Re: [isabelle] map, difference, image, etc.
On Tue, 22 Apr 2014, Christian Sternagel wrote:
the type classes of Isabelle are restricted to a single type parameter and do
not support constructor classes (i.e., type classes of higher kind).
The latter restriction is the reason why your proposal cannot be implemented
using Isabelle's type classes.
If it is just about syntax, adhoc overloading would work. However, this can
lead to many situations where explicit type constraints have to be added in
order to avoid ambiguity. So I wouldn't go for that.
On 04/22/2014 12:23 PM, John Wickerson wrote:
I recently improved my life quite a lot by assigning an infix operator
symbol to the ‘map’ function. Expressions like “map (f x) (g y)” could
become expressions like “f x ``` g y” -- much more readable without all
those parentheses. As you can see, I chose (```) as my infix operator.
But it got me thinking: why can’t I just use (`) instead? That is, the
same symbol as is used for the image of a set. “Map” and “image” are
pretty similar functions, after all:
map : (‘a => ‘b) => ‘a list => ‘b list
image: (‘a => ‘b) => ‘a set => ‘b set
There’s no problem with (+) being polymorphic over any sort of number, so
why can’t (`) be polymorphic over any sort of “collection”? And while
we’re at it, we could make the set-minus operator (-) polymorphic too, so
that when X and Y are of type “list”, then “X-Y” is the list obtained by
removing from X all elements in Y.
Just a side-remark: Scala has this insanely complex type-system that can
do everything, if you know how it works. There are probably only a handful
of people who do. E.g. see the discussion about "map" in the Scala
The type-system of HOL is much less exciting, just a reduced version of
the ML type-system, with the addition of plain-old type classes from
original Haskell, before that became very complex in other ways.
Recently, I am often glad about that refreshing simplicity of both HOL and
ML. As can be seen on the isabelle-dev thread "Unresponsive
http://www.mail-archive.com/isabelle-dev at mailbroy.informatik.tu-muenchen.de/msg05115.html
the extremely compact Scala notation can lead to bad surprises, when
unintended combinators are added by the compiler, and the critical
difference is hardly seen in the source text.
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