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#418 series expansion, but not differentiable ←	↑	→ #42 Escaping $ is tedious...

#419 bug in type inference for anonymous functions

Edit detail for #419 bug in type inference for anonymous functions revision 1 of 1

	1
Editor: kratt6 Time: 2008/03/04 06:26:14 GMT-8
Note:

changed:
-
Possibly related to #105 is the following:

\begin{axiom}
f(x,y)==x+y
)set message bottom on
draw(x +-> f(x,3.0), 1.0..2.0)
\end{axiom}

Note that for some reason, axiom prefers to think of 'x+->f(x,3.0)' as a function to 'Point DFLOAT'.

It does help to declare the anonymous function, but only before it's first use:
\begin{axiom}
draw((x:DFLOAT):DFLOAT +-> f(x,3.0), 1.0..2.0)
g(x,y)==x+y
draw((x:DFLOAT):DFLOAT +-> g(x,3.0), 1.0..2.0)
\end{axiom}

Possibly related to #105 is the following:

axiom

f(x,y)==x+y

Type: Void

axiom

)set message bottom on

draw(x +-> f(x,3.0), 1.0..2.0)

 Function Selection for float
      Arguments: (INT,INT,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for float
      Arguments: (INT,INT,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for SEGMENT
      Arguments: (FLOAT,FLOAT) 
   -> no appropriate SEGMENT found in Float 
   -> no appropriate SEGMENT found in Float 

 Modemaps from Associated Packages 
   no modemaps

 Remaining General Modemaps 
   [1] (D1,D1) -> D from D if D has SEGCAT(D1) and D1 has TYPE

 [1]  signature:   (FLOAT,FLOAT) -> SEG(FLOAT)
      implemented: slot $(Float)(Float) from SEG(FLOAT)

 Function Selection for draw
      Arguments: (ANON,SEG(FLOAT)) 
   -> no appropriate draw found in AnonymousFunction 
   -> no appropriate draw found in Segment(Float) 
   -> no appropriate draw found in AnonymousFunction 
   -> no appropriate draw found in Segment(Float) 

 Modemaps from Associated Packages 
   no modemaps

 Remaining General Modemaps 
   [1] (List(Point(DoubleFloat)),List(DrawOption)) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [2] (List(DoubleFloat),List(DoubleFloat)) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [3] ((DoubleFloat -> Point(DoubleFloat)),Segment(Float)) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [4] (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(
            Float)) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [5] (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment(
            Float)) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [6] ((DoubleFloat -> DoubleFloat),Segment(Float)) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [7] (ParametricSpaceCurve(D4),SegmentBinding(Float)) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctions(D4)
            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
   [8] (ParametricPlaneCurve(D4),SegmentBinding(Float)) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctions(D4)
            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
   [9] (D2,SegmentBinding(Float)) -> TwoDimensionalViewport
            from TopLevelDrawFunctions(D2)
            if D2 has Join(ConvertibleTo(InputForm),SetCategory)

 [1]  signature:   ((DFLOAT -> POINT(DFLOAT)),SEG(FLOAT)) -> VIEW3D
      implemented: slot (ThreeDimensionalViewport)(Mapping (Point (DoubleFloat)) (DoubleFloat))(Segment (Float)) from DRAWCFUN
 [2]  signature:   ((DFLOAT -> DFLOAT),SEG(FLOAT)) -> VIEW2D
      implemented: slot (TwoDimensionalViewport)(Mapping (DoubleFloat) (DoubleFloat))(Segment (Float)) from DRAWCFUN

 Function Selection for float
      Arguments: (PI,NNI,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for f
      Arguments: (DFLOAT,FLOAT) 
      Target type: POINT(DFLOAT) 

 Function Selection for +
      Arguments: (DFLOAT,FLOAT) 
      Target type: POINT(DFLOAT) 
   -> no appropriate + found in DoubleFloat 
   -> no appropriate + found in Float 
   -> no appropriate + found in Point(DoubleFloat) 
   -> no appropriate + found in DoubleFloat 
   -> no appropriate + found in Float 
   -> no appropriate + found in Point(DoubleFloat) 

 Modemaps from Associated Packages 
   no modemaps

 Remaining General Modemaps 
   [1] (D,D) -> D from D
            if D has VECTCAT(D1) and D1 has TYPE and D1 has ABELSG
   [2] (D,D) -> D from D
            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
            D1) and D3 has FLAGG(D1)
   [3] (PolynomialIdeal(D1,D2,D3,D4),PolynomialIdeal(D1,D2,D3,D4)) -> 
            PolynomialIdeal(D1,D2,D3,D4)
            from PolynomialIdeal(D1,D2,D3,D4)
            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 
            has POLYCAT(D1,D2,D3)
   [4] (D,D) -> D from D
            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON

   [5] (D1,FullPartialFractionExpansion(D2,D1)) -> 
            FullPartialFractionExpansion(D2,D1)
            from FullPartialFractionExpansion(D2,D1)
            if D2 has Join(Field,CharacteristicZero) and D1 has UPOLYC(
            D2)
   [6] (D1,D) -> D from D
            if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON

   [7] (D1,Equation(D1)) -> Equation(D1) from Equation(D1)
            if D1 has ABELSG and D1 has TYPE
   [8] (Equation(D1),D1) -> Equation(D1) from Equation(D1)
            if D1 has ABELSG and D1 has TYPE
   [9] (Database(D1),Database(D1)) -> Database(D1) from Database(D1)
            if D1 has OrderedSet with 
               ?.? : (%,Symbol) -> String
               display : % -> Void
               fullDisplay : % -> Void
   [10] (Color,Color) -> Color from Color
   [11] (D,D) -> D from D if D has ABELSG

 [1]  signature:   (DFLOAT,DFLOAT) -> DFLOAT
      implemented: slot $$$ from DFLOAT

axiom

Compiling function f with type (DoubleFloat,Float) -> Point(
      DoubleFloat) 

 [1]  signature:   (DFLOAT,FLOAT) -> POINT(DFLOAT)
      implemented: local function *2;f;1;initial

   Conversion failed in the compiled user function f .

