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Submitted by : (unknown) at: 2007-11-17T22:04:52-08:00 (9 years ago)
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Axiom Version :
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These error messages indicate some serious problems with the Axiom Tuple domain:

  System error: The function |Domain| is undefined.
  The constructor Tuple takes 1 argument and you have given  2

Axiom allows functions to have a tuple as input but it fails if a function generates two or more outputs.

For example:

fricas
f:(INT,INT)->INT
Type: Void
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g:INT->(INT,INT)
The constructor Tuple takes 1 argument and you have given 2 .

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(INT,INT)
LISP output: (UNPRINTABLE UNPRINTABLE)
Type: Tuple(Type)

Tuple Any should work in a similar way to List Any and DirectProduct(2,Any).

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List Any

\label{eq1}\hbox{\axiomType{List}\ } (\hbox{\axiomType{Any}\ })(1)
Type: Type
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DirectProduct(2,Any)

\label{eq2}\hbox{\axiomType{DirectProduct}\ } (2, \hbox{\axiomType{Any}\ })(2)
Type: Type
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Tuple Any
LISP output: (UNPRINTABLE)
Type: Tuple(Type)

Axiom's non-homogeneous Record and Union domains are functionally superior to the tuple construct but it makes functional notation awkward. See SandBox Direct Product


Try this (which gets around the error messages and bug):
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a:Tuple INT
Type: Void
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a:=(1,2,3,4)

\label{eq3}\left[ 1, \: 2, \: 3, \: 4 \right](3)
Type: Tuple(Integer)
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dom:=Tuple Any

\label{eq4}\hbox{\axiomType{Tuple}\ } (\hbox{\axiomType{Any}\ })(4)
Type: Type
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b:dom:=(1::INT, 2::FLOAT,3::POLY INT)

\label{eq5}\left[ 1, \:{2.0}, \: 3 \right](5)
Type: Tuple(Any)
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h:INT->Tuple INT
Type: Void
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h(x)==(x, 2+x)
Type: Void
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h(5)
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Compiling function h with type Integer -> Tuple(Integer)

\label{eq6}\left[ 5, \: 7 \right](6)
Type: Tuple(Integer)

Any suggestions --billpage, Wed, 29 Jun 2005 01:43:26 -0500 reply
How to do composition of functions with two arguments and two outputs?

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f1:INT->Tuple INT
Type: Void
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f1(x)==(x,2+x)
Type: Void
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f2:(INT,INT)->INT
Type: Void
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f2(x,y)==x*y
Type: Void
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f2(f1(4))
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Compiling function f1 with type Integer -> Tuple(Integer) 
   There are no library operations named f2 
      Use HyperDoc Browse or issue
                                 )what op f2
      to learn if there is any operation containing " f2 " in its name.
Cannot find a definition or applicable library operation named f2 with argument type(s) Tuple(Integer)
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.


From: William Sit, July 1, 2005 06:26:00 -5:00

The following works (not as neat as it should be, of course)

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f1:INT->Tuple INT
Compiled code for f1 has been cleared.
Type: Void
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f1(x)==(x,2+x)
1 old definition(s) deleted for function or rule f1
Type: Void
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f2:(INT,INT)->INT
Type: Void
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f2(x,y)==x*y
1 old definition(s) deleted for function or rule f2
Type: Void
fricas
a:=f1(4)
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Compiling function f1 with type Integer -> Tuple(Integer)

\label{eq7}\left[ 4, \: 6 \right](7)
Type: Tuple(Integer)
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f2(select(a,0), select(a,1))
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Compiling function f2 with type (Integer,Integer) -> Integer

\label{eq8}24(8)
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f3:Tuple INT -> INT
Type: Void
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f3(x) == reduce(*,[select(x,i::NNI) for i in 0..length(x)-1])
Type: Void
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f3(a)
There are 2 exposed and 5 unexposed library operations named length having 1 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op length to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named length with argument type(s) Tuple(Integer)
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need. FriCAS will attempt to step through and interpret the code.
fricas
Compiling function f3 with type Tuple(Integer) -> Integer 
   There are 2 exposed and 5 unexposed library operations named length 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op length
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
Cannot find a definition or applicable library operation named length with argument type(s) Tuple(Integer)
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

Note that neither f3(1,2,3,4) nor f3((1,2,3,4)) works, even though tuples are lists without the square brackets, essentially. In both cases, the reason is probably the parser treats the arities differently. Recall that the Interpreter (and Axiom) treats parenthesis as "applied to" (so f3 (1,2,3,4) is the same as applying f3 to 4 distinct arguments and f3(a) is f3 a). I do think the second form should have worked without the explicit coercion.

I do not know why in the design of Tuple S, the parts are not to be referenced with just the usual list method like a.i and must use select. Also the indexing in Tuple S starts with 0. In the very old days of Scratchpad, all aggregates indexing was zero based. Most are converted to one-based and you can have a choice. Somehow, Tuple S was not updated to reflect this.

