aboutsummaryrefslogtreecommitdiff
path: root/src/algebra/array1.spad.pamphlet
blob: 17bc88f24131c77a3e81afe0568ea0e5a156af1d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra array1.spad}
\author{Gabriel Dos Reis, Michael Monagan, Stephen Watt}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain PRIMARR PrimitiveArray}
<<domain PRIMARR PrimitiveArray>>=
)abbrev domain PRIMARR PrimitiveArray
++ This provides a fast array type with no bound checking on elt's.
++ Minimum index is 0 in this type, cannot be changed
PrimitiveArray(S:Type): OneDimensionalArrayAggregate S == add
   macro NNI == NonNegativeInteger
   import %icst0: Integer                    from Foreign Builtin
   import %vlength: % -> NNI                 from Foreign Builtin
   import %vcopy: % -> %                     from Foreign Builtin
   import %vfill: (%,S) -> %                 from Foreign Builtin
   import %aref: (%,Integer) -> S            from Foreign Builtin
   import %emptyArray: Type -> %             from Foreign Builtin
   import %list2array: (List S,Type) -> %    from Foreign Builtin
   import %simpleArray: (Type,NNI,S) -> %    from Foreign Builtin

   #x == %vlength x
   minIndex x == %icst0
   empty() == %emptyArray S
   construct l == %list2array(l,S)
   new(n, x) == %simpleArray(S,n,x)
   qelt(x, i) == %aref(x,i)
   elt(x:%, i:Integer) ==  %aref(x,i)
   qsetelt!(x, i, s) == %store(%aref(x,i),s)$Foreign(Builtin)
   setelt(x:%, i:Integer, s:S) == %store(%aref(x,i),s)$Foreign(Builtin)
   fill!(x, s) == %vfill(x,s)
   copy x == %vcopy x

@


\section{package PRIMARR2 PrimitiveArrayFunctions2}

<<package PRIMARR2 PrimitiveArrayFunctions2>>=
)abbrev package PRIMARR2 PrimitiveArrayFunctions2
++ This package provides tools for operating on primitive arrays
++ with unary and binary functions involving different underlying types
PrimitiveArrayFunctions2(A, B): Exports == Implementation where
  A, B: Type

  VA ==> PrimitiveArray A
  VB ==> PrimitiveArray B
  O2 ==> FiniteLinearAggregateFunctions2(A, VA, B, VB)
  Exports ==> with
    scan   : ((A, B) -> B, VA, B) -> VB
	++ scan(f,a,r) successively applies
	++ \spad{reduce(f,x,r)} to more and more leading sub-arrays
	++ x of primitive array \spad{a}.
	++ More precisely, if \spad{a} is \spad{[a1,a2,...]}, then
	++ \spad{scan(f,a,r)} returns
	++ \spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.
    reduce : ((A, B) -> B, VA, B) -> B
	++ reduce(f,a,r) applies function f to each
	++ successive element of the
	++ primitive array \spad{a} and an accumulant initialized to r.
	++ For example,
	++ \spad{reduce(_+$Integer,[1,2,3],0)}
	++ does \spad{3+(2+(1+0))}. Note: third argument r
	++ may be regarded as the
	++ identity element for the function f.
    map    : (A -> B, VA) -> VB
	++ map(f,a) applies function f to each member of primitive array
	++ \spad{a} resulting in a new primitive array over a
	++ possibly different underlying domain.

  Implementation ==> add
    map(f, v)       == map(f, v)$O2
    scan(f, v, b)   == scan(f, v, b)$O2
    reduce(f, v, b) == reduce(f, v, b)$O2

@
\section{domain TUPLE Tuple}
<<domain TUPLE Tuple>>=
)abbrev domain TUPLE Tuple
++ This domain is used to interface with the interpreter's notion
++ of comma-delimited sequences of values.
Tuple(S:Type): HomotopicTo (PrimitiveArray S) with
  select: (%, NonNegativeInteger) -> S
	++ select(x,n) returns the n-th element of tuple x.
	++ tuples are 0-based
  length: % -> NonNegativeInteger
	++ length(x) returns the number of elements in tuple x
  if S has CoercibleTo(OutputForm) then CoercibleTo(OutputForm)
  if S has SetCategory then SetCategory
 == add
  Rep := Record(len : NonNegativeInteger, elts : PrimitiveArray S)

  coerce(x: PrimitiveArray S): %  == [#x, x]
  coerce(x:%): PrimitiveArray(S) == x.elts
  length x == x.len

  select(x, n) ==
    n >= x.len => error "Index out of bounds"
    x.elts.n

  if S has SetCategory then
    x = y == (x.len = y.len) and (x.elts =$PrimitiveArray(S) y.elts)
  if S has CoercibleTo(OutputForm) then
    coerce(x : %): OutputForm ==
      paren [(x.elts.i)::OutputForm
             for i in minIndex x.elts .. maxIndex x.elts]$List(OutputForm)

@
\section{domain IFARRAY IndexedFlexibleArray}
<<domain IFARRAY IndexedFlexibleArray>>=
)abbrev domain IFARRAY IndexedFlexibleArray
++ Author: Michael Monagan July/87, modified SMW June/91
++ A FlexibleArray is the notion of an array intended to allow for growth
++ at the end only.  Hence the following efficient operations
++   \spad{append(x,a)} meaning append item x at the end of the array \spad{a}
++   \spad{delete(a,n)} meaning delete the last item from the array \spad{a}
++ Flexible arrays support the other operations inherited from
++ \spadtype{ExtensibleLinearAggregate}. However, these are not efficient.
++ Flexible arrays combine the \spad{O(1)} access time property of arrays
++ with growing and shrinking at the end in \spad{O(1)} (average) time.
++ This is done by using an ordinary array which may have zero or more
++ empty slots at the end.  When the array becomes full it is copied
++ into a new larger (50% larger) array.  Conversely, when the array
++ becomes less than 1/2 full, it is copied into a smaller array.
++ Flexible arrays provide for an efficient implementation of many
++ data structures in particular heaps, stacks and sets.

IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where
  A ==> PrimitiveArray S
  I ==> Integer
  N ==> NonNegativeInteger
  U ==> UniversalSegment Integer
  Exports ==
    Join(OneDimensionalArrayAggregate S,ExtensibleLinearAggregate S) with
      flexibleArray : List S -> %
	++ flexibleArray(l) creates a flexible array from the list of elements l
      physicalLength : % -> NonNegativeInteger
   	++ physicalLength(x) returns the number of elements x can accomodate before growing
      physicalLength!: (%, I) -> %
	++ physicalLength!(x,n) changes the physical length of x to be n and returns the new array.
      shrinkable: Boolean -> Boolean
	++ shrinkable(b) sets the shrinkable attribute of flexible arrays to b and returns the previous value
  Implementation == add
    Rep := Record(physLen:I, logLen:I, f:A)
    shrinkable? : Boolean := true
    growAndFill : (%, I, S) -> %
    growWith    : (%, I, S) -> %
    growAdding  : (%, I, %) -> %
    shrink: (%, I)    -> %
    newa  : (N, A) -> A

    physicalLength(r) == (r.physLen) pretend NonNegativeInteger
    physicalLength!(r, n) ==
       r.physLen = 0  => error "flexible array must be non-empty"
       growWith(r, n, r.f.0)

    empty()      == [0, 0, empty()]
    #r           == (r.logLen)::N
    fill!(r, x) == (fill!(r.f, x); r)
    maxIndex r   == r.logLen - 1 + mn
    minIndex r   == mn
    new(n, a)    == [n, n, new(n, a)]

    shrinkable(b) ==
      oldval := shrinkable?
      shrinkable? := b
      oldval

    flexibleArray l ==
       n := #l
       n = 0 => empty()
       x := l.1
       a := new(n,x)
       for i in mn + 1..mn + n-1 for y in rest l repeat a.i := y
       a

    -- local utility operations
    newa(n, a) ==
       zero? n => empty()
       new(n, a.0)

    growAdding(r, b, s) ==
       b = 0 => r
       positive?(#r) => growAndFill(r, b, (r.f).0)
       positive?(#s) => growAndFill(r, b, (s.f).0)
       error "no default filler element"

    growAndFill(r, b, x) ==
       (r.logLen := r.logLen + b) <= r.physLen => r
       -- enlarge by 50% + b
       n := r.physLen + r.physLen quo 2 + 1
       if r.logLen > n then n := r.logLen
       growWith(r, n, x)

    growWith(r, n, x) ==
       y := new(n::N, x)$PrimitiveArray(S)
       a := r.f
       for k in 0 .. r.physLen-1 repeat y.k := a.k
       r.physLen := n
       r.f := y
       r

