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
|
\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra fortcat.spad}
\author{Mike Dewar}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{category FORTFN FortranFunctionCategory}
<<category FORTFN FortranFunctionCategory>>=
)abbrev category FORTFN FortranFunctionCategory
++ Author: Mike Dewar
++ Date Created: 13 January 1994
++ Date Last Updated: 18 March 1994
++ Related Constructors: FortranProgramCategory.
++ Description:
++ \axiomType{FortranFunctionCategory} is the category of arguments to
++ NAG Library routines which return (sets of) function values.
FortranFunctionCategory():Category == FortranProgramCategory with
coerce : List FortranCode -> $
++ coerce(e) takes an object from \spadtype{List FortranCode} and
++ uses it as the body of an ASP.
coerce : FortranCode -> $
++ coerce(e) takes an object from \spadtype{FortranCode} and
++ uses it as the body of an ASP.
coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $
++ coerce(e) takes the component of \spad{e} from
++ \spadtype{List FortranCode} and uses it as the body of the ASP,
++ making the declarations in the \spadtype{SymbolTable} component.
retract : Expression Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Expression Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Expression Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Expression Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Polynomial Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Polynomial Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Polynomial Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Polynomial Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Fraction Polynomial Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Fraction Polynomial Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Fraction Polynomial Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Fraction Polynomial Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
-- NB: These ASPs also have a coerce from an appropriate instantiation
-- of FortranExpression.
@
\section{category FMC FortranMatrixCategory}
<<category FMC FortranMatrixCategory>>=
)abbrev category FMC FortranMatrixCategory
++ Author: Mike Dewar
++ Date Created: 21 March 1994
++ Date Last Updated:
++ Related Constructors: FortranProgramCategory.
++ Description:
++ \axiomType{FortranMatrixCategory} provides support for
++ producing Functions and Subroutines when the input to these
++ is an AXIOM object of type \axiomType{Matrix} or in domains
++ involving \axiomType{FortranCode}.
FortranMatrixCategory():Category == FortranProgramCategory with
coerce : Matrix MachineFloat -> $
++ coerce(v) produces an ASP which returns the value of \spad{v}.
coerce : List FortranCode -> $
++ coerce(e) takes an object from \spadtype{List FortranCode} and
++ uses it as the body of an ASP.
coerce : FortranCode -> $
++ coerce(e) takes an object from \spadtype{FortranCode} and
++ uses it as the body of an ASP.
coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $
++ coerce(e) takes the component of \spad{e} from
++ \spadtype{List FortranCode} and uses it as the body of the ASP,
++ making the declarations in the \spadtype{SymbolTable} component.
@
\section{category FORTCAT FortranProgramCategory}
<<category FORTCAT FortranProgramCategory>>=
)abbrev category FORTCAT FortranProgramCategory
++ Author: Mike Dewar
++ Date Created: November 1992
++ Date Last Updated:
++ Basic Operations:
++ Related Constructors: FortranType, FortranCode, Switch
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
++ \axiomType{FortranProgramCategory} provides various models of
++ FORTRAN subprograms. These can be transformed into actual FORTRAN
++ code.
FortranProgramCategory():Category == Join(Type,CoercibleTo OutputForm) with
outputAsFortran : $ -> Void
++ \axiom{outputAsFortran(u)} translates \axiom{u} into a legal FORTRAN
++ subprogram.
@
\section{category FVC FortranVectorCategory}
<<category FVC FortranVectorCategory>>=
)abbrev category FVC FortranVectorCategory
++ Author: Mike Dewar
++ Date Created: October 1993
++ Date Last Updated: 18 March 1994
++ Related Constructors: FortranProgramCategory.
++ Description:
++ \axiomType{FortranVectorCategory} provides support for
++ producing Functions and Subroutines when the input to these
++ is an AXIOM object of type \axiomType{Vector} or in domains
++ involving \axiomType{FortranCode}.
FortranVectorCategory():Category == FortranProgramCategory with
coerce : Vector MachineFloat -> $
++ coerce(v) produces an ASP which returns the value of \spad{v}.
coerce : List FortranCode -> $
++ coerce(e) takes an object from \spadtype{List FortranCode} and
++ uses it as the body of an ASP.
coerce : FortranCode -> $
++ coerce(e) takes an object from \spadtype{FortranCode} and
++ uses it as the body of an ASP.
coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $
++ coerce(e) takes the component of \spad{e} from
++ \spadtype{List FortranCode} and uses it as the body of the ASP,
++ making the declarations in the \spadtype{SymbolTable} component.
