Chapter 2.1 (after 2.1.1) tells us: >> The most basic category is Type. It denotes the class of all domains and subdomains. Note carefully that Type does not denote the class of all types. The type of all categories is Category. The type of Type itself is undefined. <<
This might partially explain your first consideration. Can we say that each category is an extension of Type? If so, then I don't understand why the type of Type itself shall be undefined. Must be 'higher logic' in the colloquial sense :) Am 31.10.2016 um 15:51 schrieb Bill Page: > On 31 October 2016 at 09:21, Bill Page <[email protected]> wrote: >> ... >> Yes, saying that 'Category' has no type, i.e. that 'typeOf(typeOf >> Type)' should return 'Failed' seems more sensible to me. In that case >> what FriCAS actually does is worse than what it appeared to be when >> typing 'typeOf(Category)' in the interpreter. >> >> But I also wonder why 'typeOf(Integer)' is 'Type', i.e. that specific >> category 'Type'. Why not 'Ring' or some other category that 'Integer' >> satisfies? > > Actually, thinking about this again, if 'typeOf' can return a category > as the type of some domain why doesn't 'typeOf(Integer)' return > exactly the category that appears to the right of the : when 'Integer' > is defined? > > Integer : Join(IntegerNumberSystem, LinearlyExplicitOver Integer, > PolynomialFactorizationExplicit, ConvertibleTo String, > OpenMath, Canonical, canonicalsClosed) with > random : % -> % > ++ random(n) returns a random integer from 0 to \spad{n-1}. > > Yes, this might be a bit awkward except perhaps when used programmaticaly as > in > > (1) -> Float has typeOf(Integer) > > (1) true > > where the current result seems of little value. > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
