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 Submitted by : (unknown) at: 2007-11-17T22:11:48-08:00 (11 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : Axiom Aldor Interface Axiom Compiler Axiom Library Axiom Interpreter Axiom Documentation Axiom User Interface building Axiom from source lisp system MathAction Doyen CD Reduce Axiom on Windows Axiom on Linux Severity : critical serious normal minor wishlist Status : open closed rejected not reproducible fix proposed fixed somewhere duplicate need more info Optional subject :   Optional comment :

The equality test seems to have a bug.

axiom
p:Integer->Integer
Type: Void
axiom
p(x)==x
Type: Void
axiom
p (1)
Type: FunctionCalled(p)
axiom
t:Boolean:=(p=p)
axiom
Compiling function p with type Integer -> Integer (2)
Type: Boolean
axiom
)set mess bot on
t:=(p=p)
Function Selection for =
Arguments: ((INT -> INT),(INT -> INT))
Target type: BOOLEAN
  signature:   ((INT -> INT),(INT -> INT)) -> BOOLEAN
implemented: slot (Boolean) from (INT -> INT) (3)
Type: Boolean

In fact, in variable.spad, the result should be true always. So the code has no bugs! The Interpreter uses the wrong equality test function. Moreover, even this function gives the wrong answer. According to the )set mess bot on message, the test function is taken from the domain (INT->INT), which is Mapping(INT, INT). Unfortunately, Mapping is an Axiom primitive and according to available documentation:

axiom
)show Mapping
Mapping(T, S, ...)
Mapping takes any number of arguments of the form:
T, a domain of category SetCategory
S, a domain of category SetCategory
...
Mapping(T, S, ...) denotes the class of objects which are
mappings from a source domain (S, ...) into a target domain T.
The Mapping constructor can take any number of arguments. All
but the first argument is regarded as part of a source tuple
for the mapping. For example, Mapping(T, A, B) denotes the
class of mappings from (A, B) into T.
This constructor is a primitive in FriCAS. For more
information, use the HyperDoc Browser.

In any case, according to Hyperdoc, there is only one function exported: (you guessed it) equality testing. I have no idea where the code is or how the testing is done. Equivalence of functions (lambda terms) is undecidable, so I suppose equality here means equality in implementation? But surely, p should be equal to p however you test it.

I fear there is a confusion between the value of p', and its type. The type of p' is Integer -> Integer as stated in this declaration. Consequently the mode selection takes equality from Mapping(Integer,Integer), which is to return false all the type -- even if they functions are structurally equal (unlike pointer to functions in C).

FunctionCalled? p' is the type, synthetized by the interpreter, for the value of p'. This is one of the very cases where the type of an identifier does not agree with the value it refers to in the environement.

I'm afraid the definition of FunctionCalled? shown above does not capture the reality of the computations going on -- and I agree it is misleading.

Category: Axiom Compiler => Axiom Interpreter

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