The purpose of this page is to begin the process of documenting
the function selection process used by the FriCAS interpreter.
*On [Axiom-developer] 27 Jan 2008 11:14:39 +0100 Martin Rubey wrote:*
How does the interpreter choose signatures?
Consider this example:
fricas
(1) -> <spad>
fricas
)abb package TEST Test
Test(): with
foo: Fraction Integer -> Fraction Integer
foo: PrimeField 5 -> PrimeField 5
foo: Expression Integer -> Expression Integer
== add
foo(n: Fraction Integer) == n
foo(n: PrimeField 5) == n
foo(n: Expression Integer) == n</spad>
fricas
Compiling FriCAS source code from file
/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2081003860582365004-25px001.spad
using old system compiler.
TEST abbreviates package Test
------------------------------------------------------------------------
initializing NRLIB TEST for Test
compiling into NRLIB TEST
compiling exported foo : Fraction Integer -> Fraction Integer
TEST;foo;2F;1 is replaced by n
Time: 0.01 SEC.
compiling exported foo : PrimeField 5 -> PrimeField 5
TEST;foo;2Pf;2 is replaced by n
Time: 0 SEC.
compiling exported foo : Expression Integer -> Expression Integer
TEST;foo;2E;3 is replaced by n
Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |Test| REDEFINED
;;; *** |Test| REDEFINED
Time: 0 SEC.
Cumulative Statistics for Constructor Test
Time: 0.01 seconds
finalizing NRLIB TEST
Processing Test for Browser database:
--->-->Test(constructor): Not documented!!!!
--->-->Test((foo ((Fraction (Integer)) (Fraction (Integer))))): Not documented!!!!
--->-->Test((foo ((PrimeField 5) (PrimeField 5)))): Not documented!!!!
--->-->Test((foo ((Expression (Integer)) (Expression (Integer))))): Not documented!!!!
--->-->Test(): Missing Description
; compiling file "/var/aw/var/LatexWiki/TEST.NRLIB/TEST.lsp" (written 22 FEB 2025 07:49:58 AM):
; wrote /var/aw/var/LatexWiki/TEST.NRLIB/TEST.fasl
; compilation finished in 0:00:00.004
------------------------------------------------------------------------
Test is now explicitly exposed in frame initial
Test will be automatically loaded when needed from
/var/aw/var/LatexWiki/TEST.NRLIB/TESTfricas
)set mess selection on
foo 3
Function Selection for foo
Arguments: PI
-> no appropriate foo found in PositiveInteger
-> no appropriate foo found in Integer
-> no appropriate foo found in PositiveInteger
-> no appropriate foo found in Integer
Modemaps from Associated Packages
no modemaps
Remaining General Modemaps
[1] Expression(Integer) -> Expression(Integer) from Test
[2] PrimeField(5) -> PrimeField(5) from Test
[3] Fraction(Integer) -> Fraction(Integer) from Test
[1] signature: PF(5) -> PF(5)
implemented: slot (PrimeField 5)(PrimeField 5) from TEST
[2] signature: FRAC(INT) -> FRAC(INT)
implemented: slot (Fraction (Integer))(Fraction (Integer)) from TEST
[3] signature: EXPR(INT) -> EXPR(INT)
implemented: slot (Expression (Integer))(Expression (Integer)) from TEST
Note that the interpreter seems to prefer PF 5 over FRAC INT
over EXPR INT.
Now consider:
fricas
)set mess selection off
p := z^300; s:=z=0..1;
Type: SegmentBinding
?(NonNegativeInteger
?)
fricas
)set mess selection on
fricas
)set mess time on
integrate(p, s)
Function Selection for integrate
Arguments: (POLY(INT), SEGBIND(NNI))
-> no appropriate integrate found in Polynomial(Integer)
-> no appropriate integrate found in SegmentBinding(NonNegativeInteger)
-> no appropriate integrate found in Polynomial(Integer)
-> no appropriate integrate found in SegmentBinding(NonNegativeInteger)
Modemaps from Associated Packages
[1] (Polynomial(D2),Symbol) -> Polynomial(D2) from Polynomial(D2)
if D2 has ALGEBRA(FRAC(INT)) and D2 has RING
[2] (D2,Distribution(D4)) -> D1
from DistributionPolynomialPackage(D4,D1,D2)
if D4 has COMRING and D1 has Join(COMRING,MODULE(D4)) and
D2 has UPOLYC(D1)
Remaining General Modemaps
[1] (D,D1) -> D from D
if D has MTSCAT(D2,D1) and D2 has RING and D1 has ORDSET
and D2 has ALGEBRA(FRAC(INT))
[2] (Fraction(Polynomial(D4)),Symbol) -> Union(Expression(D4),List(
Expression(D4)))
from IntegrationResultRFToFunction(D4)
if D4 has CHARZ and D4 has Join(GCDDOM,RETRACT(INT),COMPAR,
LINEXP(INT))
[3] (GeneralUnivariatePowerSeries(D2,D3,D4),Variable(D3)) ->
GeneralUnivariatePowerSeries(D2,D3,D4)
from GeneralUnivariatePowerSeries(D2,D3,D4)
if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has RING
and D4: D2
[4] (D2,Symbol) -> Union(D2,List(D2)) from FunctionSpaceIntegration(
D4,D2)
if D4 has Join(GCDDOM,COMPAR,CHARZ,PFECAT,RETRACT(INT),
LINEXP(INT)) and D2 has Join(TRANFUN,PRIMCAT,ACFS(D4))
[5] (Fraction(Polynomial(D4)),SegmentBinding(OrderedCompletion(
Fraction(Polynomial(D4))))) -> Union(f1: OrderedCompletion(
Expression(D4)),f2: List(OrderedCompletion(Expression(D4))),fail
: failed,pole: potentialPole)
from RationalFunctionDefiniteIntegration(D4)
if D4 has Join(EUCDOM,COMPAR,CHARZ,RETRACT(INT),LINEXP(INT)
)
[6] (Fraction(Polynomial(D4)),SegmentBinding(OrderedCompletion(
Expression(D4)))) -> Union(f1: OrderedCompletion(Expression(D4)),
f2: List(OrderedCompletion(Expression(D4))),fail: failed,pole:
potentialPole)
from RationalFunctionDefiniteIntegration(D4)
if D4 has Join(EUCDOM,COMPAR,CHARZ,RETRACT(INT),LINEXP(INT)
)
[7] (D2,SegmentBinding(OrderedCompletion(D2))) -> Union(f1:
OrderedCompletion(D2),f2: List(OrderedCompletion(D2)),fail:
failed,pole: potentialPole)
from ElementaryFunctionDefiniteIntegration(D4,D2)
if D2 has Join(TRANFUN,PRIMCAT,ACFS(D4)) and D4 has Join(
PFECAT,COMPAR,CHARZ,RETRACT(INT),LINEXP(INT))
[1] signature: (EXPR(INT), SEGBIND(ORDCOMP(EXPR(INT)))) -> Union(f1: ORDCOMP(EXPR(INT)),f2: LIST(ORDCOMP(EXPR(INT))),fail: failed,pole: potentialPole)
implemented: slot (Union (: f1 (OrderedCompletion (Expression (Integer)))) (: f2 (List (OrderedCompletion (Expression (Integer))))) (: fail failed) (: pole potentialPole))(Expression (Integer))(SegmentBinding (OrderedCompletion (Expression (Integer)))) from DEFINTEF(INT,EXPR(INT))
[2] signature: (FRAC(POLY(INT)), SEGBIND(ORDCOMP(EXPR(INT)))) -> Union(f1: ORDCOMP(EXPR(INT)),f2: LIST(ORDCOMP(EXPR(INT))),fail: failed,pole: potentialPole)
implemented: slot (Union (: f1 (OrderedCompletion (Expression (Integer)))) (: f2 (List (OrderedCompletion (Expression (Integer))))) (: fail failed) (: pole potentialPole))(Fraction (Polynomial (Integer)))(SegmentBinding (OrderedCompletion (Expression (Integer)))) from DEFINTRF(INT)
[3] signature: (FRAC(POLY(INT)), SEGBIND(ORDCOMP(FRAC(POLY(INT))))) -> Union(f1: ORDCOMP(EXPR(INT)),f2: LIST(ORDCOMP(EXPR(INT))),fail: failed,pole: potentialPole)
implemented: slot (Union (: f1 (OrderedCompletion (Expression (Integer)))) (: f2 (List (OrderedCompletion (Expression (Integer))))) (: fail failed) (: pole potentialPole))(Fraction (Polynomial (Integer)))(SegmentBinding (OrderedCompletion (Fraction (Polynomial (Integer))))) from DEFINTRF(INT)
Function Selection for map by coercion facility (map)
Arguments: ((NNI -> ORDCOMP(EXPR(INT))), SEGBIND(NNI))
Target type: SEGBIND(ORDCOMP(EXPR(INT)))
-> no appropriate map found in SegmentBinding(NonNegativeInteger)
-> no appropriate map found in SegmentBinding(OrderedCompletion(Expression(Integer)))
-> no appropriate map found in OrderedCompletion(Expression(Integer))
-> no appropriate map found in NonNegativeInteger
-> no appropriate map found in OrderedCompletion(Expression(Integer))
Modemaps from Associated Packages
[1] ((D4 -> D5),SegmentBinding(D4)) -> SegmentBinding(D5)
from SegmentBindingFunctions2(D4,D5)
if D4 has TYPE and D5 has TYPE
[1] signature: ((NNI -> ORDCOMP(EXPR(INT))), SEGBIND(NNI)) -> SEGBIND(ORDCOMP(EXPR(INT)))
implemented: slot (SegmentBinding (OrderedCompletion (Expression (Integer))))(Mapping (OrderedCompletion (Expression (Integer))) (NonNegativeInteger))(SegmentBinding (NonNegativeInteger)) from SEGBIND2(NNI,ORDCOMP(EXPR(INT)))
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
fricas
Time: 0.04 (EV) + 0.07 (OT) = 0.11 sec
fricas
)set mess time off
There are many things I do not understand:
- why doesn't the interpreter choose the "General Modemap":
[8] (Fraction Polynomial D4,SegmentBinding OrderedCompletion
Fraction Polynomial D4)
- why is its preference different now? I.e., in package
DEFINTRF,
it seems to prefer (FRAC POLY INT,SEGBIND ORDCOMP EXPR INT)
over '(FRAC POLY INT,SEGBIND ORDCOMP FRAC POLY INT)':
[1] signature: (EXPR INT,SEGBIND ORDCOMP EXPR INT) -> Union(f1: ORDCOMP EXPR INT,f2: LIST ORDCOMP EXPR INT,fail: failed,pole: potentialPole)
implemented: slot (Union (: f1 (OrderedCompletion (Expression (Integer)))) (: f2 (List (OrderedCompletion (Expression (Integer))))) (: fail failed) (: pole potentialPole))(Expression (Integer))(SegmentBinding (OrderedCompletion (Expression (Integer)))) from DEFINTEF(INT,EXPR INT)
[2] signature: (FRAC POLY INT,SEGBIND ORDCOMP EXPR INT) -> Union(f1: ORDCOMP EXPR INT,f2: LIST ORDCOMP EXPR INT,fail: failed,pole: potentialPole)
implemented: slot (Union (: f1 (OrderedCompletion (Expression (Integer)))) (: f2 (List (OrderedCompletion (Expression (Integer))))) (: fail failed) (: pole potentialPole))(Fraction (Polynomial (Integer)))(SegmentBinding (OrderedCompletion (Expression (Integer)))) from DEFINTRF INT
[3] signature: (FRAC POLY INT,SEGBIND ORDCOMP FRAC POLY INT) -> Union(f1: ORDCOMP EXPR INT,f2: LIST ORDCOMP EXPR INT,fail: failed,pole: potentialPole)
implemented: slot (Union (: f1 (OrderedCompletion (Expression (Integer)))) (: f2 (List (OrderedCompletion (Expression (Integer))))) (: fail failed) (: pole potentialPole))(Fraction (Polynomial (Integer)))(SegmentBinding (OrderedCompletion (Fraction (Polynomial (Integer))))) from DEFINTRF INT
- why does it prefer DEFINTEF(INT,EXPR INT) over DEFINTRF INT ?
