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
|
\documentclass{article}
\usepackage{axiom}
\title{\$SPAD/src/algebra coerce.spad}
\author{Richard Jenks, Manuel Bronstein, Gabriel Dos Reis}
\begin{document}
\maketitle
\begin{abstract}
\end{abstract}
\tableofcontents
\eject
\section{category TYPE Type}
<<category TYPE Type>>=
)abbrev category TYPE Type
++ The new fundamental Type (keeping Object for 1.5 as well)
++ Author: Richard Jenks
++ Date Created: 14 May 1992
++ Date Last Updated: 14 May 1992
++ Description: The fundamental Type;
Type(): Category == with nil
@
\section{Category UnionType}
<<category UTYPE UnionType>>=
)abbrev category UTYPE UnionType
++ Author: Gabriel Dos Reis
++ Date Created: December 17, 2007
++ Date Last Modified: December 17, 2007
++ Description: The category of domains that act like unions.
++ UnionType, like Type or Category, acts mostly as a take that
++ communicates `union-like' intended semantics to the compiler.
++ A domain D that satifies UnionType should provide definitions
++ for `case' operators, with corresponding `autoCoerce' operators.
UnionType(): Category == with nil
@
\section{category KOERCE CoercibleTo}
<<category KOERCE CoercibleTo>>=
)abbrev category KOERCE CoercibleTo
++ Category for coerce
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 14 May 1991
++ Description:
++ A is coercible to B means any element of A can automatically be
++ converted into an element of B by the interpreter.
CoercibleTo(S:Type): Category == with
coerce: % -> S
++ coerce(a) transforms a into an element of S.
@
\section{category KRCFROM CoercibleFrom}
<<category KRCFROM CoercibleFrom>>=
)abbrev category KRCFROM CoercibleFrom
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: CoercibleTo
++ Description:
++ A is coercible from B iff any element of domain B can be
++ automically converted into an element of domain B. In symbols
++ A has CoercibleFrom B <=> B has CoercibleTo A
CoercibleFrom(S: Type): Category == with
coerce: S -> %
++ coerce(s) transforms `s' into an element of `%'.
@
\section{category HOMOTOP HomotopicTo}
<<category HOMOTOP HomotopicTo>>=
)abbrev category HOMOTOP HomotopicTo
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: CoercibleTo, CoercibleFrom
++ Description:
++ A is homotopic to B iff any element of domain B can be
++ automically converted into an element of domain B, and nay
++ element of domain B can be automatically converted into an A.
HomotopicTo(S: Type): Category == Join(CoercibleTo S, CoercibleFrom S)
@
\section{category KONVERT ConvertibleTo}
<<category KONVERT ConvertibleTo>>=
)abbrev category KONVERT ConvertibleTo
++ Category for convert
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 14 May 1991
++ Description:
++ A is convertible to B means any element of A
++ can be converted into an element of B,
++ but not automatically by the interpreter.
ConvertibleTo(S:Type): Category == with
convert: % -> S
++ convert(a) transforms a into an element of S.
@
\section{category KVTFROM ConvertibleFrom}
<<category KVTFROM ConvertibleFrom>>=
)abbrev category KVTFROM ConvertibleFrom
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: ConvertibleTo
++ Description:
++ A is convertible from B iff any element of domain B can be
++ explicitly converted into an element of domain B. In symbols
++ A has ConvertibleFrom B <=> B has ConvertibleTo A
ConvertibleFrom(S: Type): Category == with
convert: S -> %
++ convert(s) transforms `s' into an element of `%'.
@
\section{category RETRACT RetractableTo}
<<category RETRACT RetractableTo>>=
)abbrev category RETRACT RetractableTo
++ Category for retract
++ Author: ???
++ Date Created: ???
++ Date Last Updated: November 19, 2008
++ Related Constructor: CoercibleFrom
++ Description:
++ A is retractable to B means that some elementsif A can be converted
++ into elements of B and any element of B can be converted into an
++ element of A.
RetractableTo(S: Type): Category == CoercibleFrom S with
retractIfCan: % -> Union(S,"failed")
++ retractIfCan(a) transforms a into an element of S if possible.
++ Returns "failed" if a cannot be made into an element of S.
retract: % -> S
++ retract(a) transforms a into an element of S if possible.
++ Error: if a cannot be made into an element of S.
add
retract(s) ==
(u:=retractIfCan s) case "failed" => error "not retractable"
u
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--Copyright (C) 2007-2008, 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>>
<<category TYPE Type>>
<<category UTYPE UnionType>>
<<category KOERCE CoercibleTo>>
<<category KRCFROM CoercibleFrom>>
<<category HOMOTOP HomotopicTo>>
<<category KONVERT ConvertibleTo>>
<<category KVTFROM ConvertibleFrom>>
<<category RETRACT RetractableTo>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
