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Chapter 3

Ex 3.1

  (a)
    Strictly speaking, the definition of Algol 68 allows parentheses wherever brackets (`[` and `]`) are allowed. Fortunately or unfortunately, the a68toc compiler flags this as an error.
  (b)
    The apostrophes should be replaced by quote symbols.
  (c)
    The value `2.0` in the row-display cannot be coerced to a value of mode `INT` in a strong context (or any context, for that matter).
Ex 3.2
  `[]INT first 4 odd numbers = (1,3,5,7)`
Ex 3.3

  (a)
    `8`
  (b)
    `1`
  (c)
    `3`
Ex 3.4

  (a)
    `1 LWB a`, `1 UPB a`, `2 LWB a`, `2 UPB a`, `3 LWB a`,
    `3 UPB a`
  (b)
    `LWB b`, `UPB b`

Ex 3.5

  (a)
    `6`
  (b)
    `(9,10,11,12)`
  (c)
    `(4,8,12,16)`
Ex 3.6

  (a)
    `r[3,2]`
  (b)
    `r[2,]`
  (c)
    `r[,3]`

Ex 3.7

         [][]CHAR months=
            ("January","February","March",
             "April","May","June",
             "July","August","September",
             "October","November","December")

Ex 3.8

  (a)
    `30`
  (b)
    `(0.0,-5.4)`
  (c)
    `11.4`
  (d)
    `(6,7,8)`
  (e)
    `"pqrst"`

Ex 3.9
  This exercise is self-marking, but here is a program to print the answer to the first exercise:-

         PROGRAM ex3 9 CONTEXT VOID
         USE standard
         BEGIN
           [,]INT m = ((1,2,3,4),(5,6,7,8),
                    (9,10,11,12),(13,14,15,16));

           print(("m[2,2]=",m[2,2],newline,
                "m[3,]=",m[3,],newline,
                "m[,2 UPB m]=",m[,2 UPB m],
                newline))
         END
         FINISH

Ex 3.10

  (a)
    `Man bites dog`
  (b)
    `bbbii`

Ex 3.11

         PROGRAM ex3 11 CONTEXT VOID
         USE standard
         BEGIN
            FOR num TO 25
            DO
               print((num^3,newline))
            OD
         END
         FINISH

Ex 3.12

         PROGRAM ex3 12 CONTEXT VOID
         USE standard
         BEGIN
            FOR c FROM ABS "Z" BY -1 TO ABS "A"
            DO
               print(REPR c)
            OD
         END
         FINISH

Ex 3.13
  The main difficulty lies in computing the letter to print. The first solution uses numbers and `REPR`:-

         PROGRAM ex3 13a CONTEXT VOID
         USE standard
         BEGIN
            FOR row TO 5
            DO
               FOR letter TO 4
               DO
                  print((REPR((row-1)*5
                           +letter+ABS"@"),",")
               OD;

               print((REPR(row*5 + ABS "@"),
                      newline))
            OD
         END
         FINISH

  The second solution uses an actual alphabet and a modified inner loop. Note that the formulæ in the `FROM` and `TO` constructs are elaborated once only: before the inner loop is elaborated for the first time in each elaboration of the outer loop:-

         PROGRAM ex3 13b CONTEXT VOID
         USE standard
         BEGIN
            []CHAR alphabet =
             "ABCDEFGHIJKLMNOPQRSTUVWXYZ"[@1];

            FOR row TO 5
            DO
               INT row5 = row*5;

               FOR letter FROM row5-4 TO row5-1
               DO
                  print((alphabet[letter],","))
               OD;

               print((alphabet[row5],newline))
            OD
         END
         FINISH

Ex 3.14
  The most difficult part is in declaring the multiple. `print` will quite happily take the 3-dimensional multiple as its parameter:

         PROGRAM ex3 14 CONTEXT VOID
         USE standard
         BEGIN
            [,,]REAL m=(((1e-7,1e-6),
                         (1e-5,1e-4)),
                        ((1e-3,1e-2),
                         (1e-1,1.0)));
            print(m)
         END
         FINISH

Ex 3.15

  (a)
    The brackets for the row-display should be replaced by parentheses.
  (b)
    The number of integers in each row should be the same.
  (c)
    Nothing. The denotation of an apostrophe is not doubled.
Ex 3.16

  (a)
    `[1:2,1:3]`
  (b)
    `[1:3]`
  (c)
    `[1:2]`
Ex 3.17

  (a)
    `(6,5,4)` `[]INT`
  (b)
    `(8,5,2)` `[]INT`
  (c)
    `(7,4)` `[]INT`
  (d)
    `((6,5),(3,2))` `[,]INT`
Ex 3.18
  `"abcabcabcdefg"`
Ex 3.19
  Notice the means of avoiding the use of `BY`:

         PROGRAM ex3 18 CONTEXT VOID
         USE standard
         BEGIN
            []CHAR alphabet =
                  "abcdefghijklmnopqrstuvwxyz";
            []INT by = (1,6,11,16,21,26);

            FOR c BY --5 TO UPB alphabet
            DO
               print(alphabet[c])
            OD
         END
         FINISH