There is a function orderMms in i-funsel.boot that orders the
pre-selected signatures by cost, which is computed in mmCost.
In the case of integrate(p, s), the costs turn out to be
all the same, namely 86999.
In the case of foo$TEST, they are:
|cost: |
(((|Test|) (|Expression| (|Integer|)) (|Expression| (|Integer|)))
((|Expression| (|Integer|)) (|Expression| (|Integer|))) (NIL))
53600
|cost: |
(((|Test|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|)))
((|Fraction| (|Integer|)) (|Fraction| (|Integer|))) (NIL))
52500
|cost: |
(((|Test|) (|PrimeField| 5) (|PrimeField| 5))
((|PrimeField| 5) (|PrimeField| 5)) (NIL))
51500
I do not understand yet how cost is assigned to the various signatures, but the
results look slightly fishy to me...
Here is the code for
i-funsel.boot. We can make changes by
clicking
edit here and then test them later in this page by
clicking on
Preview.
For example see changes marked Debug: in the code below.
New Selection of Modemaps
These notes were provided as comments in the original source
(from FriCAS).
- selection of applicable modemaps is done in two steps:
first it tries to find a modemap inside an argument domain, and if
this fails, by evaluation of pattern modemaps
- the result is a list of functions with signatures, which have the
following form:
[sig,elt,cond] where
sig is the signature gained by evaluating the modemap condition
elt is the slot number to get the implementation
cond are runtime checks which are the results of evaluating the
modemap condition
- the following flags are used:
$Coerce is NIL, if function selection is done which requires exact
matches (e.g. for coercion functions)
if $SubDom is true, then runtime checks have to be compiled
boot
SETANDFILEQ($constructorExposureList, '(Boolean Integer String))
sayFunctionSelection(op,args,target,dc,func) ==
$abbreviateTypes : local := true
startTimingProcess 'debug
fsig := formatSignatureArgs args
if not LISTP fsig then fsig := LIST fsig
if func then func := bright ['"by ",func]
sayMSG concat ['%l,:bright '"Function Selection for",op,:func,'%l,
'" Arguments:",:bright fsig]
if target then sayMSG concat ['" Target type:",
:bright prefix2String target]
if dc then sayMSG concat ['" From: ",
:bright prefix2String dc]
stopTimingProcess 'debug
sayFunctionSelectionResult(op,args,mmS) ==
$abbreviateTypes : local := true
startTimingProcess 'debug
if mmS then printMms mmS
else sayMSG concat ['" -> no function",:bright op,
'"found for arguments",:bright formatSignatureArgs args]
stopTimingProcess 'debug
selectMms(op,args,$declaredMode) ==
-- selects applicable modemaps for node op and arguments args
-- if there is no local modemap, and it is not a package call, then
-- the cached function selectMms1 is called
startTimingProcess 'modemaps
n:= getUnname op
val := getValue op
opMode := objMode val
-- see if we have a functional parameter
((isSharpVarWithNum(n) and opMode) or (val and opMode)) and
opMode is ['Mapping,:ta] =>
imp :=
val => wrapped2Quote objVal val
n
[[['local,:ta], imp , NIL]]
((isSharpVarWithNum(n) and opMode) or (val and opMode)) and
opMode is ['Variable,f] =>
emptyAtree op
op.0 := f
selectMms(op,args,$declaredMode)
isSharpVarWithNum(n) and opMode is ['FunctionCalled,f] =>
op.0 := f
selectMms(op,args,$declaredMode)
types1 := getOpArgTypes(n,args)
numArgs := #args
member('(SubDomain (Domain)),types1) => NIL
member('(Domain),types1) => NIL
member($EmptyMode,types1) => NIL
tar := getTarget op
dc := getAtree(op,'dollar)
null dc and val and objMode(val) = $AnonymousFunction =>
tree := mkAtree objValUnwrap getValue op
putTarget(tree,['Mapping,tar,:types1])
bottomUp tree
val := getValue tree
[[['local,:rest objMode val], wrapped2Quote objVal val, NIL]]
if (n = 'map) and (first types1 = $AnonymousFunction)
then
tree := mkAtree objValUnwrap getValue first args
ut :=
tar => underDomainOf tar
NIL
ua := [underDomainOf x for x in rest types1]
member(NIL,ua) => NIL
putTarget(tree,['Mapping,ut,:ua])
bottomUp tree
val := getValue tree
types1 := [objMode val,:rest types1]
RPLACA(args,tree)
if numArgs = 1 and (n = "numer" or n = "denom") and
isEqualOrSubDomain(first types1,$Integer) and null dc then
dc := ['Fraction, $Integer]
putAtree(op, 'dollar, dc)
if $reportBottomUpFlag then sayFunctionSelection(n,types1,tar,dc,NIL)
identType := 'Variable
for x in types1 while not $declaredMode repeat
not EQCAR(x,identType) => $declaredMode:= x
types2 := [altTypeOf(x,y,$declaredMode) for x in types1 for y in args]
mmS:=
dc => selectDollarMms(dc,n,types1,types2)
if n = "/" and tar = $Integer then
tar := $RationalNumber
putTarget(op,tar)
-- now to speed up some standard selections
if not tar then
tar := defaultTarget(op,n,#types1,types1)
if tar and $reportBottomUpFlag then
sayMSG concat ['" Default target type:",
:bright prefix2String tar]
selectLocalMms(op,n,types1,tar) or
(VECTORP op and selectMms1(n,tar,types1,types2,'T))
if $reportBottomUpFlag then sayFunctionSelectionResult(n,types1,mmS)
stopTimingProcess 'modemaps
mmS
-- selectMms1 is in clammed.boot
selectMms2(op,tar,args1,args2,$Coerce) ==
-- decides whether to find functions from a domain or package
-- or by general modemap evaluation
or/[STRINGP arg for arg in args1] => NIL
if tar = $EmptyMode then tar := NIL
nargs := #args1
mmS := NIL
mmS :=
-- special case map for the time being
$Coerce and (op = 'map) and (2 = nargs) and
(first(args1) is ['Variable,fun]) =>
null (ud := underDomainOf CADR args1) => NIL
if tar then ut := underDomainOf(tar)
else ut := nil
null (mapMms := selectMms1(fun,ut,[ud],[NIL],true)) => NIL
mapMm := CDAAR mapMms
selectMms1(op,tar,[['Mapping,:mapMm],CADR args1],
[NIL,CADR args2],$Coerce)
$Coerce and (op = 'map) and (2 = nargs) and
(first(args1) is ['FunctionCalled,fun]) =>
null (ud := underDomainOf CADR args1) => NIL
if tar then ut := underDomainOf(tar)
else ut := nil
funNode := mkAtreeNode fun
transferPropsToNode(fun,funNode)
null (mapMms := selectLocalMms(funNode,fun,[ud],NIL)) => NIL
mapMm := CDAAR mapMms
selectMms1(op,tar,[['Mapping,:mapMm],CADR args1],
[NIL,CADR args2],$Coerce)
-- get the argument domains and the target
a := nil
for x in args1 repeat if x then a := cons(x,a)
for x in args2 repeat if x then a := cons(x,a)
if tar and not isPartialMode tar then a := cons(tar,a)
-- for typically homogeneous functions, throw in resolve too
if op in '(_= _+ _* _- ) then
r := resolveTypeList a
if r ^= nil then a := cons(r,a)
if tar and not isPartialMode tar then
if xx := underDomainOf(tar) then a := cons(xx,a)
for x in args1 repeat
PAIRP(x) and CAR(x) in '(List Vector Stream FiniteSet Array) =>
xx := underDomainOf(x) => a := cons(xx,a)
-- now extend this list with those from the arguments to
-- any Unions, Mapping or Records
a' := nil
a := nreverse REMDUP a
for x in a repeat
null x => 'iterate
x = '(RationalRadicals) => a' := cons($RationalNumber,a')
x is ['Union,:l] =>
-- check if we have a tagged union
l and first l is [":",:.] =>
for [.,.,t] in l repeat
a' := cons(t,a')
a' := append(reverse l,a')
x is ['Mapping,:l] => a' := append(reverse l,a')
x is ['Record,:l] =>
a' := append(reverse [CADDR s for s in l],a')
x is ['FunctionCalled,name] =>
(xm := get(name,'mode,$e)) and not isPartialMode xm =>
a' := cons(xm,a')
a := append(a,REMDUP a')
a := [x for x in a | PAIRP(x)]
-- step 1. see if we have one without coercing
a' := a
while a repeat
x:= CAR a
a:= CDR a
ATOM x => 'iterate
mmS := append(mmS, findFunctionInDomain(op,x,tar,args1,args2,NIL,NIL))
-- step 2. if we didn't get one, trying coercing (if we are
-- suppose to)
if null(mmS) and $Coerce then
a := a'
while a repeat
x:= CAR a
a:= CDR a
ATOM x => 'iterate
mmS := append(mmS,
findFunctionInDomain(op,x,tar,args1,args2,$Coerce,NIL))
mmS or selectMmsGen(op,tar,args1,args2)
mmS and orderMms(op, mmS,args1,args2,tar)
isAVariableType t ==
t is ['Variable,.] or t = $Symbol or t is ['OrderedVariableList,.]
