
;; |   REQUIRES       :   Uses Rackunit for testing.                       |
;; |                                                                       |
;;  -----------------------------------------------------------------------
;; |                                                                       |
;; |   MODIFIED BY    :                                                    |
;; |   DATE           :                                                    |
;; |   DESCRIPTION    :                                                    |
;; |                                                                       |
;;  -----------------------------------------------------------------------

#lang racket
(require rackunit)

; -------------------------------------------------------------------------
; map-nlst                                               (mutual recursion)
; -------------------------------------------------------------------------

(define map-nlist
  (lambda (f nlst)
    (if (null? nlst)
        '()
        (cons (map-numexp f (first nlst))
              (map-nlist  f (rest  nlst))))))

(define map-numexp
  (lambda (f numexp)
    (if (number? numexp)
        (f numexp)
        (map-nlist f numexp))))

(check-equal? (map-nlist add1 '(1 4 9 16 25 36 49 64))
              '(2 5 10 17 26 37 50 65))

(check-equal? (map-nlist even? '(1 (4 (9 (16 25)) 36 49) 64))
              '(#f (#t (#f (#t #f)) #t #f) #t))

(check-equal? (map-nlist sqr '(1 (4 (9 (16 25)) 36 49) 64))
              '(1 (16 (81 (256 625)) 1296 2401) 4096))

; -------------------------------------------------------------------------
; simple example                                       (program derivation)
; -------------------------------------------------------------------------

(define 2n-plus-1
  (lambda (n)
    (add1 (* 2 n))))

(check-equal? (2n-plus-1 15)         ; substitution 1: lambda for name
              ((lambda (n)
                 (add1 (* 2 n)))
               15))

(check-equal? ((lambda (n)           ; substitution 2: body for lambda app
                 (add1 (* 2 n)))
               15)
              (add1 (* 2 15)))

; -------------------------------------------------------------------------
; map-nlst                                             (program derivation)
; -------------------------------------------------------------------------

;; (define map-nlist
;;   (lambda (f nlst)
;;     (if (null? nlst)
;;         '()
;;         (cons (if (number? (first nlst))
;;                   (f (first nlst))
;;                   (map-nlist f (first nlst)))
;;               (map-nlist f (rest nlst))))))
;; 
;; (check-equal? (map-nlist add1 '(1 4 9 16 25 36 49 64))
;;               '(2 5 10 17 26 37 50 65))
;; 
;; (check-equal? (map-nlist even? '(1 (4 (9 (16 25)) 36 49) 64))
;;               '(#f (#t (#f (#t #f)) #t #f) #t))
;; 
;; (check-equal? (map-nlist sqr '(1 (4 (9 (16 25)) 36 49) 64))
;;               '(1 (16 (81 (256 625)) 1296 2401) 4096))

; -------------------------------------------------------------------------