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	Limits and Colimits
SandBoxEqualizerInOpenAxiom ←	↑

SandBoxProduct

Edit detail for SandBoxProduct revision 1 of 1

	1
Editor: Bill Page Time: 2017/10/14 16:50:18 GMT+0
Note:

changed:
-
\begin{spad}
)abbrev domain PRD2 Product2
rep(x) ==> x @ % pretend Rep
per(x) ==> x @ Rep pretend %
Product2(X:SetCategory,Y:SetCategory): with
    construct: (X,Y) -> %
    coerce: % -> OutputForm
    product: (A:Type, A->X,A->Y) -> (A->%)
    project1: (%) -> X
    project2: (%) -> Y
  == add
    Rep := Record(a:X,b:Y)
    import from Rep
    --
    construct(x:X,y:Y):% == per [x,y]
    coerce(x:%):OutputForm ==
      bracket([coerce(rep(x).a)$X, coerce(rep(x).b)$Y]$List(OutputForm))
    project1(x:%):X == rep(x).a
    project2(y:%):Y == rep(y).b
    product(A:Type,f:A->X,g:A->Y):(A->%) ==
       (x:A):% +-> per [f(x),g(x)]
\end{spad}

fricas

(1) -> <spad>

fricas

)abbrev domain PRD2 Product2
rep(x) ==> x @ % pretend Rep
per(x) ==> x @ Rep pretend %
Product2(X:SetCategory,Y:SetCategory): with
    construct: (X,Y) -> %
    coerce: % -> OutputForm
    product: (A:Type, A->X,A->Y) -> (A->%)
    project1: (%) -> X
    project2: (%) -> Y
  == add
    Rep := Record(a:X,b:Y)
    import from Rep
    --
    construct(x:X,y:Y):% == per [x,y]
    coerce(x:%):OutputForm ==
      bracket([coerce(rep(x).a)$X, coerce(rep(x).b)$Y]$List(OutputForm))
    project1(x:%):X == rep(x).a
    project2(y:%):Y == rep(y).b
    product(A:Type,f:A->X,g:A->Y):(A->%) ==
       (x:A):% +-> per [f(x),g(x)]</spad>

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1649910186997427983-25px001.spad
      using old system compiler.
   PRD2 abbreviates domain Product2 
------------------------------------------------------------------------
   initializing NRLIB PRD2 for Product2 
   compiling into NRLIB PRD2 
   importing Rep
   compiling exported construct : (X,Y) -> %
Time: 0 SEC.

   compiling exported coerce : % -> OutputForm
Time: 0 SEC.

   compiling exported project1 : % -> X
      PRD2;project1;%X;3 is replaced by QCAR 
Time: 0 SEC.

   compiling exported project2 : % -> Y
      PRD2;project2;%Y;4 is replaced by QCDR 
Time: 0 SEC.

   compiling exported product : (Type,A -> X,A -> Y) -> A -> %
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Product2| REDEFINED

;;;     ***       |Product2| REDEFINED
Time: 0 SEC.

   Warnings: 
      [1] construct: pretend  -- should replace by @
      [2] coerce: pretendRep -- should replace by @
      [3] project1: pretendRep -- should replace by @
      [4] project2: pretendRep -- should replace by @
      [5] product: pretend  -- should replace by @

   Cumulative Statistics for Constructor Product2
      Time: 0 seconds

   finalizing NRLIB PRD2 
   Processing Product2 for Browser database:
--->-->Product2(constructor): Not documented!!!!
--->-->Product2((construct (% X Y))): Not documented!!!!
--->-->Product2((coerce ((OutputForm) %))): Not documented!!!!
--->-->Product2((product ((Mapping % A) (Type) (Mapping X A) (Mapping Y A)))): Not documented!!!!
--->-->Product2((project1 (X %))): Not documented!!!!
--->-->Product2((project2 (Y %))): Not documented!!!!
--->-->Product2(): Missing Description
; compiling file "/var/aw/var/LatexWiki/PRD2.NRLIB/PRD2.lsp" (written 12 MAY 2025 04:47:55 AM):

; wrote /var/aw/var/LatexWiki/PRD2.NRLIB/PRD2.fasl
; compilation finished in 0:00:00.012
------------------------------------------------------------------------
   Product2 is now explicitly exposed in frame initial 
   Product2 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/PRD2.NRLIB/PRD2