defaultTarget(opNode,op,nargs,args) ==
-- this is for efficiency. Chooses standard targets for operations
-- when no target exists.
target := nil
nargs = 0 =>
op = 'nil =>
putTarget(opNode, target := '(List (None)))
target
op = 'true or op = 'false =>
putTarget(opNode, target := $Boolean)
target
op = 'pi =>
putTarget(opNode, target := ['Pi])
target
op = 'infinity =>
putTarget(opNode, target := ['OnePointCompletion, $Integer])
target
member(op, '(plusInfinity minusInfinity)) =>
putTarget(opNode, target := ['OrderedCompletion, $Integer])
target
target
a1 := CAR args
ATOM a1 => target
a1f := QCAR a1
nargs = 1 =>
op = 'kernel =>
putTarget(opNode, target := ['Kernel, ['Expression, $Integer]])
target
op = 'list =>
putTarget(opNode, target := ['List, a1])
target
target
a2 := CADR args
nargs >= 2 and op = "draw" and a1 is ['FunctionCalled,sym] and a2 is ['Segment,.] =>
-- this clears up some confusion over 2D and 3D graphics
symNode := mkAtreeNode sym
transferPropsToNode(sym,symNode)
nargs >= 3 and CADDR args is ['Segment,.] =>
selectLocalMms(symNode,sym,[$DoubleFloat, $DoubleFloat],NIL)
putTarget(opNode, target := '(ThreeDimensionalViewport))
target
(mms := selectLocalMms(symNode,sym,[$DoubleFloat],NIL)) =>
[.,targ,:.] := CAAR mms
targ = $DoubleFloat =>
putTarget(opNode, target := '(TwoDimensionalViewport))
target
targ = ['Point, $DoubleFloat] =>
putTarget(opNode, target := '(ThreeDimensionalViewport))
target
target
target
nargs >= 2 and op = "makeObject" and a1 is ['FunctionCalled,sym] and a2 is ['Segment,.] =>
-- we won't actually bother to put a target on makeObject
-- this is just to figure out what the first arg is
symNode := mkAtreeNode sym
transferPropsToNode(sym,symNode)
nargs >= 3 and CADDR args is ['Segment,.] =>
selectLocalMms(symNode,sym,[$DoubleFloat, $DoubleFloat],NIL)
target
selectLocalMms(symNode,sym,[$DoubleFloat],NIL)
target
nargs = 2 =>
op = "elt" =>
a1 = '(BasicOperator) and a2 is ['List, ['OrderedVariableList, .]] =>
['Expression, $Integer]
target
op = "eval" =>
a1 is ['Expression,b1] and a2 is ['Equation, ['Polynomial,b2]] =>
target :=
canCoerce(b2, a1) => a1
t := resolveTT(b1, b2)
(not t) or (t = $Any) => nil
resolveTT(a1, t)
if target then putTarget(opNode, target)
target
a1 is ['Equation, .] and a2 is ['Equation, .] =>
target := resolveTT(a1, a2)
if target and not (target = $Any) then putTarget(opNode,target)
else target := nil
target
a1 is ['Equation, .] and a2 is ['List, a2e] and a2e is ['Equation, .] =>
target := resolveTT(a1, a2e)
if target and not (target = $Any) then putTarget(opNode,target)
else target := nil
target
a2 is ['Equation, a2e] or a2 is ['List, ['Equation, a2e]] =>
target := resolveTT(a1, a2e)
if target and not (target = $Any) then putTarget(opNode,target)
else target := nil
target
op = "**" or op = "^" =>
a2 = $Integer =>
if (target := resolveTCat(a1,'(Field))) then
putTarget(opNode,target)
target
a1 = '(AlgebraicNumber) and (a2 = $Float or a2 = $DoubleFloat) =>
target := ['Expression, a2]
putTarget(opNode,target)
target
a1 = '(AlgebraicNumber) and a2 is ['Complex, a3] and (a3 = $Float or a3 = $DoubleFloat) =>
target := ['Expression, a3]
putTarget(opNode,target)
target
((a2 = $RationalNumber) and
(typeIsASmallInteger(a1) or isEqualOrSubDomain(a1,$Integer))) =>
putTarget(opNode, target := '(AlgebraicNumber))
target
((a2 = $RationalNumber) and (isAVariableType(a1)
or a1 is ['Polynomial,.] or a1 is ['RationalFunction,.])) =>
putTarget(opNode, target := defaultTargetFE a1)
target
isAVariableType(a1) and (a2 = $PositiveInteger or a2 = $NonNegativeInteger) =>
putTarget(opNode, target := '(Polynomial (Integer)))
target
isAVariableType(a2) =>
putTarget(opNode, target := defaultTargetFE a1)
target
a2 is ['Polynomial, D] =>
(a1 = a2) or isAVariableType(a1)
or ((a1 is ['RationalFunction, D1]) and (D1 = D)) or (a1 = D)
or ((a1 is [=$QuotientField, D1]) and (D1 = a1)) =>
putTarget(opNode, target := defaultTargetFE a2)
target
target
a2 is ['RationalFunction, D] =>
(a1 = a2) or isAVariableType(a1)
or ((a1 is ['RationalFunction, D1]) and (D1 = D)) or (a1 = D)
or ((a1 is [=$QuotientField, D1]) and (D1 = a1)) =>
putTarget(opNode, target := defaultTargetFE a2)
target
target
target
op = '_/ =>
isEqualOrSubDomain(a1, $Integer) and isEqualOrSubDomain(a2, $Integer) =>
putTarget(opNode, target := $RationalNumber)
target
a1 = a2 =>
if (target := resolveTCat(CAR args,'(Field))) then
putTarget(opNode,target)
target
a1 is ['Variable,.] and a2 is ['Variable,.] =>
putTarget(opNode,target := mkRationalFunction '(Integer))
target
isEqualOrSubDomain(a1,$Integer) and a2 is ['Variable,.] =>
putTarget(opNode,target := mkRationalFunction '(Integer))
target
a1 is ['Variable,.] and
a2 is ['Polynomial,D] =>
putTarget(opNode,target := mkRationalFunction D)
target
target
a2 is ['Variable,.] and
a1 is ['Polynomial,D] =>
putTarget(opNode,target := mkRationalFunction D)
target
target
a2 is ['Polynomial,D] and (a1 = D) =>
putTarget(opNode,target := mkRationalFunction D)
target
target
a3 := CADDR args
nargs = 3 =>
op = "eval" =>
a3 is ['List, a3e] =>
target := resolveTT(a1, a3e)
if not (target = $Any) then putTarget(opNode,target)
else target := nil
target
target := resolveTT(a1, a3)
if not (target = $Any) then putTarget(opNode,target)
else target := nil
target
target
mkRationalFunction D == ['Fraction, ['Polynomial, D]]
defaultTargetFE(a,:options) ==
a is ['Variable,.] or a = $RationalNumber or MEMQ(QCAR a,
[QCAR $Symbol, 'RationalRadicals,
'Pi]) or typeIsASmallInteger(a) or isEqualOrSubDomain(a, $Integer) or
a = '(AlgebraicNumber) =>
IFCAR options => [$FunctionalExpression, ['Complex, $Integer]]
[$FunctionalExpression, $Integer]
a is ['Complex,uD] => defaultTargetFE(uD, true)
a is [D,uD] and MEMQ(D, '(Polynomial RationalFunction Fraction)) =>
defaultTargetFE(uD, IFCAR options)
a is [=$FunctionalExpression,.] => a
IFCAR options => [$FunctionalExpression, ['Complex, a]]
[$FunctionalExpression, a]
altTypeOf(type,val,$declaredMode) ==
(EQCAR(type,'Symbol) or EQCAR(type,'Variable)) and
(a := getMinimalVarMode(objValUnwrap getValue(val),$declaredMode)) =>
a
type is ['OrderedVariableList,vl] and
INTEGERP(val1 := objValUnwrap getValue(val)) and
(a := getMinimalVarMode(vl.(val1 - 1),$declaredMode)) =>
a
type = $PositiveInteger => $Integer
type = $NonNegativeInteger => $Integer
type = '(List (PositiveInteger)) => '(List (Integer))
NIL
getOpArgTypes(opname, args) ==
l := getOpArgTypes1(opname, args)
[f(a,opname) for a in l] where
f(x,op) ==
x is ['FunctionCalled,g] and op ^= 'name =>
m := get(g,'mode,$e) =>
m is ['Mapping,:.] => m
x
x
x
getOpArgTypes1(opname, args) ==
null args => NIL
-- special cases first
opname = 'coef and args is [b,n] =>
[CAR getModeSet b, CAR getModeSetUseSubdomain n]
opname = 'monom and args is [d,c] =>
[CAR getModeSetUseSubdomain d,CAR getModeSet c]
opname = 'monom and args is [v,d,c] =>
[CAR getModeSet v,CAR getModeSetUseSubdomain d,CAR getModeSet c]
(opname = 'cons) and (2 = #args) and (CADR(args) = 'nil) =>
ms := [CAR getModeSet x for x in args]
if CADR(ms) = '(List (None)) then
ms := [first ms,['List,first ms]]
ms
nargs := #args
v := argCouldBelongToSubdomain(opname,nargs)
mss := NIL
for i in 0..(nargs-1) for x in args repeat
ms :=
v.i = 0 => CAR getModeSet x
CAR getModeSetUseSubdomain x
mss := [ms,:mss]
nreverse mss
argCouldBelongToSubdomain(op, nargs) ==
-- this returns a vector containing 0 or ^0 for each argument.
