aboutsummaryrefslogtreecommitdiff
path: root/src/algebra/mkfunc.spad.pamphlet
blob: 39c47899176035cbe2268124b9facdf71640cdb0 (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
\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra mkfunc.spad}
\author{Manuel Bronstein}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain INFORM InputForm}
<<domain INFORM InputForm>>=
)abbrev domain INFORM InputForm
++ Parser forms
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: September 18, 2008
++ Description:
++   Domain of parsed forms which can be passed to the interpreter.
++   This is also the interface between algebra code and facilities
++   in the interpreter.

--)boot $noSubsumption := true

InputForm():
  Join(SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm),
       ConvertibleTo SExpression) with
    interpret: % -> Any
      ++ interpret(f) passes f to the interpreter.
    convert  : SExpression -> %
      ++ convert(s) makes s into an input form.
    binary   : (%, List %) -> %
      ++ \spad{binary(op, [a1,...,an])} returns the input form
      ++ corresponding to  \spad{a1 op a2 op ... op an}.
    function : (%, List Symbol, Symbol) -> %
      ++ \spad{function(code, [x1,...,xn], f)} returns the input form
      ++ corresponding to \spad{f(x1,...,xn) == code}.
    lambda   : (%, List Symbol) -> %
      ++ \spad{lambda(code, [x1,...,xn])} returns the input form
      ++ corresponding to \spad{(x1,...,xn) +-> code} if \spad{n > 1},
      ++ or to \spad{x1 +-> code} if \spad{n = 1}.
    "+"      : (%, %) -> %
      ++ \spad{a + b} returns the input form corresponding to \spad{a + b}.
    "*"      : (%, %) -> %
      ++ \spad{a * b} returns the input form corresponding to \spad{a * b}.
    "/"      : (%, %) -> %
      ++ \spad{a / b} returns the input form corresponding to \spad{a / b}.
    "**"     : (%, NonNegativeInteger) -> %
      ++ \spad{a ** b} returns the input form corresponding to \spad{a ** b}.
    "**"     : (%, Integer) -> %
      ++ \spad{a ** b} returns the input form corresponding to \spad{a ** b}.
    0        : constant -> %
      ++ \spad{0} returns the input form corresponding to 0.
    1        : constant -> %
      ++ \spad{1} returns the input form corresponding to 1.
    flatten  : % -> %
      ++ flatten(s) returns an input form corresponding to s with
      ++ all the nested operations flattened to triples using new
      ++ local variables.
      ++ If s is a piece of code, this speeds up
      ++ the compilation tremendously later on.
    unparse  : % -> String
      ++ unparse(f) returns a string s such that the parser
      ++ would transform s to f.
      ++ Error: if f is not the parsed form of a string.
    parseString: String -> %
      ++ parseString is the inverse of unparse.  It parses a 
      ++ string to InputForm.
    declare  : List %   -> Symbol
      ++ declare(t) returns a name f such that f has been
      ++ declared to the interpreter to be of type t, but has
      ++ not been assigned a value yet.
      ++ Note: t should be created as \spad{devaluate(T)$Lisp} where T is the
      ++ actual type of f (this hack is required for the case where
      ++ T is a mapping type).
    compile  : (Symbol, List %) -> Symbol
      ++ \spad{compile(f, [t1,...,tn])} forces the interpreter to compile
      ++ the function f with signature \spad{(t1,...,tn) -> ?}.
      ++ returns the symbol f if successful.
      ++ Error: if f was not defined beforehand in the interpreter,
      ++ or if the ti's are not valid types, or if the compiler fails.
 == SExpression add
    Rep := SExpression

    mkProperOp: Symbol -> %
    strsym    : % -> String
    tuplify   : List Symbol -> %
    flatten0  : (%, Symbol, NonNegativeInteger) ->
                                             Record(lst: List %, symb:%)

