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--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.
)abbrev domain INFORM InputForm
++ Parser forms
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: October 14, 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.
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)$Lisp} where T is the
++ actual type of f (this hack is required for the case where
++ T is a mapping type).
compile : (Symbol, List %) -> Symbol
++ \spad{compile(f, [t1,...,tn])} forces the interpreter to compile
++ the function f with signature \spad{(t1,...,tn) -> ?}.
++ returns the symbol f if successful.
++ Error: if f was not defined beforehand in the interpreter,
++ or if the ti's are not valid types, or if the compiler fails.
== SExpression add
strsym : % -> String
tuplify : List Symbol -> %
flatten0 : (%, Symbol, NonNegativeInteger) ->
Record(lst: List %, symb:%)
0 == convert(0::Integer)
1 == convert(1::Integer)
convert(x:%):SExpression == rep x
convert(x:SExpression):% == per x
conv(ll : List %): % ==
per convert(ll pretend List SExpression)$SExpression
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
convert(x)
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, string n)::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]))@%]$List(%))@%), a]
strsym s ==
string? s => string s
symbol? s => string symbol s
error ["strsym: form", s, "is neither a string or symbol"]
unparse x ==
inputForm2String(x)$Lisp
parseString x ==
ncParseFromString(x)$Lisp
declare signature ==
declare(name := new()$Symbol, signature)$Lisp
name
compile(name, types) ==
name' := convert(name)@%
symbol car cdr car
selectLocalMms(mkAtreeForToken(name')$Lisp, name',
types, nil$List(%))$Lisp
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? l => convert(nil$List(%))
empty? rest l => convert first l
conv
concat(convert("tuple"::Symbol), [convert x for x in l]$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]$List(%)
s1:% ** n:Integer ==
s1 = 0 and positive? n => 0
s1 = 1 or zero? n => 1
one? n => s1
conv [convert("**"::Symbol), s1, convert n]$List(%)
s1:% ** n:NonNegativeInteger == s1 ** (n::Integer)
s1 / s2 ==
s2 = 1 => s1
conv [convert("/"::Symbol), s1, s2]$List(%)
-- A displayed form of an InputForm should be suitable as
-- input to the interpreter parser.
coerce(x: %): OutputForm ==
inputForm2OutputForm(x)$Lisp
)abbrev package INFORM1 InputFormFunctions1
++ 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)$AnyFunctions1(R)
)abbrev package MKFUNC MakeFunction
++ Tools for making interpreter functions from top-level expressions
++ Author: Manuel Bronstein
++ Date Created: 22 Nov 1988
++ Date Last Updated: 8 Jan 1990
++ Description: transforms top-level objects into interpreter functions.
MakeFunction(S:ConvertibleTo InputForm): Exports == Implementation where
SY ==> Symbol
Exports ==> with
function: (S, SY ) -> SY
++ function(e, foo) creates a function \spad{foo() == e}.
function: (S, SY, SY) -> SY
++ function(e, foo, x) creates a function \spad{foo(x) == e}.
function: (S, SY, SY, SY) -> SY
++ function(e, foo, x, y) creates a function \spad{foo(x, y) = e}.
function: (S, SY, List SY) -> SY
++ \spad{function(e, foo, [x1,...,xn])} creates a function
++ \spad{foo(x1,...,xn) == e}.
Implementation ==> add
function(s, name) == function(s, name, nil())
function(s:S, name:SY, x:SY) == function(s, name, [x])
function(s, name, x, y) == function(s, name, [x, y])
function(s:S, name:SY, args:List SY) ==
interpret function(convert s, args, name)$InputForm
name
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)$Lisp
Exports ==> with
unaryFunction : SY -> (D -> I)
++ unaryFunction(a) is a local function
compiledFunction: (S, SY) -> (D -> I)
++ compiledFunction(expr, x) returns a function \spad{f: D -> I}
++ defined by \spad{f(x) == expr}.
++ Function f is compiled and directly
++ applicable to objects of type D.
Implementation ==> add
import MakeFunction(S)
func: (SY, D) -> I
func(name: SY, x: D): I ==
%funcall(name, x, %nil$Foreign(Builtin))$Foreign(Builtin)
unaryFunction name == func(name, #1)
compiledFunction(e:S, x:SY) ==
t := [convert([devaluate(D)$Lisp]$List(InputForm))
]$List(InputForm)
unaryFunction compile(function(e, declare DI, x), t)
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)$Lisp
Exports ==> with
binaryFunction : SY -> ((D1, D2) -> I)
++ binaryFunction(s) is a local function
compiledFunction: (S, SY, SY) -> ((D1, D2) -> I)
++ compiledFunction(expr,x,y) returns a function \spad{f: (D1, D2) -> I}
++ defined by \spad{f(x, y) == expr}.
++ Function f is compiled and directly
++ applicable to objects of type \spad{(D1, D2)}
Implementation ==> add
import MakeFunction(S)
func(name: SY, x: D1, y: D2): I ==
%funcall(name, x, y, %nil$Foreign(Builtin))$Foreign(Builtin)
binaryFunction name == func(name, #1, #2)
compiledFunction(e, x, y) ==
t := [devaluate(D1)$Lisp, devaluate(D2)$Lisp]$List(InputForm)
binaryFunction compile(function(e, declare DI, x, y), t)
)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]$List(INF))@INF
streq?(s, st) == s = convert(st::Symbol)@INF
gencode(s, l) == convert(concat(convert(s::Symbol)@INF, l))@INF
streqlist?(s, l) == member?(string symbol s, l)
quote(f: INF): INF == gencode("QUOTE",[f])
coerceToSF(f: INF): INF ==
gencode("COERCE",[f, quote getVMType(SF)$Foreign(Builtin)])
-- return true if the form `x' is contained in `y'
contained?(x: INF, y: INF): Boolean ==
atom? y => x = y
contained?(x, car y) or contained?(x, cdr y)
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()$Symbol)@INF
body := coerceToSF mkCTOR s
unusedParms := [ p for p in lv | not contained?(p,s)]
stmts :=
null unusedParms => [body]
[gencode("DECLARE",[gencode("IGNORE", unusedParms)]),body]
stmts := concat(gencode("DECLARE",[gencode("FLOAT",lv)]), stmts)
header := [convert("DEFUN"::Symbol), name, convert lv]
fun := convert append(header,stmts)
EVAL(fun)$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"
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