-- if ^0, this indicates that there exists a modemap for the
-- op that needs a subdomain in that position
nargs = 0 => NIL
v := GETZEROVEC nargs
isMap(op) => v
mms := getModemapsFromDatabase(op,nargs)
null mms => v
nargs:=nargs-1
-- each signature has form
-- [domain of implementation, target, arg1, arg2, ...]
for [sig,cond,:.] in mms repeat
for t in CDDR sig for i in 0..(nargs) repeat
CONTAINEDisDomain(t,cond) =>
v.i := 1 + v.i
v
CONTAINEDisDomain(symbol,cond) ==
-- looks for [isSubDomain,symbol,[domain]] in cond: returning T or NIL
-- with domain being one of PositiveInteger and NonNegativeInteger
ATOM cond => false
MEMQ(QCAR cond,'(AND OR and or)) =>
or/[CONTAINEDisDomain(symbol, u) for u in QCDR cond]
EQ(QCAR cond,'isDomain) =>
EQ(symbol,CADR cond) and PAIRP(dom:=CADDR cond) and
MEMQ(dom,'(PositiveInteger NonNegativeInteger))
false
selectDollarMms(dc,name,types1,types2) ==
-- finds functions for name in domain dc
isPartialMode dc => throwKeyedMsg("S2IF0001",NIL)
mmS := findFunctionInDomain(name,dc,NIL,types1,types2,'T,'T) =>
orderMms(name, mmS,types1,types2,NIL)
if $reportBottomUpFlag then sayMSG
["%b",'" function not found in ",prefix2String dc,"%d","%l"]
NIL
selectLocalMms(op,name,types,tar) ==
-- partial rewrite, looks now for exact local modemap
mmS:= getLocalMms(name,types,tar) => mmS
obj := getValue op
obj and (objVal obj is ['MAP,:mapDef]) and
analyzeMap(op,types,mapDef,tar) and getLocalMms(name,types,tar)
-- next defn may be better, test when more time. RSS 3/11/94
-- selectLocalMms(op,name,types,tar) ==
-- mmS := getLocalMms(name,types,tar)
-- -- if no target, just return what we got
-- mmS and null tar => mmS
-- matchingMms := nil
-- for mm in mmS repeat
-- [., targ, :.] := mm
-- if tar = targ then matchingMms := cons(mm, matchingMms)
-- -- if we got some exact matchs on the target, return them
-- matchingMms => nreverse matchingMms
--
-- obj := getValue op
-- obj and (objVal obj is ['MAP,:mapDef]) and
-- analyzeMap(op,types,mapDef,tar) and getLocalMms(name,types,tar)
getLocalMms(name,types,tar) ==
-- looks for exact or subsumed local modemap in $e
mmS := NIL
for (mm:=[dcSig,:.]) in get(name,'localModemap,$e) repeat
-- check format and destructure
dcSig isnt [dc,result,:args] => NIL
-- make number of args is correct
#types ^= #args => NIL
-- check for equal or subsumed arguments
subsume := (not $useIntegerSubdomain) or (tar = result) or
get(name,'recursive,$e)
acceptableArgs :=
and/[f(b,a,subsume) for a in args for b in types] where
f(x,y,subsume) ==
if subsume
then isEqualOrSubDomain(x,y)
else x = y
not acceptableArgs =>
-- interpreted maps are ok
dc = 'interpOnly and not($Coerce)=> mmS := [mm,:mmS]
NIL
mmS := [mm,:mmS]
nreverse mmS
mmCost(name, sig,cond,tar,args1,args2) ==
cost := mmCost0(name, sig,cond,tar,args1,args2)
res := CADR sig
if res = $PositiveInteger then cost := cost - 2
else if res = $NonNegativeInteger then cost := cost - 1
else if res = $DoubleFloat then cost := cost + 1
sayMSG ['"Debug: cost=",prefix2String cost,'" for ", name,'": ",:formatSignature CDR sig]
cost
mmCost0(name, sig,cond,tar,args1,args2) ==
sigArgs := CDDR sig
n:=
null cond => 1
not (or/cond) => 1
0
-- try to favor homogeneous multiplication
--if name = "*" and 2 = #sigArgs and first sigArgs ^= first rest sigArgs then n := n + 1
-- because of obscure problem in evalMm, sometimes we will have extra
-- modemaps with the wrong number of arguments if we want to the one
-- with no arguments and the name is overloaded. Thus check for this.
if args1 then
for x1 in args1 for x2 in args2 for x3 in sigArgs repeat
n := n +
isEqualOrSubDomain(x1,x3) => 0
topcon := first deconstructT x1
topcon2 := first deconstructT x3
topcon = topcon2 => 3
CAR topcon2 = 'Mapping => 2
-- Testing: Expression can be expensive - especially for integration!
-- Thus we assign a higher cost if something of type
-- Expression is passed as an argument
CAR topcon2 = 'Expression => 5
4
else if sigArgs then n := n + 100000000000
res := CADR sig
res=tar => 10000*n
10000*n + 1000*domainDepth(res) + hitListOfTarget(res)
orderMms(name, mmS,args1,args2,tar) ==
-- it counts the number of necessary coercions of the argument types
-- if this isn't enough, it compares the target types
mmS and null rest mmS => mmS
mS:= NIL
N:= NIL
for mm in MSORT mmS repeat
[sig,.,cond]:= mm
b:= 'T
p:= CONS(m := mmCost(name, sig,cond,tar,args1,args2),mm)
mS:=
null mS => list p
m < CAAR mS => CONS(p,mS)
S:= mS
until b repeat
b:= null CDR S or m < CAADR S =>
RPLACD(S,CONS(p,CDR S))
S:= CDR S
mS
mmS and [CDR p for p in mS]
domainDepth(d) ==
-- computes the depth of lisp structure d
atom d => 0
-- Debug: Suppose I don't like PrimeField - WSP
EQ(CAR d,'PrimeField) => 9
MAX(domainDepth(CAR d)+1,domainDepth(CDR d))
hitListOfTarget(t) ==
-- assigns a number between 1 and 998 to a type t
-- want to make it hard to go to Polynomial Pi
t = '(Polynomial (Pi)) => 90000
EQ(CAR t, 'Polynomial) => 300
EQ(CAR t, 'List) => 400
EQ(CAR t,'Matrix) => 910
EQ(CAR t,'UniversalSegment) => 501
EQ(CAR t,'RationalFunction) => 900
EQ(CAR t,'Union) => 999
EQ(CAR t,'Expression) => 1600
500
isOpInDomain(opName,dom,nargs) ==
-- returns true only if there is an op in the given domain with
-- the given number of arguments
mmList := ASSQ(opName,getOperationAlistFromLisplib CAR dom)
mmList := subCopy(mmList,constructSubst dom)
null mmList => NIL
gotOne := NIL
nargs := nargs + 1
for mm in CDR mmList while not gotOne repeat
nargs = #CAR mm => gotOne := [mm, :gotOne]
gotOne
findCommonSigInDomain(opName,dom,nargs) ==
-- this looks at all signatures in dom with given opName and nargs
-- number of arguments. If no matches, returns NIL. Otherwise returns
-- a "signature" where a type position is non-NIL only if all
-- signatures shares that type .
CAR(dom) in '(Union Record Mapping) => NIL
mmList := ASSQ(opName,getOperationAlistFromLisplib CAR dom)
mmList := subCopy(mmList,constructSubst dom)
null mmList => NIL
gotOne := NIL
nargs := nargs + 1
vec := NIL
for mm in CDR mmList repeat
nargs = #CAR mm =>
null vec => vec := LIST2VEC CAR mm
for i in 0.. for x in CAR mm repeat
if vec.i and vec.i ^= x then vec.i := NIL
VEC2LIST vec
findUniqueOpInDomain(op,opName,dom) ==
-- return function named op in domain dom if unique, choose one if not
mmList := ASSQ(opName,getOperationAlistFromLisplib CAR dom)
mmList := subCopy(mmList,constructSubst dom)
null mmList =>
throwKeyedMsg("S2IS0021",[opName,dom])
if #CDR mmList > 1 then
mm := selectMostGeneralMm CDR mmList
sayKeyedMsg("S2IS0022",[opName,dom,['Mapping,:CAR mm]])
else mm := CADR mmList
[sig,slot,:.] := mm
fun :=
--+
$genValue =>
compiledLookupCheck(opName,sig,evalDomain dom)
NRTcompileEvalForm(opName, sig, evalDomain dom)
NULL(fun) or NULL(PAIRP(fun)) => NIL
CAR fun = function(Undef) => throwKeyedMsg("S2IS0023",[opName,dom])
binVal :=
$genValue => wrap fun
fun
putValue(op,objNew(binVal,m:=['Mapping,:sig]))
putModeSet(op,[m])
selectMostGeneralMm mmList ==
-- selects the modemap in mmList with arguments all the other
-- argument types can be coerced to
-- also selects function with #args closest to 2
min := 100
mml := mmList
while mml repeat
[mm,:mml] := mml
sz := #CAR mm
if (met := ABS(sz - 3)) < min then
min := met
fsz := sz
mmList := [mm for mm in mmList | (#CAR mm) = fsz]
mml := CDR mmList
genMm := CAR mmList
while mml repeat
[mm,:mml] := mml
and/[canCoerceFrom(genMmArg,mmArg) for mmArg in CDAR mm
for genMmArg in CDAR genMm] => genMm := mm
genMm
findFunctionInDomain(op,dc,tar,args1,args2,$Coerce,$SubDom) ==
-- looks for a modemap for op with signature args1 -> tar
-- in the domain of computation dc
-- tar may be NIL (= unknown)
null isLegitimateMode(tar, nil, nil) => nil
dcName:= CAR dc
member(dcName,'(Union Record Mapping Enumeration)) =>
-- First cut code that ignores args2, $Coerce and $SubDom
-- When domains no longer have to have Set, the hard coded 6 and 7
-- should go.