    0                        == convert(0::Integer)
    1                        == convert(1::Integer)
    convert(x:%):SExpression == x pretend SExpression
    convert(x:SExpression):% == x

    conv(ll : List %): % ==
      convert(ll pretend List SExpression)$SExpression pretend %

    lambda(f,l) == conv([convert("+->"::Symbol),tuplify l,f]$List(%))

    interpret x ==
      v := interpret(x)$Lisp
      objNew(unwrap(objVal(v)$Lisp)$Lisp, objMode(v)$Lisp)$Lisp

    convert(x:DoubleFloat):% ==
      zero? x => 0
--      one? x => 1
      (x = 1) => 1
      convert(x)$Rep

    flatten s ==
      -- will not compile if I use 'or'
      atom? s => s
      every?(atom?,destruct s)$List(%) => s
      sy := new()$Symbol
      n:NonNegativeInteger := 0
      l := destruct s
      l2 := [flatten0(x, sy, n := n + 1) for x in rest l]
      conv(concat(convert("SEQ"::Symbol)@%,
        concat(concat [u.lst for u in l2], conv(
           [convert("exit"::Symbol)@%, 1$%, conv(concat(first l,
               [u.symb for u in l2]))@%]$List(%))@%)))@%

    flatten0(s, sy, n) ==
      atom? s => [nil(), s]
      a := convert(concat(string sy, convert(n)@String)::Symbol)@%
      l := destruct s
      l2 := [flatten0(x, sy, n := n+1) for x in rest l]
      [concat(concat [u.lst for u in l2], conv([convert(
        "LET"::Symbol)@%, a, conv(concat(first l,
             [u.symb for u in l2]))@%]$List(%))@%), a]

    strsym s ==
      string? s => string s
      symbol? s => string symbol s
      error ["strsym: form", s, "is neither a string or symbol"]

    unparse x ==
      atom?(s:% := form2String(x)$Lisp) => strsym s
      concat [strsym a for a in destruct s]

    parseString x ==
      ncParseFromString(x)$Lisp

    declare signature ==
      declare(name := new()$Symbol, signature)$Lisp
      name

    compile(name, types) ==
      symbol car cdr car
        selectLocalMms(mkProperOp name, convert(name)@%,
          types, nil$List(%))$Lisp

    mkProperOp name ==
      op := mkAtree(nme := convert(name)@%)$Lisp
      transferPropsToNode(nme, op)$Lisp
      convert op

    binary(op, args) ==
      (n := #args) < 2 => error "Need at least 2 arguments"
      n = 2 => convert([op, first args, last args]$List(%))
      convert([op, first args, binary(op, rest args)]$List(%))

    tuplify l ==
      empty? rest l => convert first l
      conv
        concat(convert("Tuple"::Symbol), [convert x for x in l]$List(%))

    function(f, l, name) ==
      nn := convert(new(1 + #l, convert(nil()$List(%)))$List(%))@%
      conv([convert("DEF"::Symbol), conv(cons(convert(name)@%,
                        [convert(x)@% for x in l])), nn, nn, f]$List(%))

    s1 + s2 ==
      s1 = 0 => s2
      s2 = 0 => s1
      conv [convert("+"::Symbol), s1, s2]$List(%)

    s1 * s2 ==
      s1 = 0 or s2 = 0 => 0
      s1 = 1 => s2
      s2 = 1 => s1
      conv [convert("*"::Symbol), s1, s2]$List(%)

    s1:% ** n:Integer ==
      s1 = 0 and n > 0 => 0
      s1 = 1 or zero? n => 1
--      one? n => s1
      (n = 1) => s1
      conv [convert("**"::Symbol), s1, convert n]$List(%)

    s1:% ** n:NonNegativeInteger == s1 ** (n::Integer)

    s1 / s2 ==
      s2 = 1 => s1
      conv [convert("/"::Symbol), s1, s2]$List(%)

@
\section{package INFORM1 InputFormFunctions1}
<<package INFORM1 InputFormFunctions1>>=
)abbrev package INFORM1 InputFormFunctions1
--)boot $noSubsumption := false

++ Tools for manipulating input forms
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 19 April 1991
++ Description: Tools for manipulating input forms.

