Section 16 Want more of a challenge? View in iconic form (experimental)

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       # MATH illustrate lists and some list operators
       # to make list describable as a function, need to preceed lists
       # ... with an argument count
       # Lists keep an explicit record of their length
       # this is to avoid the need for using a special 'nil' symbol
       # ... which cannot itself be placed in the list.
       #
       # missing - intro to cons, car, cdr
       # used to be pure-cons pure-car pure-cdr but changed for better interface to scheme
       # also should introduce number? check function
       #
[hear] (define list-helper /
         ? n /
         ? ret /
         if (> (n) 1)
          (? x /
           list-helper
            (- (n) 1)
            (? y /
             ? z /
             ret (+ 1 (y)) (cons (x) (z))))
          (? x /
           ret 1 (x)));

[hear] (define list /
         ? n /
         if (= (n) 0)
          (cons 0 0)
          (list-helper (n) (? y / ? z / cons (y) (z))));

[hear] (define head /
         ? lst /
         if (= (car / lst) 0)
          (undefined)
          (if (= (car / lst) 1)
            (cdr /
             lst)
            (car /
             cdr /
             lst)));

[hear] (define tail /
         ? lst /
         if (= (car / lst) 0)
          (undefined)
          (if (= (car / lst) 1)
            (cons 0 0)
            (cons (- (car / lst) 1) (cdr / cdr / lst))));

[hear] (define list-length / ? lst / car / lst);

[hear] (define list-ref /
         ? lst /
         ? n /
         if (= (list-ref / lst) 0)
          (undefined)
          (if (= (n) 0)
            (head /
             lst)
            (list-ref (tail / lst) (- (n) 1))));

[hear] (define prepend /
         ? x /
         ? lst /
         if (= (list-length / lst) 0)
          (cons 1 (x))
          (cons (+ (list-length / lst) 1)
                (cons (x) (cdr / lst))));

[hear] (define equal /
         ? x /
         ? y /
         if (= (number? (x)) (number? (y)))
          (if (number? (x)) (= (x) (y)) (list= (x) (y)))
          (false));

[hear] (define list= /
         ? x /
         ? y /
         if (= (list-length / x) (list-length / y))
          (if (> (list-length / x) 0)
            (and (equal (head / x) (head / y))
                 (list= (tail / x) (tail / y)))
            (true))
          (false));

[hear] (= (list-length / (list 5) 8 5 9 2 3) 5);

[hear] (= (list-length / (list 0)) 0);

[hear] (= (list-length / (list 4) 6 5 8 4) 4);

[hear] (= (list-length / (list 8) 8 3 1 6 0 2 7 4) 8);

[hear] (= (list-length / (list 1) 3) 1);

[hear] (= (head / (list 8) 2 4 7 5 14 14 16 1) 2);

[hear] (list= (tail /
                (list 8) 2 4 7 5 14 14 16 1)
               ((list 7) 4 7 5 14 14 16 1));

[hear] (= (head / (list 9) 6 15 18 17 2 12 12 16 8) 6);

[hear] (list= (tail /
                (list 9) 6 15 18 17 2 12 12 16 8)
               ((list 8) 15 18 17 2 12 12 16 8));

[hear] (= (head / (list 2) 16 13) 16);

[hear] (list= (tail / (list 2) 16 13) ((list 1) 13));

[hear] (= (head / (list 8) 18 9 10 15 2 12 15 17) 18);

[hear] (list= (tail /
                (list 8) 18 9 10 15 2 12 15 17)
               ((list 7) 9 10 15 2 12 15 17));

[hear] (= (head / (list 2) 1 15) 1);

[hear] (list= (tail / (list 2) 1 15) ((list 1) 15));

[hear] (= (head /
            (list 10) 1 14 7 3 5 11 1 17 13 15)
           1);

[hear] (list= (tail /
                (list 10) 1 14 7 3 5 11 1 17 13 15)
               ((list 9) 14 7 3 5 11 1 17 13 15));

[hear] (= (head / (list 4) 10 19 16 4) 10);

[hear] (list= (tail /
                (list 4) 10 19 16 4)
               ((list 3) 19 16 4));

[hear] (= (head / (list 1) 15) 15);

[hear] (list= (tail / (list 1) 15) ((list 0)));

[hear] (= (head / (list 8) 11 5 11 8 5 8 3 14) 11);

[hear] (list= (tail /
                (list 8) 11 5 11 8 5 8 3 14)
               ((list 7) 5 11 8 5 8 3 14));

[hear] (= (head / (list 5) 6 2 13 5 1) 6);

[hear] (list= (tail /
                (list 5) 6 2 13 5 1)
               ((list 4) 2 13 5 1));

[hear] (= (list-ref ((list 1) 18) 0) 18);

[hear] (= (list-ref ((list 3) 3 15 16) 2) 16);

[hear] (= (list-ref ((list 5) 12 0 0 0 8) 0) 12);

[hear] (= (list-ref ((list 1) 3) 0) 3);

[hear] (= (list-ref ((list 2) 16 16) 0) 16);

[hear] (= (list-ref ((list 1) 0) 0) 0);

[hear] (= (list-ref ((list 2) 9 0) 1) 0);