@
\section{category FMTC FortranMachineTypeCategory}
<<category FMTC FortranMachineTypeCategory>>=
)abbrev category FMTC FortranMachineTypeCategory
++ Author: Mike Dewar
++ Date Created: December 1993
++ Date Last Updated:
++ Basic Operations:
++ Related Domains:
++ Also See: FortranExpression, MachineInteger, MachineFloat, MachineComplex
++ AMS Classifications:
++ Keywords:
++ Examples:
++ References:
++ Description: A category of domains which model machine arithmetic
++ used by machines in the AXIOM-NAG link.
FortranMachineTypeCategory():Category == Join(IntegralDomain,OrderedSet,
RetractableTo(Integer) )
@
\section{category FMFUN FortranMatrixFunctionCategory}
<<category FMFUN FortranMatrixFunctionCategory>>=
)abbrev category FMFUN FortranMatrixFunctionCategory
++ Author: Mike Dewar
++ Date Created: March 18 1994
++ Date Last Updated:
++ Related Constructors: FortranProgramCategory.
++ Description:
++ \axiomType{FortranMatrixFunctionCategory} provides support for
++ producing Functions and Subroutines representing matrices of
++ expressions.
FortranMatrixFunctionCategory():Category == FortranProgramCategory with
coerce : List FortranCode -> $
++ coerce(e) takes an object from \spadtype{List FortranCode} and
++ uses it as the body of an ASP.
coerce : FortranCode -> $
++ coerce(e) takes an object from \spadtype{FortranCode} and
++ uses it as the body of an ASP.
coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $
++ coerce(e) takes the component of \spad{e} from
++ \spadtype{List FortranCode} and uses it as the body of the ASP,
++ making the declarations in the \spadtype{SymbolTable} component.
retract : Matrix Expression Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Matrix Expression Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Matrix Expression Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Matrix Expression Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Matrix Polynomial Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Matrix Polynomial Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Matrix Polynomial Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Matrix Polynomial Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Matrix Fraction Polynomial Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Matrix Fraction Polynomial Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Matrix Fraction Polynomial Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Matrix Fraction Polynomial Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
-- NB: These ASPs also have a coerce from an appropriate instantiation
-- of Matrix FortranExpression.
@
\section{category FVFUN FortranVectorFunctionCategory}
<<category FVFUN FortranVectorFunctionCategory>>=
)abbrev category FVFUN FortranVectorFunctionCategory
++ Author: Mike Dewar
++ Date Created: 11 March 1994
++ Date Last Updated: 18 March 1994
++ Related Constructors: FortranProgramCategory.
++ Description:
++ \axiomType{FortranVectorFunctionCategory} is the catagory of arguments
++ to NAG Library routines which return the values of vectors of functions.
FortranVectorFunctionCategory():Category == FortranProgramCategory with
coerce : List FortranCode -> $
++ coerce(e) takes an object from \spadtype{List FortranCode} and
++ uses it as the body of an ASP.
coerce : FortranCode -> $
++ coerce(e) takes an object from \spadtype{FortranCode} and
++ uses it as the body of an ASP.
coerce : Record(localSymbols:SymbolTable,code:List(FortranCode)) -> $
++ coerce(e) takes the component of \spad{e} from
++ \spadtype{List FortranCode} and uses it as the body of the ASP,
++ making the declarations in the \spadtype{SymbolTable} component.
retract : Vector Expression Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Vector Expression Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Vector Expression Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Vector Expression Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Vector Polynomial Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Vector Polynomial Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Vector Polynomial Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Vector Polynomial Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Vector Fraction Polynomial Float -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Vector Fraction Polynomial Float -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retract : Vector Fraction Polynomial Integer -> $
++ retract(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
retractIfCan : Vector Fraction Polynomial Integer -> Union($,"failed")
++ retractIfCan(e) tries to convert \spad{e} into an ASP, checking that
++ legal Fortran-77 is produced.
-- NB: These ASPs also have a coerce from an appropriate instantiation
-- of Vector FortranExpression.
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--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 FORTFN FortranFunctionCategory>>
<<category FMC FortranMatrixCategory>>
<<category FORTCAT FortranProgramCategory>>
<<category FVC FortranVectorCategory>>
<<category FMTC FortranMachineTypeCategory>>
<<category FMFUN FortranMatrixFunctionCategory>>
<<category FVFUN FortranVectorFunctionCategory>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