op = '_= =>
#args1 ^= 2 or args1.0 ^= dc or args1.1 ^= dc => NIL
tar and tar ^= '(Boolean) => NIL
[[[dc, '(Boolean), dc, dc], ['(Boolean),'$,'$], [NIL, NIL]]]
op = 'coerce =>
dcName='Enumeration and (args1.0=$Symbol or tar=dc)=>
[[[dc, dc, $Symbol], ['$,$Symbol], [NIL, NIL]]]
args1.0 ^= dc => NIL
tar and tar ^= $Expression => NIL
[[[dc, $Expression, dc], [$Expression,'$], [NIL, NIL]]]
member(dcName,'(Record Union)) =>
findFunctionInCategory(op,dc,tar,args1,args2,$Coerce,$SubDom)
NIL
fun:= NIL
( p := ASSQ(op,getOperationAlistFromLisplib dcName) ) and
SL := constructSubst dc
-- if the arglist is homogeneous, first look for homogeneous
-- functions. If we don't find any, look at remaining ones
if isHomogeneousList args1 then
q := NIL
r := NIL
for mm in CDR p repeat
-- CDAR of mm is the signature argument list
if isHomogeneousList CDAR mm then q := [mm,:q]
else r := [mm,:r]
q := allOrMatchingMms(q,args1,tar,dc)
for mm in q repeat
fun:= nconc(fun,findFunctionInDomain1(mm,op,tar,args1,args2,SL))
r := reverse r
else r := CDR p
r := allOrMatchingMms(r,args1,tar,dc)
if not fun then -- consider remaining modemaps
for mm in r repeat
fun:= nconc(fun,findFunctionInDomain1(mm,op,tar,args1,args2,SL))
if not fun and $reportBottomUpFlag then
sayMSG concat
['" -> no appropriate",:bright op,'"found in",
:bright prefix2String dc]
fun
allOrMatchingMms(mms,args1,tar,dc) ==
-- if there are exact matches on the arg types, return them
-- otherwise return the original list
null mms or null rest mms => mms
x := NIL
for mm in mms repeat
[sig,:.] := mm
[res,:args] := MSUBSTQ(dc,"$",sig)
args ^= args1 => nil
x := CONS(mm,x)
if x then x
else mms
isHomogeneousList y ==
y is [x] => true
y and rest y =>
z := CAR y
"and"/[x = z for x in CDR y]
NIL
findFunctionInDomain1(omm,op,tar,args1,args2,SL) ==
dc:= CDR (dollarPair := ASSQ('$,SL))
-- need to drop '$ from SL
mm:= subCopy(omm, SL)
-- tests whether modemap mm is appropriate for the function
-- defined by op, target type tar and argument types args
$RTC:local:= NIL
-- $RTC is a list of run-time checks to be performed
[sig,slot,cond,y] := mm
[osig,:.] := omm
osig := subCopy(osig, SUBSTQ(CONS('$,'$), dollarPair, SL))
if CONTAINED('_#, sig) or CONTAINED('construct, sig) then
sig := [replaceSharpCalls t for t in sig]
matchMmCond cond and matchMmSig(mm,tar,args1,args2) and
EQ(y,'Subsumed) and
-- hmmmm: do Union check in following because (as in DP)
-- Unions are subsumed by total modemaps which are in the
-- mm list in findFunctionInDomain.
y := 'ELT -- if subsumed fails try it again
not $SubDom and CAR sig isnt ['Union,:.] and slot is [tar,:args] and
(f := findFunctionInDomain(op,dc,tar,args,args,NIL,NIL)) => f
EQ(y,'ELT) => [[CONS(dc,sig),osig,nreverse $RTC]]
EQ(y,'CONST) => [[CONS(dc,sig),osig,nreverse $RTC]]
EQ(y,'ASCONST) => [[CONS(dc,sig),osig,nreverse $RTC]]
y is ['XLAM,:.] => [[CONS(dc,sig),y,nreverse $RTC]]
sayKeyedMsg("S2IF0006",[y])
NIL
--------------------> NEW DEFINITION (override in xrun.boot.pamphlet)
findFunctionInCategory(op,dc,tar,args1,args2,$Coerce,$SubDom) ==
-- looks for a modemap for op with signature args1 -> tar
-- in the domain of computation dc
-- tar may be NIL (= unknown)
dcName:= CAR dc
not MEMQ(dcName,'(Record Union Enumeration)) => NIL
fun:= NIL
-- cat := constructorCategory dc
makeFunc := GETL(dcName,"makeFunctionList") or
systemErrorHere '"findFunctionInCategory"
[funlist,.] := FUNCALL(makeFunc,"$",dc,$CategoryFrame)
-- get list of implementations and remove sharps
maxargs := -1
impls := nil
for [a,b,d] in funlist repeat
not EQ(a,op) => nil
d is ['XLAM,xargs,:.] =>
if PAIRP(xargs) then maxargs := MAX(maxargs,#xargs)
else maxargs := MAX(maxargs,1)
impls := cons([b,nil,true,d],impls)
impls := cons([b,d,true,d],impls)
impls := NREVERSE impls
if maxargs ^= -1 then
SL:= NIL
for i in 1..maxargs repeat
impls := SUBSTQ(GENSYM(),INTERNL('"#",STRINGIMAGE i),impls)
impls and
SL:= constructSubst dc
for mm in impls repeat
fun:= nconc(fun,findFunctionInDomain1(mm,op,tar,args1,args2,SL))
if not fun and $reportBottomUpFlag then
sayMSG concat
['" -> no appropriate",:bright op,'"found in",
:bright prefix2String dc]
fun
matchMmCond(cond) ==
-- tests the condition, which comes with a modemap
-- cond is 'T or a list, but I hate to test for 'T (ALBI)
$domPvar: local := nil
atom cond or
cond is ['AND,:conds] or cond is ['and,:conds] =>
and/[matchMmCond c for c in conds]
cond is ['OR,:conds] or cond is ['or,:conds] =>
or/[matchMmCond c for c in conds]
cond is ['has,dom,x] =>
hasCaty(dom,x,NIL) ^= 'failed
cond is ['not,cond1] => not matchMmCond cond1
keyedSystemError("S2GE0016",
['"matchMmCond",'"unknown form of condition"])
matchMmSig(mm,tar,args1,args2) ==
-- matches the modemap signature against args1 -> tar
-- if necessary, runtime checks are created for subdomains
-- then the modemap condition is evaluated
[sig,:.]:= mm
if CONTAINED('_#, sig) then
sig := [replaceSharpCalls COPY t for t in sig]
null args1 => matchMmSigTar(tar,CAR sig)
a:= CDR sig
arg:= NIL
for i in 1.. while args1 and args2 and a until not b repeat
x1:= CAR args1
args1:= CDR args1
x2:= CAR args2
args2:= CDR args2
x:= CAR a
a:= CDR a
rtc:= NIL
if x is ['SubDomain,y,:.] then x:= y
b := isEqualOrSubDomain(x1,x) or
(STRINGP(x) and (x1 is ['Variable,v]) and (x = PNAME v)) or
$SubDom and isSubDomain(x,x1) => rtc:= 'T
$Coerce => x2=x or canCoerceFrom(x1,x)
x1 is ['Variable,:.] and x = '(Symbol)
$RTC:= CONS(rtc,$RTC)
null args1 and null a and b and matchMmSigTar(tar,CAR sig)
matchMmSigTar(t1,t2) ==
-- t1 is a target type specified by :: or by a declared variable
-- t2 is the target of a modemap signature
null t1 or
isEqualOrSubDomain(t2,t1) => true
if t2 is ['Union,a,b] then
if a='"failed" then return matchMmSigTar(t1, b)
if b='"failed" then return matchMmSigTar(t1, a)
$Coerce and
isPartialMode t1 => resolveTM(t2,t1)
-- I think this should be true -SCM
-- true
canCoerceFrom(t2,t1)
constructSubst(d) ==
-- constructs a substitution which substitutes d for $
-- and the arguments of d for #1, #2 ..
SL:= list CONS('$,d)
for x in CDR d for i in 1.. repeat
SL:= CONS(CONS(INTERNL('"#",STRINGIMAGE i),x),SL)
SL
filterModemapsFromPackages(mms, names, op) ==
-- mms is a list of modemaps
-- names is a list of domain constructors
-- this returns a 2-list containing those modemaps that have one
-- of the names in the package source of the modemap and all the
-- rest of the modemaps in the second element.
good := NIL
bad := NIL
-- hack to speed up factorization choices for mpolys and to overcome
-- some poor naming of packages
mpolys := '("Polynomial" "MultivariatePolynomial"
"DistributedMultivariatePolynomial"
"HomogeneousDistributedMultivariatePolynomial")
mpacks := '("MFactorize" "MRationalFactorize")
for mm in mms repeat
isFreeFunctionFromMm(mm) => bad := cons(mm, bad)
type := getDomainFromMm mm
null type => bad := cons(mm,bad)
if PAIRP type then type := first type
GETDATABASE(type,'CONSTRUCTORKIND) = 'category => bad := cons(mm,bad)
name := object2String type
found := nil
for n in names while not found repeat
STRPOS(n,name,0,NIL) => found := true
-- hack, hack
(op = 'factor) and member(n,mpolys) and member(name,mpacks) =>
found := true
if found
then good := cons(mm, good)
else bad := cons(mm,bad)
[good,bad]
isTowerWithSubdomain(towerType,elem) ==
not PAIRP towerType => NIL
dt := deconstructT towerType
2 ^= #dt => NIL
s := underDomainOf(towerType)
isEqualOrSubDomain(s,elem) and constructM(first dt,[elem])
selectMmsGen(op,tar,args1,args2) ==
-- general modemap evaluation of op with argument types args1
-- evaluates the condition and looks for the slot number
-- returns all functions which are applicable
-- args2 is a list of polynomial types for symbols
$Subst: local := NIL
$SymbolType: local := NIL
null (S := getModemapsFromDatabase(op,QLENGTH args1)) => NIL
if (op = 'map) and (2 = #args1) and
(CAR(args1) is ['Mapping,., elem]) and
(a := isTowerWithSubdomain(CADR args1,elem))
then args1 := [CAR args1,a]
-- we first split the modemaps into two groups:
-- haves: these are from packages that have one of the top level
-- constructor names in the package name
-- havenots: everything else
-- get top level constructor names for constructors with parameters
conNames := nil
if op = 'reshape then args := APPEND(rest args1, rest args2)
else args := APPEND(args1,args2)
if tar then args := [tar,:args]
-- for common aggregates, use under domain also
for a in REMDUP args repeat
a =>
atom a => nil
fa := QCAR a
fa in '(Record Union) => NIL
conNames := insert(STRINGIMAGE fa, conNames)
if conNames
then [haves,havenots] := filterModemapsFromPackages(S,conNames,op)
else
haves := NIL
havenots := S
mmS := NIL
if $reportBottomUpFlag then
sayMSG ['%l,:bright '"Modemaps from Associated Packages"]
if haves then
[havesExact,havesInexact] := exact?(haves,tar,args1) where
exact?(mmS,tar,args) ==
ex := inex := NIL
for (mm := [sig,[mmC,:.],:.]) in mmS repeat
[c,t,:a] := sig
ok := true
for pat in a for arg in args while ok repeat
not CONTAINED(['isDomain,pat,arg],mmC) => ok := NIL
ok => ex := CONS(mm,ex)
inex := CONS(mm,inex)
[ex,inex]
if $reportBottomUpFlag then
for mm in APPEND(havesExact,havesInexact) for i in 1.. repeat
sayModemapWithNumber(mm,i)
if havesExact then
mmS := matchMms(havesExact,op,tar,args1,args2) where
matchMms(mmaps,op,tar,args1,args2) ==
mmS := NIL
for [sig,mmC] in mmaps repeat
-- sig is [dc,result,:args]
$Subst :=
tar and not isPartialMode tar =>
-- throw in the target if it is not the same as one
-- of the arguments
res := CADR sig
member(res,CDDR sig) => NIL
[[res,:tar]]
NIL
[c,t,:a] := sig
if a then matchTypes(a,args1,args2)
not EQ($Subst,'failed) =>
mmS := nconc(evalMm(op,tar,sig,mmC),mmS)
mmS
if mmS then
if $reportBottomUpFlag then
sayMSG '" found an exact match!"
