Specific denotations for pure types

Achim Schneider barsoap at web.de
Fri Mar 20 20:13:46 EDT 2009

Conal Elliott <conal at conal.net> wrote:

> Consider
>     big :: Int
>     big = 2147483647
>     dodgy :: Bool
>     dodgy = big + 1 > big
>     oops :: ()
>     oops =  if dodgy then () else undefined
> Assuming compositional semantics, the meaning of oops depends on the
> meaning of dodgy, which depends on the meaning of big+1, which is
> implementation-dependent.
yes, but dodgy isn't Bool, it's _a_ Bool. You're worried about the
semantics of (>) :: Int -> Int -> Bool, (+) :: Int -> Int -> Int and
that forall n > 0 . x + n > x doesn't hold for Int. There are
infinitely many ways to get a Bool out of things that don't happen to
be Int (not to mention infinitely many ways to get a Bool out of an
Int in an architecture-independent manner), which makes me think it's
quite err... fundamentalistic to generalise that forall Bool .
MachineInfo -> Bool. In fact, if you can prove for a certain Bool that
MachineInfo -> ThatBool, you (most likely) just found a bug in the

Shortly put: All that dodginess is fine with me, as long as it isn't
the only way. Defaulting to machine-independent semantics at the
expense of performance would be a most sensible thing, and Conal
seems to think _way_ too abstractly.

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