One final puzzle: In axiom output messages for (9) above, what is the G1433 (or whatever) function from Integer->Boolean? I tried

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)clear all
All user variables and function definitions have been cleared. f3:Tuple INT->INT
Type: Void
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f3 x == reduce(*,[select(x,i::NNI) for i in 0..length(x)-1])
Type: Void
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a:Tuple INT:=(2,3)

\label{eq9}\left[ 2, \: 3 \right](9)
Type: Tuple(Integer)
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f3 a
There are 2 exposed and 5 unexposed library operations named length having 1 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op length to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named length with argument type(s) Tuple(Integer)
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need. FriCAS will attempt to step through and interpret the code.
fricas
Compiling function f3 with type Tuple(Integer) -> Integer 
   There are 2 exposed and 5 unexposed library operations named length 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op length
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
Cannot find a definition or applicable library operation named length with argument type(s) Tuple(Integer)
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

and there is no such function. Also, f3 a actually works.

William

display of tuple --unknown, Fri, 01 Jul 2005 06:49:16 -0500 reply
Why tuples are displayed as list ?

I prefer to read (2,3) or 2,3 for tuple, and [2,3] only for lists.

Students and I make errors when the display is the same, even if there is a type information.


From William Sit, Fri Jul 1 08:50:00 -0500 2005

There seems to be some bug in the display, because the code in Tuple (array1.spad) uses parenthesis, not brackets.

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coerce(a)$Tuple INT

\label{eq10}\left(2, \: 3 \right)(10)
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coerce(a)@PRIMARR INT

\label{eq11}\left[ 2, \: 3 \right](11)
Type: PrimitiveArray?(Integer)

This "bug" may be due to the Interpreter coercing Tuple INT to PRIMARR INT and then to OutputForm, which perhaps uses the List output. The order of coercion may be governed by the conditional on coerce to Outputform in Tuple S (S needs to be of SetCategory).

William

See related discussion: Tuples Products And Records

infinite loop in parsing? --wyscc, Sun, 21 Oct 2007 22:07:17 -0500 reply
A named tuple cannot be assigned to a tuple of identifiers. The last (commented out) line '[1 for (a,b) in g]? seems to cause a freeze in Axiom; no output, not even if )set mess bot on. If you try it by uncommenting the line, you have to use cancel. (It should have reported syntax error similar to (a,b):=f' (although there shouldn't be an error because f is of type Tuple (Positive) Integer. However, even (a,b):=(f::Tuple Integer) does not work.) This may be related to the convention that select rather than apply is used to get components in a tuple.

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)clear all
All user variables and function definitions have been cleared. g:=[(1,2),(3,4)]

\label{eq12}\left[{\left(1, \: 2 \right)}, \:{\left(3, \: 4 \right)}\right](12)
Type: List(Tuple(PositiveInteger))
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[(a:=e;(a,a)) for e in g]

\label{eq13}\left[{\left({\left(1, \: 2 \right)}, \:{\left(1, \: 2 \right)}\right)}, \:{\left({\left(3, \: 4 \right)}, \:{\left(3, \: 4 \right)}\right)}\right](13)
Type: List(Tuple(Tuple(PositiveInteger)))
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[((a,b):=(select(e,0),select(e,1));(a,a,b,c)) for e in g]

\label{eq14}\left[{\left(1, \: 1, \: 2, \: c \right)}, \:{\left(3, \: 3, \: 4, \: c \right)}\right](14)
Type: List(Tuple(Polynomial(Integer)))
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f:=g.1

\label{eq15}\left[ 1, \: 2 \right](15)
Type: Tuple(PositiveInteger)
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(a,b):=f
If there is a tuple on the left-hand side of an assignment then there must also be one on the right-hand side.

On my system, the following message finally:

   >> System error:
   The storage for CONS is exhausted.
   Currently, 85895 pages are allocated.
   Use ALLOCATE to expand the space.

It's clearly an infinite loop.

Category: Axiom Programming => Axiom Compiler Severity: serious => normal

Accident due to lack of abstraction --gdr, Wed, 20 Feb 2008 00:27:44 -0800 reply
This is issue is the result of lack of abstraction rampant in both the compiler and interpreter. More precisely, there is no proper separation between the internal name used to tag internal ASTs? and name used for category/domain constructor. Tuple is both the name of a constructor and the tag given to an AST that represents tuples. As a consequence the semantics analyzer cannot disguish between when Tupel is effectively used a domain constructor, as opposed to just the name of a tag.

display of tuple --gdr, Wed, 20 Feb 2008 21:00:39 -0800 reply
Display problem fixed in OpenAxiom-1.1.1 and later.

(INT,INT) does not necessarily designate a type --gdr, Thu, 21 Feb 2008 20:52:00 -0800 reply
Looking at the original report, the notation (INT,INT) does not necessarily designate a type. It does so only in a very specific cases. However, in general, it designates an object that is not of domain type, just like [INT,INT]? is not a domain.




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