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Everyone is allowed to try out SPAD by editing this page. Don't be affraid to destroy anything. The purpose of this page is exactly to give a place for everyone to experiment.

Just hit the "edit" link in the upper right corner.

spad
)abbrev category MYMON MyMonoid
MyMonoid: Category == with
    1: %
    _*: (%, %) -> %
rep x ==> (x@%) pretend Rep per x ==> (x@Rep) pretend %
)abbrev domain MYFUN MyFun MyFun(S: SetCategory): MyMonoid with coerce: (S -> S) -> % coerce: % -> (S -> S) == add Rep ==> S -> S coerce(f: S -> S): % == per f coerce(x: %): S -> S == rep x 1: % == per((s: S): S +-> s) ((x: %) * (y: %)): % == per( (s: S): S +-> (rep x)(rep y)s )
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5443222399567089399-25px001.spad
      using old system compiler.
   MYMON abbreviates category MyMonoid 
------------------------------------------------------------------------
   initializing NRLIB MYMON for MyMonoid 
   compiling into NRLIB MYMON 
;;; *** |MyMonoid| REDEFINED Time: 0 SEC.
finalizing NRLIB MYMON Processing MyMonoid for Browser database: --->-->MyMonoid(constructor): Not documented!!!! --->-->MyMonoid(((One) (%) constant)): Not documented!!!! --->-->MyMonoid((* (% % %))): Not documented!!!! --->-->MyMonoid(): Missing Description ; compiling file "/var/aw/var/LatexWiki/MYMON.NRLIB/MYMON.lsp" (written 14 FEB 2014 12:52:37 PM):
; /var/aw/var/LatexWiki/MYMON.NRLIB/MYMON.fasl written ; compilation finished in 0:00:00.005 ------------------------------------------------------------------------ MyMonoid is now explicitly exposed in frame initial MyMonoid will be automatically loaded when needed from /var/aw/var/LatexWiki/MYMON.NRLIB/MYMON
MYFUN abbreviates domain MyFun ------------------------------------------------------------------------ initializing NRLIB MYFUN for MyFun compiling into NRLIB MYFUN processing macro definition Rep ==> S -> S compiling exported coerce : S -> S -> $ MYFUN;coerce;M$;1 is replaced by f Time: 0 SEC.
compiling exported coerce : $ -> S -> S MYFUN;coerce;$M;2 is replaced by x Time: 0 SEC.
compiling exported One : () -> $ Time: 0 SEC.
compiling exported * : ($,$) -> $ Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |MyFun| REDEFINED
;;; *** |MyFun| REDEFINED Time: 0.01 SEC.
Cumulative Statistics for Constructor MyFun Time: 0.01 seconds
finalizing NRLIB MYFUN Processing MyFun for Browser database: --->-->MyFun(constructor): Not documented!!!! --->-->MyFun(((One) (%) constant)): Not documented!!!! --->-->MyFun((* (% % %))): Not documented!!!! --->-->MyFun(constructor): Not documented!!!! --->-->MyFun((coerce (% (Mapping S S)))): Not documented!!!! --->-->MyFun((coerce ((Mapping S S) %))): Not documented!!!! --->-->MyFun(): Missing Description ; compiling file "/var/aw/var/LatexWiki/MYFUN.NRLIB/MYFUN.lsp" (written 14 FEB 2014 12:52:38 PM):
; /var/aw/var/LatexWiki/MYFUN.NRLIB/MYFUN.fasl written ; compilation finished in 0:00:00.018 ------------------------------------------------------------------------ MyFun is now explicitly exposed in frame initial MyFun will be automatically loaded when needed from /var/aw/var/LatexWiki/MYFUN.NRLIB/MYFUN

fricas
I ==> Integer
Type: Void
fricas
II ==> I -> I
Type: Void
fricas
MI ==> MyFun I
Type: Void
fricas
inc(i: I): I == i+1
Function declaration inc : Integer -> Integer has been added to workspace.
Type: Void
fricas
double(i: I): I == 2*i
Function declaration double : Integer -> Integer has been added to workspace.
Type: Void
fricas
minc := inc :: MI
fricas
Compiling function inc with type Integer -> Integer 
LISP output: (#<FUNCTION |*1;inc;1;initial|>)
Type: MyFun?(Integer)
fricas
mdouble := double :: MI
fricas
Compiling function double with type Integer -> Integer 
LISP output: (#<FUNCTION |*1;double;1;initial|>)
Type: MyFun?(Integer)
fricas
f := (mdouble * minc) :: II

\label{eq1}\mbox{theMap (...)}(1)
Type: (Integer -> Integer)
fricas
g := (minc * mdouble) :: II

\label{eq2}\mbox{theMap (...)}(2)
Type: (Integer -> Integer)
fricas
f 1

\label{eq3}4(3)
fricas
g 1

\label{eq4}3(4)




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