   Cannot convert from type DoubleFloat to Point(DoubleFloat) for value
   4.0

Note that for some reason, axiom prefers to think of x+->f(x,3.0) as a function to Point DFLOAT.

It does help to declare the anonymous function, but only before it's first use:

axiom

draw((x:DFLOAT):DFLOAT +-> f(x,3.0), 1.0..2.0)

 Function Selection for float
      Arguments: (PI,NNI,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for f
      Arguments: (DFLOAT,FLOAT) 
      Target type: DFLOAT 

 [1]  signature:   (DFLOAT,FLOAT) -> POINT(DFLOAT)
      implemented: local function *2;f;1;initial

 Function Selection for float
      Arguments: (INT,INT,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for float
      Arguments: (INT,INT,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for SEGMENT
      Arguments: (FLOAT,FLOAT) 

 [1]  signature:   (FLOAT,FLOAT) -> SEG(FLOAT)
      implemented: slot $(Float)(Float) from SEG(FLOAT)

 Function Selection for draw
      Arguments: ((DFLOAT -> DFLOAT),SEG(FLOAT)) 
   -> no appropriate draw found in Segment(Float) 
   -> no appropriate draw found in DoubleFloat 
   -> no appropriate draw found in Segment(Float) 
   -> no appropriate draw found in DoubleFloat 

 Modemaps from Associated Packages 
   no modemaps

 Remaining General Modemaps 
   [1] (List(Point(DoubleFloat)),List(DrawOption)) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [2] (List(DoubleFloat),List(DoubleFloat)) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForPoints
   [3] ((DoubleFloat -> Point(DoubleFloat)),Segment(Float)) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [4] (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(
            Float)) -> ThreeDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [5] (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment(
            Float)) -> TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [6] ((DoubleFloat -> DoubleFloat),Segment(Float)) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctionsForCompiledFunctions
   [7] (ParametricSpaceCurve(D4),SegmentBinding(Float)) -> 
            ThreeDimensionalViewport
            from TopLevelDrawFunctions(D4)
            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
   [8] (ParametricPlaneCurve(D4),SegmentBinding(Float)) -> 
            TwoDimensionalViewport
            from TopLevelDrawFunctions(D4)
            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
   [9] (D2,SegmentBinding(Float)) -> TwoDimensionalViewport
            from TopLevelDrawFunctions(D2)
            if D2 has Join(ConvertibleTo(InputForm),SetCategory)

 [1]  signature:   ((DFLOAT -> DFLOAT),SEG(FLOAT)) -> VIEW2D
      implemented: slot (TwoDimensionalViewport)(Mapping (DoubleFloat) (DoubleFloat))(Segment (Float)) from DRAWCFUN

   Conversion failed in the compiled user function f .

   Cannot convert from type DoubleFloat to Point(DoubleFloat) for value
   4.0

g(x,y)==x+y

Type: Void

axiom

draw((x:DFLOAT):DFLOAT +-> g(x,3.0), 1.0..2.0)

 Function Selection for float
      Arguments: (PI,NNI,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for g
      Arguments: (DFLOAT,FLOAT) 
      Target type: DFLOAT 

 Function Selection for +
      Arguments: (DFLOAT,FLOAT) 
      Target type: DFLOAT 
   -> no appropriate + found in DoubleFloat 
   -> no appropriate + found in Float 
   -> no appropriate + found in Float 

 [1]  signature:   (DFLOAT,DFLOAT) -> DFLOAT
      implemented: slot $$$ from DFLOAT

axiom

Compiling function g with type (DoubleFloat,Float) -> DoubleFloat 

 [1]  signature:   (DFLOAT,FLOAT) -> DFLOAT
      implemented: local function *2;g;1;initial

 Function Selection for float
      Arguments: (INT,INT,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for float
      Arguments: (INT,INT,PI) 
      Target type: FLOAT 
      From:      FLOAT 

 [1]  signature:   (INT,INT,PI) -> FLOAT
      implemented: slot $(Integer)(Integer)(PositiveInteger) from FLOAT

 Function Selection for SEGMENT
      Arguments: (FLOAT,FLOAT) 

 [1]  signature:   (FLOAT,FLOAT) -> SEG(FLOAT)
      implemented: slot $(Float)(Float) from SEG(FLOAT)

 Function Selection for draw
      Arguments: ((DFLOAT -> DFLOAT),SEG(FLOAT)) 

 [1]  signature:   ((DFLOAT -> DFLOAT),SEG(FLOAT)) -> VIEW2D
      implemented: slot (TwoDimensionalViewport)(Mapping (DoubleFloat) (DoubleFloat))(Segment (Float)) from DRAWCFUN

   Graph data being transmitted to the viewport manager...
   FriCAS2D data being transmitted to the viewport manager...

$\label{eq1}\mbox{\rm \hbox{\axiomType{TwoDimensionalViewport}\ } :}\mbox{\tt "FriCAS2D"}$

(1)

Type: TwoDimensionalViewport?