InputFormFunctions1(R:Type):with
  packageCall: Symbol -> InputForm
    ++ packageCall(f) returns the input form corresponding to f$R.
  interpret  : InputForm -> R
    ++ interpret(f) passes f to the interpreter, and transforms
    ++ the result into an object of type R.
 == add
  Rname := devaluate(R)$Lisp :: InputForm

  packageCall name ==
    convert([convert("$elt"::Symbol), Rname,
                                convert name]$List(InputForm))@InputForm

  interpret form ==
    retract(interpret(convert([convert("@"::Symbol), form,
          Rname]$List(InputForm))@InputForm)$InputForm)$AnyFunctions1(R)

@
\section{package MKFUNC MakeFunction}
<<package MKFUNC MakeFunction>>=
)abbrev package MKFUNC MakeFunction
++ Tools for making interpreter functions from top-level expressions
++ Author: Manuel Bronstein
++ Date Created: 22 Nov 1988
++ Date Last Updated: 8 Jan 1990
++ Description: transforms top-level objects into interpreter functions.
MakeFunction(S:ConvertibleTo InputForm): Exports == Implementation where
  SY ==> Symbol

  Exports ==> with
    function: (S, SY         ) -> SY
      ++ function(e, foo) creates a function \spad{foo() == e}.
    function: (S, SY,      SY) -> SY
      ++ function(e, foo, x) creates a function \spad{foo(x) == e}.
    function: (S, SY, SY,  SY) -> SY
      ++ function(e, foo, x, y) creates a function \spad{foo(x, y) = e}.
    function: (S, SY, List SY) -> SY
      ++ \spad{function(e, foo, [x1,...,xn])} creates a function
      ++ \spad{foo(x1,...,xn) == e}.

  Implementation ==> add
    function(s, name)            == function(s, name, nil())
    function(s:S, name:SY, x:SY) == function(s, name, [x])
    function(s, name, x, y)      == function(s, name, [x, y])

    function(s:S, name:SY, args:List SY) ==
      interpret function(convert s, args, name)$InputForm
      name

@

\section{package MKUCFUNC MakeUnaryCompiledFunction}

<<package MKUCFUNC MakeUnaryCompiledFunction>>=
import Type
import Symbol
import ConvertibleTo InputForm
)abbrev package MKUCFUNC MakeUnaryCompiledFunction
++ Tools for making compiled functions from top-level expressions
++ Author: Manuel Bronstein
++ Date Created: 1 Dec 1988
++ Date Last Updated: 5 Mar 1990
++ Description: transforms top-level objects into compiled functions.
MakeUnaryCompiledFunction(S, D, I): Exports == Implementation where
  S: ConvertibleTo InputForm
  D, I: Type

  SY  ==> Symbol
  DI  ==> devaluate(D -> I)$Lisp

  Exports ==> with
    unaryFunction   : SY -> (D -> I)
      ++ unaryFunction(a) is a local function
    compiledFunction: (S, SY) -> (D -> I)
      ++ compiledFunction(expr, x) returns a function \spad{f: D -> I}
      ++ defined by \spad{f(x) == expr}. 
      ++ Function f is compiled and directly
      ++ applicable to objects of type D.

