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

[Bill Page]

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.):

address@hidden:~/aldor-src/aldor/install/aldor# aldor Categories.as
address@hidden:~/aldor-src/aldor/install/aldor# diff -au Categoris.as_orig
Categories.as
diff: Categoris.as_orig: No such file or directory
address@hidden:~/aldor-src/aldor/install/aldor# diff -au Categories.as_orig
Categories.as
--- Categories.as_orig  2007-11-08 10:09:11.000000000 -0800
+++ Categories.as       2007-11-08 10:11:54.000000000 -0800
@@ -64,14 +64,14 @@
 define Product(Obj:Category):Category == with
     Product: (A:Obj,B:Obj) -> ( AB:Obj, AB->A, AB->B,
(X:Obj)->(X->A,X->B)->(X->AB) )
     Product: (A1:Obj,B1:Obj,  A2:Obj,B2:Obj) ->
(AB1:Obj,AB2:Obj,(A1->A2,B1->B2)->(AB1->AB2))
-    *:(Obj,Obj)->Obj
+    *:(Obj,Obj)->Obj with {}
     default
         
Product(A1:Obj,B1:Obj,A2:Obj,B2:Obj):(AB1:Obj,AB2:Obj,(A1->A2,B1->B2)->(AB1->AB2))
==
            (ab1:Obj,pa1:ab1->A1,pb1:ab1->B1, product1: (X:Obj) ->
(X->A1,X->B1) -> (X->ab1)) == Product(A1,B1)
            (ab2:Obj,pa2:ab2->A2,pb2:ab2->B2, product2: (X:Obj) ->
(X->A2,X->B2) -> (X->ab2)) == Product(A2,B2)
            (f:A1->A2)*(g:B1->B2):(ab1->ab2) == product2 ( ab1 )(
(x:ab1):A2 +-> f pa1 x, (x:ab1):B2 +-> g pb1 x )
            (ab1,ab2,*)
-        (A:Obj)*(B:Obj):Obj ==
+        (A:Obj)*(B:Obj):Obj with {} ==
             (AB:Obj,pa:AB->A,pb:AB->B,product:(X:Obj)->(X->A,X->B)->(X->AB))
== Product(A,B)
             AB add

@@ -81,14 +81,14 @@
 define CoProduct(Obj:Category):Category == with
     CoProduct: (A:Obj,B:Obj) -> ( AB:Obj, A->AB, B->AB,
(X:Obj)->(A->X,B->X)->(AB->X) )
     CoProduct: (A1:Obj,B1:Obj, A2:Obj,B2:Obj) ->
(AB1:Obj,AB2:Obj,(A2->A1,B2->B1)->(AB2->AB1))
-    +:(Obj,Obj)->Obj
+    +:(Obj,Obj)->Obj with {}
     default
         
CoProduct(A1:Obj,B1:Obj,A2:Obj,B2:Obj):(AB1:Obj,AB2:Obj,(A2->A1,B2->B1)->(AB2->AB1))
==
            (ab1:Obj,ia1:A1->ab1,ib1:B1->ab1, sum1: (X:Obj) ->
(A1->X,B1->X) -> (ab1->X)) == CoProduct(A1,B1)
            (ab2:Obj,ia2:A2->ab2,ib2:B2->ab2, sum2: (X:Obj) ->
(A2->X,B2->X) -> (ab2->X)) == CoProduct(A2,B2)
            (f:A2->A1)+(g:B2->B1):(ab2->ab1) == sum2 ( ab1 ) (
(x:A2):ab1 +-> ia1 f x, (x:B2):ab1 +-> ib1 g x )
            (ab1,ab2,+)
-        (A:Obj)+(B:Obj):Obj ==
+        (A:Obj)+(B:Obj):Obj with {} ==
             (AB:Obj,ia:A->AB,ib:B->AB,product:(X:Obj)->(A->X,B->X)->(AB->X))
== CoProduct(A,B)
             AB add

