/usr/share/axiom-20170501/src/algebra/OMEXPR.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | )abbrev package OMEXPR ExpressionToOpenMath
++ Author: Mike Dewar & Vilya Harvey
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{ExpressionToOpenMath} provides support for
++ converting objects of type \spadtype{Expression} into OpenMath.
ExpressionToOpenMath(R) : SIG == CODE where
R : Join(OpenMath, OrderedSet, Ring)
SIG ==> with
OMwrite : Expression R -> String
OMwrite : (Expression R, Boolean) -> String
OMwrite : (OpenMathDevice, Expression R) -> Void
OMwrite : (OpenMathDevice, Expression R, Boolean) -> Void
CODE ==> add
import Expression R
SymInfo ==> Record(cd:String, name:String)
import SymInfo
import Record(key: Symbol, entry: SymInfo)
import AssociationList(Symbol, SymInfo)
import OMENC
----------------------------
-- Local translation tables.
----------------------------
nullaryFunctionAList : AssociationList(Symbol, SymInfo) := construct [_
[pi, ["nums1", "pi"]] ]
unaryFunctionAList : AssociationList(Symbol, SymInfo) := construct [_
[exp, ["transc1", "exp"]],_
[log, ["transc1", "ln"]],_
[sin, ["transc1", "sin"]],_
[cos, ["transc1", "cos"]],_
[tan, ["transc1", "tan"]],_
[cot, ["transc1", "cot"]],_
[sec, ["transc1", "sec"]],_
[csc, ["transc1", "csc"]],_
[asin, ["transc1", "arcsin"]],_
[acos, ["transc1", "arccos"]],_
[atan, ["transc1", "arctan"]],_
[acot, ["transc1", "arccot"]],_
[asec, ["transc1", "arcsec"]],_
[acsc, ["transc1", "arccsc"]],_
[sinh, ["transc1", "sinh"]],_
[cosh, ["transc1", "cosh"]],_
[tanh, ["transc1", "tanh"]],_
[coth, ["transc1", "coth"]],_
[sech, ["transc1", "sech"]],_
[csch, ["transc1", "csch"]],_
[asinh, ["transc1", "arcsinh"]],_
[acosh, ["transc1", "arccosh"]],_
[atanh, ["transc1", "arctanh"]],_
[acoth, ["transc1", "arccoth"]],_
[asech, ["transc1", "arcsech"]],_
[acsch, ["transc1", "arccsch"]],_
[factorial, ["integer1", "factorial"]],_
[abs, ["arith1", "abs"]] ]
-- Still need the following unary functions:
-- digamma
-- Gamma
-- airyAi
-- airyBi
-- erf
-- Ei
-- Si
-- Ci
-- li
-- dilog
-- Still need the following binary functions:
-- Gamma(a, x)
-- Beta(x,y)
-- polygamma(k,x)
-- besselJ(v,x)
-- besselY(v,x)
-- besselI(v,x)
-- besselK(v,x)
-- permutation(n, m)
-- summation(x:%, n:Symbol) : as opposed to "definite" sum
-- product(x:%, n:Symbol) : ditto
------------------------
-- Forward declarations.
------------------------
outputOMExpr : (OpenMathDevice, Expression R) -> Void
-------------------------
-- Local helper functions
-------------------------
outputOMArith1(dev: OpenMathDevice, sym: String, _
args: List Expression R): Void ==
OMputApp(dev)
OMputSymbol(dev, "arith1", sym)
for arg in args repeat
OMwrite(dev, arg, false)
OMputEndApp(dev)
outputOMLambda(dev: OpenMathDevice, ex: Expression R, _
var: Expression R): Void ==
OMputBind(dev)
OMputSymbol(dev, "fns1", "lambda")
OMputBVar(dev)
OMwrite(dev, var, false)
OMputEndBVar(dev)
OMwrite(dev, ex, false)
OMputEndBind(dev)
outputOMInterval(dev: OpenMathDevice, _
lo: Expression R, hi: Expression R): Void ==
OMputApp(dev)
OMputSymbol(dev, "interval1", "interval")
OMwrite(dev, lo, false)
OMwrite(dev, hi, false)
OMputEndApp(dev)
outputOMIntInterval(dev:OpenMathDevice, lo:Expression R, hi:Expression R)_
:Void ==
OMputApp(dev)
OMputSymbol(dev, "interval1", "integer__interval")
OMwrite(dev, lo, false)
OMwrite(dev, hi, false)
OMputEndApp(dev)
outputOMBinomial(dev: OpenMathDevice, args: List Expression R): Void ==
not #args=2 => error "Wrong number of arguments to binomial"
OMputApp(dev)
OMputSymbol(dev, "combinat1", "binomial")
for arg in args repeat
OMwrite(dev, arg, false)
OMputEndApp(dev)
outputOMPower(dev: OpenMathDevice, args: List Expression R): Void ==
not #args=2 => error "Wrong number of arguments to power"
outputOMArith1(dev, "power", args)
outputOMDefsum(dev: OpenMathDevice, args: List Expression R): Void ==
#args ^= 5 => error "Unexpected number of arguments to a defsum"
OMputApp(dev)
OMputSymbol(dev, "arith1", "sum")
outputOMIntInterval(dev, args.4, args.5)
outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
OMputEndApp(dev)
outputOMDefprod(dev: OpenMathDevice, args: List Expression R): Void ==
#args ^= 5 => error "Unexpected number of arguments to a defprod"
OMputApp(dev)
OMputSymbol(dev, "arith1", "product")