return mmS
mmS := matchMms(havesInexact,op,tar,args1,args2)
else if $reportBottomUpFlag then sayMSG '" no modemaps"
mmS => mmS
if $reportBottomUpFlag then
sayMSG ['%l,:bright '"Remaining General Modemaps"]
-- for mm in havenots for i in 1.. repeat sayModemapWithNumber(mm,i)
if havenots then
[havesNExact,havesNInexact] := exact?(havenots,tar,args1)
if $reportBottomUpFlag then
for mm in APPEND(havesNExact,havesNInexact) for i in 1.. repeat
sayModemapWithNumber(mm,i)
if havesNExact then
mmS := matchMms(havesNExact,op,tar,args1,args2)
if mmS then
if $reportBottomUpFlag then
sayMSG '" found an exact match!"
return mmS
mmS := matchMms(havesNInexact,op,tar,args1,args2)
else if $reportBottomUpFlag then sayMSG '" no modemaps"
mmS
matchTypes(pm,args1,args2) ==
-- pm is a list of pattern variables, args1 a list of argument types,
-- args2 a list of polynomial types for symbols
-- the result is a match from pm to args, if one exists
for v in pm for t1 in args1 for t2 in args2 until $Subst='failed repeat
p:= ASSQ(v,$Subst) =>
t:= CDR p
t=t1 => $Coerce and EQCAR(t1,'Symbol) and
(q := ASSQ(v,$SymbolType)) and t2 and
(t3 := resolveTT(CDR q, t2)) and
RPLACD(q, t3)
$Coerce =>
if EQCAR(t,'Symbol) and (q := ASSQ(v,$SymbolType)) then
t := CDR q
if EQCAR(t1,'Symbol) and t2 then t1:= t2
t0 := resolveTT(t,t1) => RPLACD(p,t0)
$Subst:= 'failed
$Subst:= 'failed
$Subst:= CONS(CONS(v,t1),$Subst)
if EQCAR(t1,'Symbol) and t2 then $SymbolType:= CONS(CONS(v,t2),$SymbolType)
evalMm(op,tar,sig,mmC) ==
-- evaluates a modemap with signature sig and condition mmC
-- the result is a list of lists [sig,slot,cond] or NIL
--if $Coerce is NIL, tar has to be the same as the computed target type
--if CONTAINED('LinearlyExplicitRingOver,mmC) then hohoho()
mS:= NIL
for st in evalMmStack mmC repeat
SL:= evalMmCond(op,sig,st)
not EQ(SL,'failed) =>
SL := fixUpTypeArgs SL
sig:= [subCopy(deepSubCopy(x,SL),$Subst) for x in sig]
not containsVars sig =>
isFreeFunctionFromMmCond mmC and (m := evalMmFreeFunction(op,tar,sig,mmC)) =>
mS:= nconc(m,mS)
"or"/[^isValidType(arg) for arg in sig] => nil
[dc,t,:args]:= sig
$Coerce or null tar or tar=t =>
mS:= nconc(findFunctionInDomain(op,dc,t,args,args,NIL,'T),mS)
mS
evalMmFreeFunction(op,tar,sig,mmC) ==
[dc,t,:args]:= sig
$Coerce or null tar or tar=t =>
nilArgs := nil
for a in args repeat nilArgs := [NIL,:nilArgs]
[[[["__FreeFunction__",:dc],t,:args], [t, :args], nilArgs]]
nil
evalMmStack(mmC) ==
-- translates the modemap condition mmC into a list of stacks
mmC is ['AND,:a] =>
["NCONC"/[evalMmStackInner cond for cond in a]]
mmC is ['OR,:args] => [:evalMmStack a for a in args]
mmC is ['partial,:mmD] => evalMmStack mmD
mmC is ['ofCategory,pvar,cat] and cat is ['Join,:args] =>
evalMmStack CONS('AND,[['ofCategory,pvar,c] for c in args])
mmC is ['ofType,:.] => [NIL]
mmC is ['has,pat,x] =>
MEMQ(x,'(ATTRIBUTE SIGNATURE)) =>
[[['ofCategory,pat,['CATEGORY,'unknown,x]]]]
[['ofCategory,pat,x]]
[[mmC]]
evalMmStackInner(mmC) ==
mmC is ['OR,:args] =>
keyedSystemError("S2GE0016",
['"evalMmStackInner",'"OR condition nested inside an AND"])
mmC is ['partial,:mmD] => evalMmStackInner mmD
mmC is ['ofCategory,pvar,cat] and cat is ['Join,:args] =>
[['ofCategory, pvar, c] for c in args]
mmC is ['ofType,:.] => NIL
mmC is ['isAsConstant] => NIL
mmC is ['has,pat,x] =>
MEMQ(x,'(ATTRIBUTE SIGNATURE)) =>
[['ofCategory,pat,['CATEGORY,'unknown,x]]]
[['ofCategory,pat,x]]
[mmC]
evalMmCond(op,sig,st) ==
$insideEvalMmCondIfTrue : local := true
evalMmCond0(op,sig,st)
evalMmCond0(op,sig,st) ==
-- evaluates the nonempty list of modemap conditions st
-- the result is either 'failed or a substitution list
SL:= evalMmDom st
SL='failed => 'failed
for p in SL until p1 and not b repeat b:=
p1:= ASSQ(CAR p,$Subst)
p1 and
t1:= CDR p1
t:= CDR p
t=t1 or
containsVars t =>
if $Coerce and EQCAR(t1,'Symbol) then t1:= getSymbolType CAR p
resolveTM1(t1,t)
$Coerce and
-- if we are looking at the result of a function, the coerce
-- goes the opposite direction
(t1 = $AnonymousFunction and t is ['Mapping, :.]) => t
CAR p = CADR sig and not member(CAR p, CDDR sig) =>
canCoerceFrom(t,t1) => 'T
NIL
canCoerceFrom(t1,t) => 'T
isSubDomain(t,t1) => RPLACD(p,t1)
EQCAR(t1,'Symbol) and canCoerceFrom(getSymbolType CAR p,t)
( SL and p1 and not b and 'failed ) or evalMmCat(op,sig,st,SL)
fixUpTypeArgs SL ==
for (p := [v, :t2]) in SL repeat
t1 := LASSOC(v, $Subst)
null t1 => RPLACD(p,replaceSharpCalls t2)
RPLACD(p, coerceTypeArgs(t1, t2, SL))
SL
replaceSharpCalls t ==
noSharpCallsHere t => t
doReplaceSharpCalls t
doReplaceSharpCalls t ==
ATOM t => t
t is ['_#, l] => #l
t is ['construct,: l] => EVAL ['LIST,:l]
[CAR t,:[ doReplaceSharpCalls u for u in CDR t]]
noSharpCallsHere t ==
t isnt [con, :args] => true
MEMQ(con,'(construct _#)) => NIL
and/[noSharpCallsHere u for u in args]
coerceTypeArgs(t1, t2, SL) ==
-- if the type t has type-valued arguments, coerce them to the new types,
-- if needed.
t1 isnt [con1, :args1] or t2 isnt [con2, :args2] => t2
con1 ^= con2 => t2
coSig := CDR GETDATABASE(CAR t1, 'COSIG)
and/coSig => t2
csub1 := constructSubst t1
csub2 := constructSubst t2
cs1 := CDR getConstructorSignature con1
cs2 := CDR getConstructorSignature con2
[con1, :
[makeConstrArg(arg1, arg2, constrArg(c1,csub1,SL),
constrArg(c2,csub2,SL), cs)
for arg1 in args1 for arg2 in args2 for c1 in cs1 for c2 in cs2
for cs in coSig]]
constrArg(v,sl,SL) ==
x := LASSOC(v,sl) =>
y := LASSOC(x,SL) => y
y := LASSOC(x, $Subst) => y
x
y := LASSOC(x, $Subst) => y
v
makeConstrArg(arg1, arg2, t1, t2, cs) ==
if arg1 is ['_#, l] then arg1 := # l
if arg2 is ['_#, l] then arg2 := # l
cs => arg2
t1 = t2 => arg2
obj1 := objNewWrap(arg1, t1)
obj2 := coerceInt(obj1, t2)
null obj2 => throwKeyedMsgCannotCoerceWithValue(wrap arg1,t1,t2)
objValUnwrap obj2
evalMmDom(st) ==
-- evals all isDomain(v,d) of st
SL:= NIL
for mmC in st until SL='failed repeat
mmC is ['isDomain,v,d] =>
STRINGP d => SL:= 'failed
p:= ASSQ(v,SL) and not (d=CDR p) => SL:= 'failed
d1:= subCopy(d,SL)
CONSP(d1) and MEMQ(v,d1) => SL:= 'failed
SL:= augmentSub(v,d1,SL)
mmC is ['isFreeFunction,v,fun] =>
SL:= augmentSub(v,subCopy(fun,SL),SL)
SL
orderMmCatStack st ==
-- tries to reorder stack so that free pattern variables appear
-- as parameters first
null(st) or null rest(st) => st
vars := DELETE_-DUPLICATES [CADR(s) for s in st | isPatternVar(CADR(s))]
null vars => st
havevars := nil
haventvars := nil
for s in st repeat
cat := CADDR s
mem := nil
for v in vars while not mem repeat
if MEMQ(v,cat) then
mem := true
havevars := cons(s,havevars)
if not mem then haventvars := cons(s,haventvars)
null havevars => st
st := nreverse nconc(haventvars,havevars)
SORT(st, function mmCatComp)
mmCatComp(c1, c2) ==
b1 := ASSQ(CADR c1, $Subst)
b2 := ASSQ(CADR c2, $Subst)
b1 and null(b2) => true
false
evalMmCat(op,sig,stack,SL) ==
-- evaluates all ofCategory's of stack as soon as possible
$hope:local:= NIL
numConds:= #stack
stack:= orderMmCatStack [mmC for mmC in stack | EQCAR(mmC,'ofCategory)]
while stack until not makingProgress repeat
st := stack
stack := NIL
makingProgress := NIL
for mmC in st repeat
S:= evalMmCat1(mmC,op, SL)
S='failed and $hope =>
stack:= CONS(mmC,stack)
S = 'failed => return S
not atom S =>
makingProgress:= 'T
SL:= mergeSubs(S,SL)
if stack or S='failed then 'failed else SL
evalMmCat1(mmC is ['ofCategory,d,c],op, SL) ==
-- evaluates mmC using information from the lisplib
-- d may contain variables, and the substitution list $Subst is used
-- the result is a substitution or failed
$domPvar: local := NIL
$hope:= NIL
NSL:= hasCate(d,c,SL)
NSL='failed and isPatternVar d and $Coerce and ( p:= ASSQ(d,$Subst) )
and (EQCAR(CDR p,'Variable) or EQCAR(CDR p,'Symbol)) =>
RPLACD(p,getSymbolType d)
hasCate(d,c,SL)
NSL='failed and isPatternVar d =>
-- following is hack to take care of the case where we have a
-- free substitution variable with a category condition on it.
