MathAction #114 Map on Functions crash

#113 Compile fail on Suse 9.2 ← ↑ → #115 color highlighting of Axiom compiler output

#114 Map on Functions crash
last edited 18 years ago

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This problem does not occur on the NAG version:

 \begin{axiom}
 dom:=(INT->INT)
 g(f:dom):dom== x+->(f(x))^2
 p(x:INT):INT == x-1
 \end{axiom}

The next line crashes Axiom. (Here the crash is indicated by not showing the result for q which should be something like theMap(LAMBDA_ibs3ze_708.174) (from NAG version):

 \begin{axiom}
 q:= g p
 \end{axiom}

Below is the transcript for the NAG version:

G82322 (1) -> dom:= (INT->INT) (1) (Integer -> Integer)
 Type: Domain
G82322 (2) -> g(f:dom):dom== x+->(f(x))^2
 Function declaration g : (Integer -> Integer) -> (Integer -> Integer
 ) has been added to workspace.
 Type: Void
G82322 (3) -> p(x:INT):INT==x-1
 Function declaration p : Integer -> Integer has been added to 
 workspace.
 Type: Void
G82322 (4) -> q:= g p
 Compiling function p with type Integer -> Integer 
 Compiling function g with type (Integer -> Integer) -> (Integer -> 
 Integer)

+++ |*1;g;1;G82322| redefined

 (4) theMap(LAMBDA_ibs3ze_708,174)
 Type: (Integer -> Integer)
G82322 (5) -> q 3
 (5) 4
 Type: PositiveInteger

property change --wyscc, 2005年3月04日 04:37:59 -0600 reply

Name: #114 Maps on Function crash => #114 Map on Functions crash

Here is one way that works: 2005年3月04日 05:18:25 -0600 reply

fricas

(1) -> )clear all

 All user variables and function definitions have been cleared.

We can avoid the use of an anonymous function and use function composition to define the functional g as follows:

fricas

dom ==> INT -> INT

Type: Void

fricas

g(f:dom):dom ==
 function(x^2,sq,x)
 sq * f

 Function declaration g : (Integer -> Integer) -> (Integer -> Integer
 ) has been added to workspace.

Type: Void

fricas

p(x:INT):INT == x-1

 Function declaration p : Integer -> Integer has been added to 
 workspace.

Type: Void

fricas

q := g p

fricas

Compiling function p with type Integer -> Integer 
 There are 31 exposed and 40 unexposed library operations named * 
 having 2 argument(s) but none was determined to be applicable. 
 Use HyperDoc Browse, or issue
 )display op *
 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 * 
 with argument type(s) 
 Variable(sq)
 (Integer -> 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 g with type (Integer -> Integer) -> (Integer -> 
 Integer) 
 Compiled code for g has been cleared.

fricas

Compiling function sq with type Integer -> Integer

\label{eq1}\mbox{theMap (...)} (1)

Type: (Integer -> Integer)

fricas

q 3

\label{eq2}4 (2)

Type: PositiveInteger?

Using the SPAD compiler --Bill Page, 2005年3月04日 07:03:34 -0600 reply

Take a look at FunctionalMapping? for an example of this sort thing written in SPAD.

anonymous function --wyscc, 2005年3月04日 23:51:55 -0600 reply

Thanks to both contributions and guides to use composition. However, this is a bug still since the original code works under the NAG version. We should figure out why the open source version breaks down. Afterall, anonymous functions are convenience that the system should be able to handle by assigning intermediate variables automatically.