outputOMIntInterval(dev, args.4, args.5)
outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
OMputEndApp(dev)
outputOMDefint(dev: OpenMathDevice, args: List Expression R): Void ==
#args ^= 5 => error "Unexpected number of arguments to a defint"
OMputApp(dev)
OMputSymbol(dev, "calculus1", "defint")
outputOMInterval(dev, args.4, args.5)
outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
OMputEndApp(dev)
outputOMInt(dev: OpenMathDevice, args: List Expression R): Void ==
#args ^= 3 => error "Unexpected number of arguments to a defint"
OMputApp(dev)
OMputSymbol(dev, "calculus1", "int")
outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
OMputEndApp(dev)
outputOMFunction(dev: OpenMathDevice, op: Symbol, _
args: List Expression R): Void ==
nargs := #args
zero? nargs =>
omOp: Union(SymInfo, "failed") := search(op, nullaryFunctionAList)
omOp case "failed" =>
error
concat ["No OpenMath definition for nullary function ",coerce op]
OMputSymbol(dev, omOp.cd, omOp.name)
(nargs = 1) =>
omOp: Union(SymInfo, "failed") := search(op, unaryFunctionAList)
omOp case "failed" =>
error
concat ["No OpenMath definition for unary function ", coerce op]
OMputApp(dev)
OMputSymbol(dev, omOp.cd, omOp.name)
for arg in args repeat
OMwrite(dev, arg, false)
OMputEndApp(dev)
-- Most of the binary operators cannot be handled trivialy like the
-- unary ones since they have bound variables of one kind or another.
-- The special functions should be straightforward, but we don't have
-- a CD for them yet :-)
op = %defint => outputOMDefint(dev, args)
op = integral => outputOMInt(dev, args)
op = %defsum => outputOMDefsum(dev, args)
op = %defprod => outputOMDefprod(dev, args)
op = %power => outputOMPower(dev, args)
op = binomial => outputOMBinomial(dev, args)
error concat ["No OpenMath definition for function ", string op]
outputOMExpr(dev: OpenMathDevice, ex: Expression R): Void ==
ground? ex => OMwrite(dev, ground ex, false)
not((v := retractIfCan(ex)@Union(Symbol,"failed")) case "failed") =>
OMputVariable(dev, v)
not((w := isPlus ex) case "failed") => outputOMArith1(dev, "plus", w)
not((w := isTimes ex) case "failed") => outputOMArith1(dev, "times", w)
--not((y := isMult ex) case "failed") =>
-- outputOMArith("times", [OMwrite(y.coef)$Integer,
-- OMwrite(coerce y.var)])
-- At the time of writing we don't need both isExpt and isPower
-- here but they may be relevent when we integrate this stuff into
-- the main Expression code. Note that if we don't check that
-- the exponent is non-trivial we get thrown into an infinite recursion.
not (((x := isExpt ex) case "failed") or (x.exponent = 1)) =>
not((s := symbolIfCan(x.var)@Union(Symbol,"failed")) case "failed") =>
--outputOMPower(dev, [s::Expression(R), (x.exponent)::Expression(R)])
OMputApp(dev)
OMputSymbol(dev, "arith1", "power")
OMputVariable(dev, s)
OMputInteger(dev, x.exponent)
OMputEndApp(dev)
-- TODO: add error handling code here...
not (((z := isPower ex) case "failed") or (z.exponent = 1)) =>
outputOMPower(dev, [ z.val, z.exponent::Expression R ])
--OMputApp(dev)
--OMputSymbol(dev, "arith1", "power")
--outputOMExpr(dev, z.val)
--OMputInteger(dev, z.exponent)
--OMputEndApp(dev)
-- Must only be one top-level Kernel by this point
k : Kernel Expression R := first kernels ex
outputOMFunction(dev, name operator k, argument k)
----------
-- Exports
----------
OMwrite(ex: Expression R): String ==
s: String := ""
sp := OM_-STRINGTOSTRINGPTR(s)$Lisp
dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML())
OMputObject(dev)
outputOMExpr(dev, ex)
OMputEndObject(dev)
OMclose(dev)
s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String
s
OMwrite(ex: Expression R, wholeObj: Boolean): String ==
s: String := ""
sp := OM_-STRINGTOSTRINGPTR(s)$Lisp
dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML())
if wholeObj then
OMputObject(dev)
outputOMExpr(dev, ex)
if wholeObj then
OMputEndObject(dev)
OMclose(dev)
s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String
s
OMwrite(dev: OpenMathDevice, ex: Expression R): Void ==
OMputObject(dev)
outputOMExpr(dev, ex)
OMputEndObject(dev)
OMwrite(dev: OpenMathDevice, ex: Expression R, wholeObj: Boolean): Void ==
if wholeObj then
OMputObject(dev)
outputOMExpr(dev, ex)
if wholeObj then
OMputEndObject(dev)
|