[Axiom-developer] [Sanbox Functional Addition] (new)

[Bill Page]

Changes 
http://page.axiom-developer.org/zope/mathaction/SanboxFunctionalAddition/diff
--
This library code is based directly on MappingPackage3 in
'mappkg.spad.pamphlet'

\begin{axiom}
)abbrev package MAPHAC2X MapPackInternalHac2x
++ Description:
++ This package defines the function to be returned by
++ functional operator below.

MapPackInternalHac2x(A: SetCategory, B: Ring):
  MPcat == MPdef where

    MPcat == with
        addit:  (A->B, A->B, A) -> B
          ++\spad{comp(f,g,x)} is \spad{f(g x)}.

    MPdef == add
        addit(g,h,x)  == ((g x) + (h x))$B
\end{axiom}


\begin{axiom}
)abbrev package MAPPK2X MappingPackage2x
++ Description: various Currying operations.
MappingPackage2x(A:SetCategory, B:Ring):
  MPcat == MPdef where

    MPcat ==  with

        "+":   (A->B, A->B) -> (A->B)
          ++\spad{f+g} is the function \spad{h}
          ++ such that \spad{h x = f x + g x}.

    MPdef == add


        MapPackInternalHac2x(A, B)

        fab:  A -> B

        -- Functional addition
        fab+fab == addit(fab,fab,#1)

\end{axiom}

\begin{axiom}
f := (x:INT):INT +-> 3*x
g := (x:INT):INT +-> 2*x+3
(f+g)(3)
\end{axiom}




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forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden