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
|
\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{src/algebra aggcat2.spad}
\author{Robert S. Sutor}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{package FLAGG2 FiniteLinearAggregateFunctions2}
<<package FLAGG2 FiniteLinearAggregateFunctions2>>=
import Type
import FiniteLinearAggregate
)abbrev package FLAGG2 FiniteLinearAggregateFunctions2
--% FiniteLinearAggregateFunctions2
++ Author: ???
++ Date Created: ???
++ Date Last Updated: ???
++ Description:
++ FiniteLinearAggregateFunctions2 provides functions involving two
++ FiniteLinearAggregates where the underlying domains might be
++ different. An example of this might be creating a list of rational
++ numbers by mapping a function across a list of integers where the
++ function divides each integer by 1000.
FiniteLinearAggregateFunctions2(S, A, R, B):
Exports == Implementation where
S, R: Type
A : FiniteLinearAggregate S
B : FiniteLinearAggregate R
Exports ==> with
map : (S -> R, A) -> B ++ map(f,a) applies function f to each member of aggregate
++ \spad{a} resulting in a new aggregate over a
++ possibly different underlying domain.
reduce : ((S, R) -> R, A, R) -> R ++ reduce(f,a,r) applies function f to each
++ successive element of the
++ aggregate \spad{a} and an accumulant initialized to r.
++ For example,
++ \spad{reduce(_+$Integer,[1,2,3],0)}
++ does \spad{3+(2+(1+0))}. Note: third argument r
++ may be regarded as the
++ identity element for the function f.
scan : ((S, R) -> R, A, R) -> B ++ scan(f,a,r) successively applies
++ \spad{reduce(f,x,r)} to more and more leading sub-aggregates
++ x of aggregrate \spad{a}.
++ More precisely, if \spad{a} is \spad{[a1,a2,...]}, then
++ \spad{scan(f,a,r)} returns
++ \spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.
Implementation ==> add
getRSample(): R ==
R has sample: R => sample$R
R has random: () -> R => random()$R
NIL$Lisp -- R got to be non-trivial.
if A has ListAggregate(S) then -- A is a list-oid
reduce(fn, l, ident) ==
empty? l => ident
reduce(fn, rest l, fn(first l, ident))
if B has ListAggregate(R) or not(B has ShallowlyMutableAggregate R) then
-- A is a list-oid, and B is either list-oids or not mutable
map(f, l) == construct [f s for s in entries l]
scan(fn, l, ident) ==
empty? l => empty()
val := fn(first l, ident)
concat(val, scan(fn, rest l, val))
else -- A is a list-oid, B a mutable array-oid
map(f, l) ==
i := minIndex(w := new(#l,getRSample())$B)
for a in entries l repeat (qsetelt!(w, i, f a); i := inc i)
w
scan(fn, l, ident) ==
i := minIndex(w := new(#l,getRSample())$B)
vl := ident
for a in entries l repeat
vl := qsetelt!(w, i, fn(a, vl))
i := inc i
w
else -- A is an array-oid
reduce(fn, v, ident) ==
val := ident
for i in minIndex v .. maxIndex v repeat
val := fn(qelt(v, i), val)
val
if B has ListAggregate(R) then -- A is an array-oid, B a list-oid
map(f, v) ==
construct [f qelt(v, i) for i in minIndex v .. maxIndex v]
scan(fn, v, ident) ==
w := empty()$B
for i in minIndex v .. maxIndex v repeat
ident := fn(qelt(v, i), ident)
w := concat(ident, w)
reverse! w
else -- A and B are array-oid's
if B has ShallowlyMutableAggregate R then -- B is also mutable
map(f, v) ==
w := new(#v,getRSample())$B
for i in minIndex w .. maxIndex w repeat
qsetelt!(w, i, f qelt(v, i))
w
scan(fn, v, ident) ==
w := new(#v,getRSample())$B
vl := ident
for i in minIndex v .. maxIndex v repeat
vl := qsetelt!(w, i, fn(qelt(v, i), vl))
w
else -- B non mutable array-oid
map(f, v) ==
construct [f qelt(v, i) for i in minIndex v .. maxIndex v]
scan(fn, v, ident) ==
w := empty()$B
for i in minIndex v .. maxIndex v repeat
ident := fn(qelt(v, i), ident)
w := concat(w, ident)
w
@
\section{package FSAGG2 FiniteSetAggregateFunctions2}
<<package FSAGG2 FiniteSetAggregateFunctions2>>=
import SetCategory
import FiniteSetAggregate
)abbrev package FSAGG2 FiniteSetAggregateFunctions2
--% FiniteSetAggregateFunctions2
++ Author: Robert S. Sutor
++ Date Created: 15 May 1990
++ Date Last Updated: 14 Oct 1993
++ Description:
++ FiniteSetAggregateFunctions2 provides functions involving two
++ finite set aggregates where the underlying domains might be
++ different. An example of this is to create a set of rational
++ numbers by mapping a function across a set of integers, where the
++ function divides each integer by 1000.
FiniteSetAggregateFunctions2(S, A, R, B): Exports == Implementation where
S, R: SetCategory
A : FiniteSetAggregate S
B : FiniteSetAggregate R
Exports ==> with
map : (S -> R, A) -> B ++ map(f,a) applies function f to each member of
++ aggregate \spad{a}, creating a new aggregate with
++ a possibly different underlying domain.
reduce : ((S, R) -> R, A, R) -> R ++ reduce(f,a,r) applies function f to each
++ successive element of the aggregate \spad{a} and an
++ accumulant initialised to r.
++ For example,
++ \spad{reduce(_+$Integer,[1,2,3],0)}
++ does a \spad{3+(2+(1+0))}.
++ Note: third argument r may be regarded
++ as an identity element for the function.
scan : ((S, R) -> R, A, R) -> B ++ scan(f,a,r) successively applies \spad{reduce(f,x,r)}
++ to more and more leading sub-aggregates x of
++ aggregate \spad{a}.
++ More precisely, if \spad{a} is \spad{[a1,a2,...]}, then
++ \spad{scan(f,a,r)} returns
++ \spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.
Implementation ==> add
map(fn, a) ==
set(map(fn, members a)$ListFunctions2(S, R))$B
reduce(fn, a, ident) ==
reduce(fn, members a, ident)$ListFunctions2(S, R)
scan(fn, a, ident) ==
set(scan(fn, members a, ident)$ListFunctions2(S, R))$B
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2009, 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>>
<<package FLAGG2 FiniteLinearAggregateFunctions2>>
<<package FSAGG2 FiniteSetAggregateFunctions2>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
