Jean-Philippe Bernardy schrieb:
On Sun, Jun 20, 2010 at 12:47 PM, Janis Voigtländer
<j...@informatik.uni-bonn.de> wrote:
Sebastian Fischer schrieb:
Hello,
I tried to use the free theorem generator in order to check whether the
only values of type `(Bool -> a) -> a` are `($True)` and `($False)`.
Did you manage to do this now?
Driven by Andreas' comment about what he considers "free theorems",
statements like the above about an exhaustive enumeration of possible
values of a given type, like
- ($True) and ($False) for type (Bool -> a) -> a
- id for type a -> a
In any case, for additional possibilities like "exhaustive value
enumeration (where possible at all)", I don't yet have a generic
strategy.
Using the main result of our ESOP paper (Testing Polymorphic Properties),
you can get there for a large class of input types.
http://publications.lib.chalmers.se/cpl/record/index.xsql?pubid=99387
Yes, kind of. I had this in mind when asking Andreas for a kind of
characterization akin to his "f :: a -> a can only be identity" example,
but for the type [a] -> [a]. The point being that one doesn't get a
finite enumeration of possible values, except in very few cases.
BTW, can one get a characterization from your results, establishing
*when* the class of possible (semantic) values of a type is finite?
Ciao,
Janis.
--
Jun.-Prof. Dr. Janis Voigtländer
http://www.iai.uni-bonn.de/~jv/
mailto:j...@iai.uni-bonn.de
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