  Implementation ==> add
    import MakeFunction(S)

    func: (SY, D) -> I

    func(name, x)       == FUNCALL(name, x, NIL$Lisp)$Lisp
    unaryFunction name  == func(name, #1)

    compiledFunction(e:S, x:SY) ==
      t := [convert([devaluate(D)$Lisp]$List(InputForm))
           ]$List(InputForm)
      unaryFunction compile(function(e, declare DI, x), t)

@

\section{package MKBCFUNC MakeBinaryCompiledFunction}

<<package MKBCFUNC MakeBinaryCompiledFunction>>=
import Type
import CoercibleTo InputForm
import Symbol
)abbrev package MKBCFUNC MakeBinaryCompiledFunction
++ Tools for making compiled functions from top-level expressions
++ Author: Manuel Bronstein
++ Date Created: 1 Dec 1988
++ Date Last Updated: 5 Mar 1990
++ Description: transforms top-level objects into compiled functions.
MakeBinaryCompiledFunction(S, D1, D2, I):Exports == Implementation where
  S: ConvertibleTo InputForm
  D1, D2, I: Type

  SY  ==> Symbol
  DI  ==> devaluate((D1, D2) -> I)$Lisp

  Exports ==> with
    binaryFunction  : SY -> ((D1, D2) -> I)
      ++ binaryFunction(s) is a local function
    compiledFunction: (S, SY, SY) -> ((D1, D2) -> I)
      ++ compiledFunction(expr,x,y) returns a function \spad{f: (D1, D2) -> I}
      ++ defined by \spad{f(x, y) == expr}.
      ++ Function f is compiled and directly
      ++ applicable to objects of type \spad{(D1, D2)}

  Implementation ==> add
    import MakeFunction(S)

    func: (SY, D1, D2) -> I

    func(name, x, y)   == FUNCALL(name, x, y, NIL$Lisp)$Lisp
    binaryFunction name == func(name, #1, #2)

    compiledFunction(e, x, y) ==
      t := [devaluate(D1)$Lisp, devaluate(D2)$Lisp]$List(InputForm)
      binaryFunction compile(function(e, declare DI, x, y), t)

@
\section{package MKFLCFN MakeFloatCompiledFunction}
<<package MKFLCFN MakeFloatCompiledFunction>>=
)abbrev package MKFLCFN MakeFloatCompiledFunction
++ Tools for making compiled functions from top-level expressions
++ Author: Manuel Bronstein
++ Date Created: 2 Mar 1990
++ Date Last Updated: 2 Dec 1996 (MCD)
++ Description:
++ MakeFloatCompiledFunction transforms top-level objects into
++ compiled Lisp functions whose arguments are Lisp floats.
++ This by-passes the \Language{} compiler and interpreter,
++ thereby gaining several orders of magnitude.
MakeFloatCompiledFunction(S): Exports == Implementation where
  S: ConvertibleTo InputForm

  INF ==> InputForm
  SF  ==> DoubleFloat
  DI1 ==> devaluate(SF -> SF)$Lisp
  DI2 ==> devaluate((SF, SF) -> SF)$Lisp

  Exports ==> with
    makeFloatFunction: (S, Symbol)         -> (SF -> SF)
      ++ makeFloatFunction(expr, x) returns a Lisp function
      ++ \spad{f: \axiomType{DoubleFloat} -> \axiomType{DoubleFloat}}
      ++ defined by \spad{f(x) == expr}. 
      ++ Function f is compiled and directly
      ++ applicable to objects of type \axiomType{DoubleFloat}.
    makeFloatFunction: (S, Symbol, Symbol) -> ((SF, SF) -> SF)
      ++ makeFloatFunction(expr, x, y) returns a Lisp function
      ++ \spad{f: (\axiomType{DoubleFloat}, \axiomType{DoubleFloat}) -> \axiomType{DoubleFloat}}
      ++ defined by \spad{f(x, y) == expr}.
      ++ Function f is compiled and directly
      ++ applicable to objects of type \spad{(\axiomType{DoubleFloat}, \axiomType{DoubleFloat})}.