    shrink(r, i) ==
       r.logLen := r.logLen - i
       negative?(n := r.logLen) => error "internal bug in flexible array"
       2*n+2 > r.physLen => r
       not shrinkable? => r
       if n < r.logLen then error "cannot shrink flexible array to indicated size"
       n = 0 => empty()
       r.physLen := n
       y := newa(n::N, a := r.f)
       for k in 0 .. n-1 repeat y.k := a.k
       r.f := y
       r

    copy r ==
       n := #r
       a := r.f
       v := newa(n, a := r.f)
       for k in 0..n-1 repeat v.k := a.k
       [n, n, v]


    elt(r:%, i:I) ==
       i < mn or i >= r.logLen + mn =>
           error "index out of range"
       r.f.(i-mn)

    setelt(r:%, i:I, x:S) ==
       i < mn or i >= r.logLen + mn =>
           error "index out of range"
       r.f.(i-mn) := x

    -- operations inherited from extensible aggregate
    merge(g, a, b)   == merge!(g, copy a, b)
    concat(x:S, r:%) == insert!(x, r, mn)

    concat!(r:%, x:S) ==
       growAndFill(r, 1, x)
       r.f.(r.logLen-1) := x
       r

    concat!(a:%, b:%) ==
       if eq?(a, b) then b := copy b
       n := #a
       growAdding(a, #b, b)
       copyInto!(a, b, n + mn)

    remove!(g:(S->Boolean), a:%) ==
       k:I := 0
       for i in 0..maxIndex a - mn repeat
          if not g(a.i) then (a.k := a.i; k := k+1)
       shrink(a, #a - k)

    delete!(r:%, i1:I) ==
       i := i1 - mn
       negative? i or i > r.logLen => error "index out of range"
       for k in i..r.logLen-2 repeat r.f.k := r.f.(k+1)
       shrink(r, 1)

    delete!(r:%, i:U) ==
       l := lo i - mn; m := maxIndex r - mn
       h := (hasHi i => hi i - mn; m)
       negative? l or h > m => error "index out of range"
       for j in l.. for k in h+1..m repeat r.f.j := r.f.k
       shrink(r, max(0,h-l+1))

    insert!(x:S, r:%, i1:I):% ==
       i := i1 - mn
       n := r.logLen
       negative? i or i > n => error "index out of range"
       growAndFill(r, 1, x)
       for k in n-1 .. i by -1 repeat r.f.(k+1) := r.f.k
       r.f.i := x
       r

    insert!(a:%, b:%, i1:I):% ==
       i := i1 - mn
       if eq?(a, b) then b := copy b
       m := #a; n := #b
       negative? i or i > n => error "index out of range"
       growAdding(b, m, a)
       for k in n-1 .. i by -1 repeat b.f.(m+k) := b.f.k
       for k in m-1 .. 0 by -1 repeat b.f.(i+k) := a.f.k
       b

    merge!(g, a, b) ==
       m := #a; n := #b; growAdding(a, n, b)
       for i in m-1..0 by -1 for j in m+n-1.. by -1 repeat a.f.j := a.f.i
       i := n; j := 0
       k : Integer := 0
       while i < n+m and j < n repeat
          if g(a.f.i,b.f.j) then (a.f.k := a.f.i; i := i+1)
          else (a.f.k := b.f.j; j := j+1)
          k := k + 1
       for j' in j..n-1 repeat
         a.f.k := b.f.j'
         k := k + 1
       a

    select!(g:(S->Boolean), a:%) ==
       k:I := 0
       for i in 0..maxIndex a - mn repeat if g(a.f.i) then (a.f.k := a.f.i;k := k+1)
       shrink(a, #a - k)

    if S has SetCategory then
      removeDuplicates! a ==
         ct := #a
         ct < 2 => a

         i     := mn
         nlim  := mn + ct
         nlim0 := nlim
         while i < nlim repeat
            j := i+1
            for k in j..nlim-1 | a.k ~= a.i repeat
                a.j := a.k
                j := j+1
            nlim := j
            i := i+1
         nlim ~= nlim0 => delete!(a, i..)
         a