@@ -97,9 +97,9 @@
 +++
 define MultiProduct(Obj:Category):Category == with
     Product:(A:Obj,n:Integer)   ->
(Prod:Obj,Integer->(Prod->A),(X:Obj)->(Tuple (X->A))->(X->Prod))
-    ^:(Obj,Integer) -> Obj
+    ^:(Obj,Integer) -> Obj with {}
     default
-        (A:Obj)^(n:Integer):Obj ==
+        (A:Obj)^(n:Integer):Obj with {} ==
            (Prod:Obj,project:Integer->(Prod->A),product:(X:Obj)->(Tuple
(X->A))->(X->Prod)) == Product(A,n)
            Prod add

@@ -108,9 +108,9 @@
 +++
 define CoMultiProduct(Obj:Category):Category == with
     CoProduct:(A:Obj,n:Integer) -> (
Sum:Obj,Integer->(A->Sum),(X:Obj)->(Tuple (A->X))->(Sum->X))
-    ..:(Obj,Integer) -> Obj
+    ..:(Obj,Integer) -> Obj with {}
     default
-        (A:Obj)..(n:Integer):Obj ==
+        (A:Obj)..(n:Integer):Obj with {} ==
            (Sum:Obj,insert:Integer->(A->Sum),sum:(X:Obj)->(Tuple
(A->X))->(Sum->X)) == CoProduct(A,n)
            Sum add

address@hidden:~/aldor-src/aldor/install/aldor#

--------

Regards,
Bill Page.


On 11/8/07, Ralf Hemmecke <address@hidden> wrote:
> Thank you Saul,
>
> First, thank you very much for your code. Under which license is it?
> Public domain, mBSD, GPL, ... ?
>
> Unfortunately, the compiler has changed a bit.
>
> woodpecker:~/scratch/Youssef/london>aldor Basics.as
> woodpecker:~/scratch/Youssef/london>aldor Categories.as
>
> #1 (Error) There are 2 meanings for the operator `+'.
>         Meaning 1: (Obj, Obj) -> Obj
>         Meaning 2: (A: Obj, B: Obj) -> (
>                  Obj with
>                ...
> #2 (Error) There are 2 meanings for the operator `..'.
>         Meaning 1: (Obj, Integer) -> Obj
>         Meaning 2: (A: Obj, n: Integer) -> (
>                  Obj with
>            ...
> #3 (Error) There are 2 meanings for the operator `*'.
>         Meaning 1: (Obj, Obj) -> Obj
>         Meaning 2: (A: Obj, B: Obj) -> (
>                  Obj with
>                ...
> #4 (Error) There are 2 meanings for the operator `^'.
>         Meaning 1: (Obj, Integer) -> Obj
>         Meaning 2: (A: Obj, n: Integer) -> (
>                  Obj with
>            ...
>
> In fact, I don't quite know how to resolve that problem.
> Actually, I wonder why I don't see any line numbers here.
>
> > I'm attaching my code from the time (~3k lines) which includes the
> > bits in the paper.  It all actually at least used to compile and work
> > in 2001.
>
> I guess the commands "ao" and "ai" that I find in "compile" and
> "exercise" mean something like
>
> alias ao=aldor -fao
> alias ai=aldor -G interp
>
> Or did you use other scripts?
>
> >      One of the things that encouraged me at the time was thinking
> > about the simplest Aldor category in the mathematical sense: objects
> > of the category are Aldor domains satisfying
> >
> > Domain: Category == with  # no signatures (my favorite base category
> > for a library)
>
> I wonder why you called it "Domain" and not something else? In some way
> you are right
>
> A: Domain
>
> then says that A is a domain. Sounds not too bad.
>
> Ralf
>
> _______________________________________________
> Aldor-l mailing list
> address@hidden
> http://aldor.org/mailman/listinfo/aldor-l_aldor.org
>

Categories.patch
Description: Binary data