In a domain and in categories referenced in a domain the notation %
represents "this domain" (or self in some programming languages). So
we commonly write for example:
with
f: (%,%) -> %
to indicate a function f which takes a pair of values in this domain
and returns a value in this same domain - whatever domain we happen
to be talking about in this context.
But what if we are interested in the domain as a functor? Suppose I
was writing an "endofunctor" domain constructor like Set and I
wanted to treat constructions like Set Set R, i.e. sets of sets as
something special. E.g.
\begin{spad}
)abbrev domain MYSET MySet?
MySet?(T:SetCategory?): SetAggregate?(T) with
finiteAggregate
join: MySet? MySet? T -> MySet? T
== add
Rep == List T
--rep(x:%):Rep == x pretend Rep
--per(x:Rep):% == x pretend %
Rep2 := List List T
rep2(x:MySet? MySet? T):Rep2 == x pretend Rep2
per2(x:Rep2):MySet? MySet? T == x pretend MySet? MySet? T
coerce(x:%):OutputForm? == brace [i::OutputForm for i in rep x]?
x = y == rep(x) = rep(y)
construct(x) == per removeDuplicates(x)$Rep
parts(x:%):List T == rep x
join x == construct concat rep2 x
\end{spad}
\begin{axiom}
m1:MySet?(Integer) := construct([1,2,3]?)$MySet?(Integer)
m2:MySet?(Integer) := construct([4,5,6]?)$MySet?(Integer)
ml:=[m1,m2]?
mm:MySet? MySet? Integer := construct([m1,m2]?)$MySet?(MySet?(Integer))
join mm
\end{axiom}
Some or all expressions may not have rendered properly,
because Axiom returned the following error:
Error: export FRICAS=/usr/local/lib/open-axiom/x86_64-unknown-linux-gnu/1.4.0-2011-02-20; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=/usr/local/lib/open-axiom/x86_64-unknown-linux-gnu/1.4.0-2011-02-20/lib; LANG=en_US.UTF-8 $FRICAS/bin/FRICASsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7590631627605034976-25px.axm
/bin/sh: /usr/local/lib/open-axiom/x86_64-unknown-linux-gnu/1.4.0-2011-02-20/bin/FRICASsys: not found
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$
l.140 \end{spad}
\newpage
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(see the transcript file for additional information)
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