@
\section{domain FARRAY FlexibleArray}
<<domain FARRAY FlexibleArray>>=
)abbrev domain FARRAY FlexibleArray
++ A FlexibleArray is the notion of an array intended to allow for growth
++ at the end only.  Hence the following efficient operations
++   \spad{append(x,a)} meaning append item x at the end of the array \spad{a}
++   \spad{delete(a,n)} meaning delete the last item from the array \spad{a}
++ Flexible arrays support the other operations inherited from
++ \spadtype{ExtensibleLinearAggregate}. However, these are not efficient.
++ Flexible arrays combine the \spad{O(1)} access time property of arrays
++ with growing and shrinking at the end in \spad{O(1)} (average) time.
++ This is done by using an ordinary array which may have zero or more
++ empty slots at the end.  When the array becomes full it is copied
++ into a new larger (50% larger) array.  Conversely, when the array
++ becomes less than 1/2 full, it is copied into a smaller array.
++ Flexible arrays provide for an efficient implementation of many
++ data structures in particular heaps, stacks and sets.

FlexibleArray(S: Type) == Implementation where
  ARRAYMININDEX ==> 1       -- if you want to change this, be my guest
  Implementation ==> IndexedFlexibleArray(S, ARRAYMININDEX)
-- Join(OneDimensionalArrayAggregate S, ExtensibleLinearAggregate S)

@
\section{domain IARRAY1 IndexedOneDimensionalArray}
<<domain IARRAY1 IndexedOneDimensionalArray>>=
)abbrev domain IARRAY1 IndexedOneDimensionalArray
++ Author Micheal Monagan Aug/87
++ This is the basic one dimensional array data type.

IndexedOneDimensionalArray(S:Type, mn:Integer):
 OneDimensionalArrayAggregate S == add
   macro Qmax == maxIndexOfSimpleArray$Foreign(Builtin)
   macro Qsetelt == setSimpleArrayEntry$Foreign(Builtin)
   macro I == Integer

   import %icst0: I                         from Foreign Builtin
   import %icst1: I                         from Foreign Builtin
   import %ilt: (I,I) -> Boolean            from Foreign Builtin
   import %vlength: % -> NonNegativeInteger from Foreign Builtin
   import %aref: (%,Integer) -> S           from Foreign Builtin

   Rep == PrimitiveArray S

   newArray(n: Integer): % ==
     makeSimpleArray(getVMType(S)$Foreign(Builtin),n)$Foreign(Builtin)

   #x == # rep x
   copy x == per copy rep x
   fill!(x, s) == per fill!(rep x, s)
   minIndex x == mn

   empty() == per empty()$Rep
   new(n, s) == per new(n,s)$Rep
   construct l == per construct(l)$Rep

   map!(f, s1)  ==
      n: Integer := Qmax(s1)
      negative? n => s1
      for i in %icst0..n repeat Qsetelt(s1,i,f %aref(s1,i))
      s1

   map(f, s1)       ==
      n:Integer := Qmax(s1)
      negative? n => s1
      ss2:% := newArray(n+1)
      for i in %icst0..n repeat Qsetelt(ss2,i,f %aref(s1,i))
      ss2

   map(f, a, b)   ==
      maxind:Integer := min(Qmax a, Qmax b)
      negative? maxind => empty()
      c:% := newArray(maxind + %icst1)
      for i in %icst0..maxind repeat
        Qsetelt(c,i,f(%aref(a,i),%aref(b,i)))
      c

   if zero? mn then
     qelt(x, i)       == %aref(x, i)
     qsetelt!(x, i, s) == Qsetelt(x, i, s)

     elt(x:%, i:I) ==
       negative? i or i > maxIndex(x) => error "index out of range"
       qelt(x, i)

     setelt(x:%, i:I, s:S) ==
       negative? i or i > maxIndex(x) => error "index out of range"
       qsetelt!(x, i, s)

   else if one? mn then
     maxIndex x       == %vlength x
     qelt(x, i)       == %aref(x, i - %icst1)
     qsetelt!(x, i, s) == Qsetelt(x, i - %icst1, s)

     elt(x:%, i:I) ==
       %ilt(i,%icst1) or %ilt(%vlength x,i) =>
         error "index out of range"
       %aref(x, i - %icst1)

     setelt(x:%, i:I, s:S) ==
       %ilt(i,%icst1) or %ilt(%vlength x,i) =>
         error "index out of range"
       Qsetelt(x, i - %icst1, s)

    else
       qelt(x, i)       == %aref(x, i - mn)
       qsetelt!(x, i, s) == Qsetelt(x, i - mn, s)

       elt(x:%, i:I) ==
         i < mn or i > maxIndex(x) => error "index out of range"
         qelt(x, i)

       setelt(x:%, i:I, s:S) ==
         i < mn or i > maxIndex(x) => error "index out of range"
         qsetelt!(x, i, s)