  Implementation ==> add
    import MakeUnaryCompiledFunction(S, SF, SF)
    import MakeBinaryCompiledFunction(S, SF, SF, SF)

    streq?    : (INF, String) -> Boolean
    streqlist?: (INF, List String) -> Boolean
    gencode   : (String, List INF) -> INF
    mkLisp    : INF -> Union(INF, "failed")
    mkLispList: List INF -> Union(List INF, "failed")
    mkDefun   : (INF, List INF) -> INF
    mkLispCall: INF -> INF
    mkPretend : INF -> INF
    mkCTOR : INF -> INF

    lsf := convert([convert("DoubleFloat"::Symbol)@INF]$List(INF))@INF

    streq?(s, st)    == s = convert(st::Symbol)@INF
    gencode(s, l)    == convert(concat(convert(s::Symbol)@INF, l))@INF
    streqlist?(s, l) == member?(string symbol s, l)

    mkPretend form ==
      convert([convert("pretend"::Symbol), form, lsf]$List(INF))@INF

    mkCTOR form ==
      convert([convert("C-TO-R"::Symbol), form]$List(INF))@INF


    mkLispCall name ==
      convert([convert("$elt"::Symbol),
                           convert("Lisp"::Symbol), name]$List(INF))@INF

    mkDefun(s, lv) ==
      name := convert(new()$Symbol)@INF
      fun  := convert([convert("DEFUN"::Symbol), name, convert lv,
              gencode("DECLARE",[gencode("FLOAT",lv)]),mkCTOR s]$List(INF))@INF
      EVAL(fun)$Lisp
      if _$compileDontDefineFunctions$Lisp then COMPILE(name)$Lisp
      name

    makeFloatFunction(f, x, y) ==
      (u := mkLisp(convert(f)@INF)) case "failed" =>
        compiledFunction(f, x, y)
      name := mkDefun(u::INF, [ix := convert x, iy := convert y])
      t    := [lsf, lsf]$List(INF)
      spadname := declare DI2
      spadform:=mkPretend convert([mkLispCall name,ix,iy]$List(INF))@INF
      interpret function(spadform, [x, y], spadname)
      binaryFunction compile(spadname, t)

    makeFloatFunction(f, var) ==
      (u := mkLisp(convert(f)@INF)) case "failed" =>
        compiledFunction(f, var)
      name := mkDefun(u::INF, [ivar := convert var])
      t    := [lsf]$List(INF)
      spadname := declare DI1
      spadform:= mkPretend convert([mkLispCall name,ivar]$List(INF))@INF
      interpret function(spadform, [var], spadname)
      unaryFunction compile(spadname, t)

    mkLispList l ==
      ans := nil()$List(INF)
      for s in l repeat
        (u := mkLisp s) case "failed" => return "failed"
        ans := concat(u::INF, ans)
      reverse_! ans
    

    mkLisp s ==
      atom? s => s
      op := first(l := destruct s)
      (u := mkLispList rest l) case "failed" => "failed"
      ll := u::List(INF)
      streqlist?(op, ["+","*","/","-"]) => convert(concat(op, ll))@INF
      streq?(op, "**") => gencode("EXPT", ll)
      streqlist?(op, ["exp","sin","cos","tan","atan", 
         "log", "sinh","cosh","tanh","asinh","acosh","atanh","sqrt"]) =>
            gencode(upperCase string symbol op, ll)
      streq?(op, "nthRoot") =>
        second ll = convert(2::Integer)@INF =>gencode("SQRT",[first ll])
        gencode("EXPT", concat(first ll, [1$INF / second ll]))
      streq?(op, "float") =>
        a := ll.1
        e := ll.2
        b := ll.3
        _*(a, EXPT(b, e)$Lisp)$Lisp pretend INF
      "failed"

@
\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>>

<<domain INFORM InputForm>>
<<package INFORM1 InputFormFunctions1>>
<<package MKFUNC MakeFunction>>
<<package MKUCFUNC MakeUnaryCompiledFunction>>
<<package MKBCFUNC MakeBinaryCompiledFunction>>
<<package MKFLCFN MakeFloatCompiledFunction>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}