-- This would arise, for example, where a package has an argument
-- that is not in a needed modemap. After making the following
-- dummy substitutions, the package can be instantiated and the
-- modemap used. RSS 12-22-85
-- If c is not Set, Ring or Field then the more general mechanism
dom := defaultTypeForCategory(c, SL)
null dom =>
op ^= 'coerce => 'failed -- evalMmCatLastChance(d,c,SL)
null (p := ASSQ(d,$Subst)) =>
dom =>
NSL := [CONS(d,dom)]
op ^= 'coerce => 'failed -- evalMmCatLastChance(d,c,SL)
if containsVars dom then dom := resolveTM(CDR p, dom)
$Coerce and canCoerce(CDR p, dom) =>
NSL := [CONS(d,dom)]
op ^= 'coerce => 'failed -- evalMmCatLastChance(d,c,SL)
NSL
hasCate(dom,cat,SL) ==
-- asks whether dom has cat under SL
-- augments substitution SL or returns 'failed
dom = $EmptyMode => NIL
isPatternVar dom =>
(p:= ASSQ(dom,SL)) and ((NSL := hasCate(CDR p,cat,SL)) ^= 'failed) =>
NSL
(p:= ASSQ(dom,$Subst)) or (p := ASSQ(dom, SL)) =>
-- S:= hasCate(CDR p,cat,augmentSub(CAR p,CDR p,copy SL))
S:= hasCate1(CDR p,cat,SL, dom)
not (S='failed) => S
hasCateSpecial(dom,CDR p,cat,SL)
if SL ^= 'failed then $hope:= 'T
'failed
SL1 := [[v,:d] for [v,:d] in SL | not containsVariables d]
if SL1 then cat := subCopy(cat, SL1)
hasCaty(dom,cat,SL)
hasCate1(dom, cat, SL, domPvar) ==
$domPvar:local := domPvar
hasCate(dom, cat, SL)
hasCateSpecial(v,dom,cat,SL) ==
-- v is a pattern variable, dom it's binding under $Subst
-- tries to change dom, so that it has category cat under SL
-- the result is a substitution list or 'failed
dom is ['FactoredForm,arg] =>
if isSubDomain(arg,$Integer) then arg := $Integer
d := ['FactoredRing,arg]
SL:= hasCate(arg,'(Ring),augmentSub(v,d,SL))
SL = 'failed => 'failed
hasCaty(d,cat,SL)
EQCAR(cat,'Field) or EQCAR(cat, 'DivisionRing) =>
if isSubDomain(dom,$Integer) then dom := $Integer
d:= eqType [$QuotientField, dom]
hasCaty(dom,'(IntegralDomain),augmentSub(v,d,SL))
cat is ['PolynomialCategory, d, :.] =>
dom' := ['Polynomial, d]
(containsVars d or canCoerceFrom(dom, dom'))
and hasCaty(dom', cat, augmentSub(v,dom',SL))
isSubDomain(dom,$Integer) =>
NSL:= hasCate($Integer,cat,augmentSub(v,$Integer,SL))
NSL = 'failed =>
hasCateSpecialNew(v, dom, cat, SL)
hasCaty($Integer,cat,NSL)
hasCateSpecialNew(v, dom, cat, SL)
-- to be used in $newSystem only
hasCateSpecialNew(v,dom,cat,SL) ==
fe := member(QCAR cat, '(ElementaryFunctionCategory
TrigonometricFunctionCategory ArcTrigonometricFunctionCategory
HyperbolicFunctionCategory ArcHyperbolicFunctionCategory
PrimitiveFunctionCategory SpecialFunctionCategory Evalable
CombinatorialOpsCategory TranscendentalFunctionCategory
AlgebraicallyClosedFunctionSpace ExpressionSpace
LiouvillianFunctionCategory FunctionSpace))
alg := member(QCAR cat, '(RadicalCategory AlgebraicallyClosedField))
fefull := fe or alg or EQCAR(cat, 'CombinatorialFunctionCategory)
partialResult :=
EQCAR(dom, 'Variable) or EQCAR(dom, 'Symbol) =>
CAR(cat) in
'(SemiGroup AbelianSemiGroup Monoid AbelianGroup AbelianMonoid
PartialDifferentialRing Ring InputForm) =>
d := ['Polynomial, $Integer]
augmentSub(v, d, SL)
EQCAR(cat, 'Group) =>
d := ['Fraction, ['Polynomial, $Integer]]
augmentSub(v, d, SL)
fefull =>
d := defaultTargetFE dom
augmentSub(v, d, SL)
'failed
isEqualOrSubDomain(dom, $Integer) =>
fe =>
d := defaultTargetFE $Integer
augmentSub(v, d, SL)
alg =>
d := '(AlgebraicNumber)
--d := defaultTargetFE $Integer
augmentSub(v, d, SL)
'failed
underDomainOf dom = $ComplexInteger =>
d := defaultTargetFE $ComplexInteger
hasCaty(d,cat,augmentSub(v, d, SL))
(dom = $RationalNumber) and alg =>
d := '(AlgebraicNumber)
--d := defaultTargetFE $Integer
augmentSub(v, d, SL)
fefull =>
d := defaultTargetFE dom
augmentSub(v, d, SL)
'failed
partialResult = 'failed => 'failed
hasCaty(d, cat, partialResult)
hasCaty(d,cat,SL) ==
-- calls hasCat, which looks up a hashtable and returns:
-- 1. T, NIL or a (has x1 x2) condition, if cat is not parameterized
-- 2. a list of pairs (argument to cat,condition) otherwise
-- then the substitution SL is augmented, or the result is 'failed
cat is ['CATEGORY,.,:y] => hasAttSig(d,subCopy(y,constructSubst d),SL)
cat is ['SIGNATURE,foo,sig] =>
hasSig(d,foo,subCopy(sig,constructSubst d),SL)
cat is ['ATTRIBUTE,a] => hasAtt(d,subCopy(a,constructSubst d),SL)
x:= hasCat(opOf d,opOf cat) =>
y:= KDR cat =>
S := constructSubst d
for [z,:cond] in x until not (S1='failed) repeat
S' := [[p, :mkDomPvar(p, d, z, y)] for [p,:d] in S]
if $domPvar then
dom := [CAR d, :[domArg(arg, i, z, y) for i in 0..
for arg in CDR d]]
SL := augmentSub($domPvar, dom, copy SL)
z' := [domArg2(a, S, S') for a in z]
S1:= unifyStruct(y,z',copy SL)
if not (S1='failed) then S1:=
atom cond => S1
ncond := subCopy(cond, S)
ncond is ['has, =d, =cat] => 'failed
hasCaty1(ncond,S1)
S1
atom x => SL
ncond := subCopy(x, constructSubst d)
ncond is ['has, =d, =cat] => 'failed
hasCaty1(ncond, SL)
'failed
mkDomPvar(p, d, subs, y) ==
l := MEMQ(p, $FormalMapVariableList) =>
domArg(d, #$FormalMapVariableList - #l, subs, y)
d
domArg(type, i, subs, y) ==
p := MEMQ($FormalMapVariableList.i, subs) =>
y.(#subs - #p)
type
domArg2(arg, SL1, SL2) ==
isSharpVar arg => subCopy(arg, SL1)
arg = '_$ and $domPvar => $domPvar
subCopy(arg, SL2)
hasCaty1(cond,SL) ==
-- cond is either a (has a b) or an OR clause of such conditions
-- SL is augmented, if cond is true, otherwise the result is 'failed
$domPvar: local := NIL
cond is ['has,a,b] => hasCate(a,b,SL)
cond is ['AND,:args] =>
for x in args while not (S='failed) repeat S:=
x is ['has,a,b] => hasCate(a,b, SL)
-- next line is for an obscure bug in the table
x is [['has,a,b]] => hasCate(a,b, SL)
--'failed
hasCaty1(x, SL)
S
cond is ['OR,:args] =>
for x in args until not (S='failed) repeat S:=
x is ['has,a,b] => hasCate(a,b,copy SL)
-- next line is for an obscure bug in the table
x is [['has,a,b]] => hasCate(a,b,copy SL)
--'failed
hasCaty1(x, copy SL)
S
keyedSystemError("S2GE0016",
['"hasCaty1",'"unexpected condition from category table"])
hasAttSig(d,x,SL) ==
-- d is domain, x a list of attributes and signatures
-- the result is an augmented SL, if d has x, 'failed otherwise
for y in x until SL='failed repeat SL:=
y is ['ATTRIBUTE,a] => hasAtt(d,a,SL)
y is ['SIGNATURE,foo,s] => hasSig(d,foo,s,SL)
keyedSystemError("S2GE0016",
['"hasAttSig",'"unexpected form of unnamed category"])
SL
hasSigAnd(andCls, S0, SL) ==
dead := NIL
SA := 'failed
for cls in andCls while not dead repeat
SA :=
atom cls => copy SL
cls is ['has,a,b] =>
hasCate(subCopy(a,S0),subCopy(b,S0),copy SL)
keyedSystemError("S2GE0016",
['"hasSigAnd",'"unexpected condition for signature"])
if SA = 'failed then dead := true
SA
hasSigOr(orCls, S0, SL) ==
found := NIL
SA := 'failed
for cls in orCls until found repeat
SA :=
atom cls => copy SL
cls is ['has,a,b] =>
hasCate(subCopy(a,S0),subCopy(b,S0),copy SL)
cls is ['AND,:andCls] or cls is ['and,:andCls] =>
hasSigAnd(andCls, S0, SL)
keyedSystemError("S2GE0016",
['"hasSigOr",'"unexpected condition for signature"])
if SA ^= 'failed then found := true
SA
hasSig(dom,foo,sig,SL) ==
-- tests whether domain dom has function foo with signature sig
-- under substitution SL
$domPvar: local := nil
fun:= constructor? CAR dom =>
S0:= constructSubst dom
p := ASSQ(foo,getOperationAlistFromLisplib CAR dom) =>
for [x,.,cond,.] in CDR p until not (S='failed) repeat
S:=
atom cond => copy SL
cond is ['has,a,b] =>
hasCate(subCopy(a,S0),subCopy(b,S0),copy SL)
cond is ['AND,:andCls] or cond is ['and,:andCls] =>
hasSigAnd(andCls, S0, SL)
cond is ['OR,:orCls] or cond is ['or,:orCls] =>
hasSigOr(orCls, S0, SL)
keyedSystemError("S2GE0016",
['"hasSig",'"unexpected condition for signature"])
not (S='failed) => S:= unifyStruct(subCopy(x,S0),sig,S)
S
'failed
'failed
hasAtt(dom,att,SL) ==
-- tests whether dom has attribute att under SL
-- needs S0 similar to hasSig above ??
