[Haskell-cafe] Free theorems for dependent types?

Joe Fredette jfredett at gmail.com
Sun May 17 22:51:38 EDT 2009

This word has piqued my interest, I've hear it tossed around the 
community quite a bit, but never fully understood what it meant. What 
exactly is a 'free theorem'?

Eugene Kirpichov wrote:
> Hello,
> Is there any research on applying free theorems / parametricity to
> type systems more complex than System F; namely, Fomega, or calculus
> of constructions and alike?
> This seems very promising to me for the following reason: Take the
> free theorem for 'sort::(a->a->Bool)->[a]->[a]'. The theorem could
> possibly be a lot more powerful if there were a way to encode in the
> type of 'sort' that it accepts a reflexive transitive antisymmetric
> predicate, but the only way to express that is with dependent types.
> Looks like the only thing one needs to add to System F is the
> relational translation rule for a dependent product; but I haven't
> tried doing it myself.
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