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[Axiom-math] Re: [Aldor-l] Type equivalence of domains in Axiom and Aldo


From: Ralf Hemmecke
Subject: [Axiom-math] Re: [Aldor-l] Type equivalence of domains in Axiom and Aldor
Date: Fri, 23 Nov 2007 17:00:19 +0100
User-agent: Thunderbird 2.0.0.9 (X11/20071031)

Hello Bill,

I think, I don't like your suggestion.
I'd rather change it into

define Product(Obj:Category):Category == with {
        ...
--        *:(Obj,Obj)->Obj;
    default {
        local mult(A:Obj, B:Obj):Obj == {
                (
                    AB:Obj,
                    pa:AB->A,
                    pb:AB->B,
                    product:(X:Obj)->(X->A,X->B)->(X->AB)
                ) == Product(A,B);
                AB add;
        }
        *: (Obj,Obj)->Obj == mult;
    }
}

The "default" is like defining an anonymous "add" body which exports
anything on the left of == that is not declared local. So

  *: (Obj,Obj)->Obj

will get exported by Product(Obj) even if you put a "--" as I did above.

Ralf


On 11/08/2007 07:51 PM, Bill Page wrote:
Ralf,

Here is another version that is slightly more friendly to the #pile
syntax (-: no {}  required :-). I presume that the compiler generates
the same code...

--- Categories.as_orig  2007-11-08 10:09:11.000000000 -0800
+++ Categories.as       2007-11-08 10:45:51.000000000 -0800
@@ -66,3 +66,3 @@
     Product: (A1:Obj,B1:Obj,  A2:Obj,B2:Obj) ->
(AB1:Obj,AB2:Obj,(A1->A2,B1->B2)->(AB1->AB2))
-    *:(Obj,Obj)->Obj
+    *:(Obj,Obj)-> with Obj
     default
@@ -73,3 +73,3 @@
            (ab1,ab2,*)
-        (A:Obj)*(B:Obj):Obj ==
+        (A:Obj)*(B:Obj): with Obj ==
             (AB:Obj,pa:AB->A,pb:AB->B,product:(X:Obj)->(X->A,X->B)->(X->AB))
== Product(A,B)
@@ -83,3 +83,3 @@
     CoProduct: (A1:Obj,B1:Obj, A2:Obj,B2:Obj) ->
(AB1:Obj,AB2:Obj,(A2->A1,B2->B1)->(AB2->AB1))
-    +:(Obj,Obj)->Obj
+    +:(Obj,Obj)-> with Obj
     default
@@ -90,3 +90,3 @@
            (ab1,ab2,+)
-        (A:Obj)+(B:Obj):Obj ==
+        (A:Obj)+(B:Obj): with Obj ==
             (AB:Obj,ia:A->AB,ib:B->AB,product:(X:Obj)->(A->X,B->X)->(AB->X))
== CoProduct(A,B)
@@ -99,5 +99,5 @@
     Product:(A:Obj,n:Integer)   ->
(Prod:Obj,Integer->(Prod->A),(X:Obj)->(Tuple (X->A))->(X->Prod))
-    ^:(Obj,Integer) -> Obj
+    ^:(Obj,Integer) -> with Obj
     default
-        (A:Obj)^(n:Integer):Obj ==
+        (A:Obj)^(n:Integer): with Obj ==
            (Prod:Obj,project:Integer->(Prod->A),product:(X:Obj)->(Tuple
(X->A))->(X->Prod)) == Product(A,n)
@@ -110,5 +110,5 @@
     CoProduct:(A:Obj,n:Integer) -> (
Sum:Obj,Integer->(A->Sum),(X:Obj)->(Tuple (A->X))->(Sum->X))
-    ..:(Obj,Integer) -> Obj
+    ..:(Obj,Integer) -> with Obj
     default
-        (A:Obj)..(n:Integer):Obj ==
+        (A:Obj)..(n:Integer): with Obj ==
            (Sum:Obj,insert:Integer->(A->Sum),sum:(X:Obj)->(Tuple
(A->X))->(Sum->X)) == CoProduct(A,n)
address@hidden:~/aldor-src/aldor/install/aldor#

----

Regards,
Bill Page.

On 11/8/07, Bill Page <address@hidden> wrote:
Ralf,

I think the problem here is that the new version of the Aldor compiler
needs a little more help just be reassured that you really are writing
a function that returns a domain. The empty 'with {}' clause seems to
do the trick.

Here is a patch to 'Categories.as' that allows it to compile... but I
have not yet compiled the rest so I am not 100% sure that the end
result will be ok. (Also attached as a file.):






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