$domPvar: local := nil
fun:= CAR dom =>
atts:= subCopy(GETDATABASE(fun,'ATTRIBUTES),constructSubst dom) =>
PAIRP (u := getInfovec CAR dom) =>
--UGH! New world has attributes stored as pairs not as lists!!
for [x,:cond] in atts until not (S='failed) repeat
S:= unifyStruct(x,att,copy SL)
not atom cond and not (S='failed) => S := hasCatExpression(cond,S)
S
for [x,cond] in atts until not (S='failed) repeat
S:= unifyStruct(x,att,copy SL)
not atom cond and not (S='failed) => S := hasCatExpression(cond,S)
S
'failed
'failed
hasCatExpression(cond,SL) ==
cond is ['OR,:l] =>
or/[(y:=hasCatExpression(x,SL)) ^= 'failed for x in l] => y
cond is ['AND,:l] =>
and/[(SL:= hasCatExpression(x,SL)) ^= 'failed for x in l] => SL
cond is ['has,a,b] => hasCate(a,b,SL)
keyedSystemError("S2GE0016",
['"hasSig",'"unexpected condition for attribute"])
unifyStruct(s1,s2,SL) ==
-- tests for equality of s1 and s2 under substitutions SL and $Subst
-- the result is a substitution list or 'failed
s1=s2 => SL
if s1 is ['_:,x,.] then s1:= x
if s2 is ['_:,x,.] then s2:= x
if ^atom s1 and CAR s1 = '_# then s1:= LENGTH CADR s1
if ^atom s2 and CAR s2 = '_# then s2:= LENGTH CADR s2
s1=s2 => SL
isPatternVar s1 => unifyStructVar(s1,s2,SL)
isPatternVar s2 => unifyStructVar(s2,s1,SL)
atom s1 or atom s2 => 'failed
until null s1 or null s2 or SL='failed repeat
SL:= unifyStruct(CAR s1,CAR s2,SL)
s1:= CDR s1
s2:= CDR s2
s1 or s2 => 'failed
SL
unifyStructVar(v,s,SL) ==
-- the first argument is a pattern variable, which is not substituted
-- by SL
CONTAINED(v,s) => 'failed
ps := LASSOC(s, SL)
s1 := (ps => ps; s)
(s0 := LASSOC(v, SL)) or (s0 := LASSOC(v,$Subst)) =>
S:= unifyStruct(s0,s1,copy SL)
S='failed =>
$Coerce and not atom s0 and constructor? CAR s0 =>
containsVars s0 or containsVars s1 =>
ns0 := subCopy(s0, SL)
ns1 := subCopy(s1, SL)
containsVars ns0 or containsVars ns1 =>
$hope:= 'T
'failed
if canCoerce(ns0, ns1) then s3 := s1
else if canCoerce(ns1, ns0) then s3 := s0
else s3 := nil
s3 =>
if (s3 ^= s0) then SL := augmentSub(v,s3,SL)
if (s3 ^= s1) and isPatternVar(s) then SL := augmentSub(s,s3,SL)
SL
'failed
$domPvar =>
s3 := resolveTT(s0,s1)
s3 =>
if (s3 ^= s0) then SL := augmentSub(v,s3,SL)
if (s3 ^= s1) and isPatternVar(s) then SL := augmentSub(s,s3,SL)
SL
'failed
-- isSubDomain(s,s0) => augmentSub(v,s0,SL)
'failed
'failed
augmentSub(v,s,S)
augmentSub(v,s,SL)
ofCategory(dom,cat) ==
-- entry point to category evaluation from other points than type
-- analysis
-- the result is true or NIL
$Subst:local:= NIL
$hope:local := NIL
IDENTP dom => NIL
cat is ['Join,:cats] => and/[ofCategory(dom,c) for c in cats]
(hasCaty(dom,cat,NIL) ^= 'failed)
printMms(mmS) ==
-- mmS a list of modemap signatures
sayMSG '" "
for [sig,imp,.] in mmS for i in 1.. repeat
istr := STRCONC('"[",STRINGIMAGE i,'"]")
if QCSIZE(istr) = 3 then istr := STRCONC(istr,'" ")
sayMSG [:bright istr,'"signature: ",:formatSignature CDR sig]
CAR sig='local =>
sayMSG ['" implemented: local function ",imp]
imp is ['XLAM,:.] =>
sayMSG concat('" implemented: XLAM from ",
prefix2String CAR sig)
sayMSG concat('" implemented: slot ",imp,
'" from ",prefix2String CAR sig)
sayMSG '" "
containsVars(t) ==
-- tests whether term t contains a * variable
atom t => isPatternVar t
containsVars1(t)
containsVars1(t) ==
-- recursive version, which works on a list
[t1,:t2]:= t
atom t1 =>
isPatternVar t1 or
atom t2 => isPatternVar t2
containsVars1(t2)
containsVars1(t1) or
atom t2 => isPatternVar t2
containsVars1(t2)
-- [[isPartialMode]] tests whether m contains [[$EmptyMode]]. The
-- constant [[$EmptyMode]] (defined in bootfuns.lisp) evaluates to
-- [[|$EmptyMode|]]. This constants is inserted in a modemap during
-- compile time if the modemap is not yet complete.
isPartialMode m ==
CONTAINED($EmptyMode,m)
getSymbolType var ==
-- var is a pattern variable
p:= ASSQ(var,$SymbolType) => CDR p
t:= '(Polynomial (Integer))
$SymbolType:= CONS(CONS(var,t),$SymbolType)
t
isEqualOrSubDomain(d1,d2) ==
-- last 2 parts are for tagged unions (hack for now, RSS)
(d1=d2) or isSubDomain(d1,d2) or
(atom(d1) and ((d2 is ['Variable,=d1]) or (d2 is [=d1])))
or (atom(d2) and ((d1 is ['Variable,=d2]) or (d1 is [=d2])))
defaultTypeForCategory(cat, SL) ==
-- this function returns a domain belonging to cat
-- note that it is important to note that in some contexts one
-- might not want to use this result. For example, evalMmCat1
-- calls this and should possibly fail in some cases.
cat := subCopy(cat, SL)
c := CAR cat
d := GETDATABASE(c, 'DEFAULTDOMAIN)
d => [d, :CDR cat]
cat is [c] =>
c = 'Field => $RationalNumber
c in '(Ring IntegralDomain EuclideanDomain GcdDomain
OrderedRing DifferentialRing) => '(Integer)
c = 'OrderedSet => $Symbol
c = 'FloatingPointSystem => '(Float)
NIL
cat is [c,p1] =>
c = 'FiniteLinearAggregate => ['Vector, p1]
c = 'VectorCategory => ['Vector, p1]
c = 'SetAggregate => ['Set, p1]
c = 'SegmentCategory => ['Segment, p1]
NIL
cat is [c,p1,p2] =>
NIL
cat is [c,p1,p2,p3] =>
cat is ['MatrixCategory, d, ['Vector, =d], ['Vector, =d]] =>
['Matrix, d]
NIL
NIL
boot
The file
/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5248549993924115758-25px004.boot
is needed but does not exist.Now function selection will show the costs:
fricas
)clear completely
All user variables and function definitions have been cleared.
All )browse facility databases have been cleared.
Internally cached functions and constructors have been cleared.
)clear completely is finished.
fricas
)lib TEST
Test is now explicitly exposed in frame initial
Test will be automatically loaded when needed from
/var/aw/var/LatexWiki/TEST.NRLIB/TEST
fricas
)set mess selection off
foo 3
fricas
p := x^300; s:=x=0..1;
Type: SegmentBinding
?(NonNegativeInteger
?)
fricas
)set mess time on
integrate(p, s)
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
fricas
Time: 0.04 (EV) = 0.04 sec
fricas
)set mess time off
After this change (see modification to 'mmCost0'above):
-- Testing: Expression can be expensive - especially for integration!
-- Thus we assign a higher cost if something of type
-- Expression is passed as an argument
CAR topcon2 = 'Expression => 5
the time taken for the integration:
integrate(x^300, x=0..1)
shown above (0.04 sec), compared to the time required for the
same calculation before the change (0.74 sec) makes it clear
that FriCAS has chosen a different integration algorithm for this
computation.
See related issue: #105
Of course a change like this might have a big (and possibly
undesirable) impact on how other expressions evaluated by the
interpreter. So this would require a lot of regression testing.
Using Category Theory to Design Implicit Conversions and Generic Operators, John C. Reynolds, 1980.
ftp://ftp.cs.cmu.edu/user/jcr/cattheodesign.pdf
from
http://lambda-the-ultimate.org/node/2078
