🚀 go-pugleaf

In article  <28190@dime.cs.umass.edu> victor yodaiken writes:

]Mathematical literature is full of statements of the form
]"let X be a finite set", let $f: S x Y -> Z$", "k ranges over
]the naturals", etc. etc., these are type declarations.

Come on, people.  I didn't say that you never see anything like
declarations in mathematics.  All I said is that you can often do
without them.  The same is true of dynamically typed languages:
sometimes you have to check the types of variables, but often you can
do without it.  And in either case, "doing without it" is neither
sloppy nor ambiguous.  If it is ambiguous then you can't do without
it in the first place; and "sloppy" is in the eye of the beholder.

]	The collection of all morphisms in a category A will 
]	bedenoted by AR(A) ("arrows of A"). We shall sometimes use the
]	symbols "f \in A(A)" to mean that f is a morphism of A ...

That isn't a declaration, it's a comment.  In other words, no formal
notation is being used to describe the type, an English description is
being given.  If you want something like a declaration in math, try

  f : A -> B
--
					David Gudeman
gudeman@cs.arizona.edu
noao!arizona!gudeman