[hear] (= (list-ref ((list 7) 11 5 7 19 9 18 2) 2) 7);

[hear] (= (list-ref ((list 3) 18 9 12) 1) 9);

[hear] (= (list-ref ((list 1) 0) 0) 0);

[hear] (list= ((list 0)) ((list 0)));

[hear] (list= ((list 1) 10) ((list 1) 10));

[hear] (list= ((list 2) 12 8) ((list 2) 12 8));

[hear] (list= ((list 3) 5 5 0) ((list 3) 5 5 0));

[hear] (list= ((list 4) 4 10 12 11)
               ((list 4) 4 10 12 11));

       # this next batch of examples are a bit misleading, should streamline
[hear] (not / list= ((list 0)) ((list 1) 4));

[hear] (not / list= ((list 0)) ((list 1) 4));

[hear] (not / list= ((list 1) 5) ((list 2) 8 5));

[hear] (not / list= ((list 1) 5) ((list 2) 5 3));

[hear] (not /
         list= ((list 2) 11 15) ((list 3) 4 11 15));

[hear] (not /
         list= ((list 2) 11 15) ((list 3) 11 15 3));

[hear] (not /
         list= ((list 3) 11 19 16) ((list 4) 4 11 19 16));

[hear] (not /
         list= ((list 3) 11 19 16) ((list 4) 11 19 16 1));

[hear] (not /
         list= ((list 4) 14 18 5 11)
               ((list 5) 6 14 18 5 11));

[hear] (not /
         list= ((list 4) 14 18 5 11)
               ((list 5) 14 18 5 11 9));

       # some helpful functions
[hear] (list= (prepend 6 ((list 0))) ((list 1) 6));

[hear] (list= (prepend 6 ((list 1) 11)) ((list 2) 6 11));

[hear] (list= (prepend 17 ((list 2) 11 4))
               ((list 3) 17 11 4));

[hear] (list= (prepend 18 ((list 3) 6 17 4))
               ((list 4) 18 6 17 4));

[hear] (list= (prepend 3 ((list 4) 8 11 1 10))
               ((list 5) 3 8 11 1 10));

[hear] (list= (prepend 7 ((list 5) 8 3 2 8 0))
               ((list 6) 7 8 3 2 8 0));

[hear] (list= (prepend 17 ((list 6) 14 15 14 19 9 3))
               ((list 7) 17 14 15 14 19 9 3));

[hear] (list= (prepend 17 ((list 7) 10 19 8 2 7 4 1))
               ((list 8) 17 10 19 8 2 7 4 1));

[hear] (define pair /
         ? x /
         ? y /
         (list 2) (x) (y));

[hear] (define first / ? lst / head / lst);

[hear] (define second /
         ? lst /
         head /
         tail /
         lst);

[hear] (list= (pair 2 8) ((list 2) 2 8));

[hear] (= (first / pair 2 8) 2);

[hear] (= (second / pair 2 8) 8);

[hear] (list= (pair 6 0) ((list 2) 6 0));

[hear] (= (first / pair 6 0) 6);

[hear] (= (second / pair 6 0) 0);

[hear] (list= (pair 9 3) ((list 2) 9 3));

[hear] (= (first / pair 9 3) 9);

[hear] (= (second / pair 9 3) 3);

[hear] (define list-find-helper /
         ? lst /
         ? key /
         ? fail /
         ? idx /
         if (= (list-length / lst) 0)
          (fail 0)
          (if (equal (head / lst) (key))
            (idx)
            (list-find-helper
              (tail /
               lst)
              (key)
              (fail)
              (+ (idx) 1))));

[hear] (define list-find /
         ? lst /
         ? key /
         ? fail /
         list-find-helper (lst) (key) (fail) 0);

[hear] (define example-fail / ? x 100);

[hear] (= (list-find ((list 1) 13) 13 (example-fail)) 0);

[hear] (= (list-find
             ((list 9) 15 17 16 12 3 15 2 4 13)
             15
             (example-fail))
           0);

[hear] (= (list-find
             ((list 9) 19 0 14 18 9 11 12 5 19)
             11
             (example-fail))
           5);

[hear] (= (list-find ((list 2) 15 1) 15 (example-fail))
           0);

[hear] (= (list-find ((list 4) 0 7 19 1) 7 (example-fail))
           1);

[hear] (= (list-find
             ((list 6) 9 9 1 10 5 19)
             10
             (example-fail))
           3);

[hear] (= (list-find ((list 2) 17 1) 1 (example-fail))
           1);

[hear] (= (list-find
             ((list 8) 0 3 16 13 19 13 18 11)
             13
             (example-fail))
           3);

[hear] (= (list-find ((list 4) 15 6 2 1) 1 (example-fail))
           3);

[hear] (= (list-find ((list 1) 3) 3 (example-fail)) 0);

[hear] (= (list-find ((list 4) 4 6 0 10) 1 (example-fail))
           100);

[hear] (= (list-find
             ((list 6) 5 7 8 16 1 0)
             13
             (example-fail))
           100);

[hear] (= (list-find
             ((list 8) 13 17 16 0 7 10 11 3)
             15
             (example-fail))
           100);