@
\section{domain ARRAY1 OneDimensionalArray}
<<domain ARRAY1 OneDimensionalArray>>=
)abbrev domain ARRAY1 OneDimensionalArray
++ This is the domain of 1-based one dimensional arrays

OneDimensionalArray(S:Type): Exports == Implementation where
  ARRAYMININDEX ==> 1       -- if you want to change this, be my guest
  Exports == OneDimensionalArrayAggregate S with
    oneDimensionalArray: List S -> %
	++ oneDimensionalArray(l) creates an array from a list of elements l
    oneDimensionalArray: (NonNegativeInteger, S) -> %
	++ oneDimensionalArray(n,s) creates an array from n copies of element s
  Implementation == IndexedOneDimensionalArray(S, ARRAYMININDEX) add
    oneDimensionalArray(u) == construct u
    oneDimensionalArray(n,s) == new(n,s)

@
\section{package ARRAY12 OneDimensionalArrayFunctions2}
<<package ARRAY12 OneDimensionalArrayFunctions2>>=
)abbrev package ARRAY12 OneDimensionalArrayFunctions2
++ This package provides tools for operating on one-dimensional arrays
++ with unary and binary functions involving different underlying types
OneDimensionalArrayFunctions2(A, B): Exports == Implementation where
  A, B: Type

  VA ==> OneDimensionalArray A
  VB ==> OneDimensionalArray B
  O2 ==> FiniteLinearAggregateFunctions2(A, VA, B, VB)

  Exports ==> with
    scan   : ((A, B) -> B, VA, B) -> VB
	++ scan(f,a,r) successively applies
	++ \spad{reduce(f,x,r)} to more and more leading sub-arrays
	++ x of one-dimensional array \spad{a}.
	++ More precisely, if \spad{a} is \spad{[a1,a2,...]}, then
	++ \spad{scan(f,a,r)} returns
	++ \spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.
    reduce : ((A, B) -> B, VA, B) -> B
	++ reduce(f,a,r) applies function f to each
	++ successive element of the
	++ one-dimensional array \spad{a} and an accumulant initialized to r.
	++ For example,
	++ \spad{reduce(_+$Integer,[1,2,3],0)}
	++ does \spad{3+(2+(1+0))}. Note: third argument r
	++ may be regarded as the
	++ identity element for the function f.
    map    : (A -> B, VA) -> VB
	++ map(f,a) applies function f to each member of one-dimensional array
	++ \spad{a} resulting in a new one-dimensional array over a
	++ possibly different underlying domain.

  Implementation ==> add
    map(f, v)       == map(f, v)$O2
    scan(f, v, b)   == scan(f, v, b)$O2
    reduce(f, v, b) == reduce(f, v, b)$O2

@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
-- Copyright (C) 2007-2013, Gabriel Dos Reis.
-- All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
--    - Redistributions of source code must retain the above copyright
--      notice, this list of conditions and the following disclaimer.
--
--    - Redistributions in binary form must reproduce the above copyright
--      notice, this list of conditions and the following disclaimer in
--      the documentation and/or other materials provided with the
--      distribution.
--
--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--      names of its contributors may be used to endorse or promote products
--      derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>

<<domain PRIMARR PrimitiveArray>>
<<package PRIMARR2 PrimitiveArrayFunctions2>>
<<domain TUPLE Tuple>>
<<domain IFARRAY IndexedFlexibleArray>>
<<domain FARRAY FlexibleArray>>
<<domain IARRAY1 IndexedOneDimensionalArray>>
<<domain ARRAY1 OneDimensionalArray>>
<<package ARRAY12 OneDimensionalArrayFunctions2>>

--%% TupleFunctions2
--TupleFunctions2(A:Type, B:Type): with
--  map: (A -> B, Tuple A) -> Tuple B
-- == add
--  map(f, t) ==
--    p:PrimitiveArray(B) := new length t
--    for i in minIndex p .. maxIndex p repeat
--      p.i := f select(t, i)
--    p::Tuple(B)

@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}