Specific denotations for pure types

[Conal Elliott]

Oh!  I think there's a misunderstanding here.  I'm not talking about
MachineInfo as visible in the types.  I'm talking about Int itself having a
MachineInfo-dependent semantic model (something like MachineInfo -> Z, where
MachineInfo, ->, and Z are *semantic* types, not Haskell types).

Making my question more specific: Can (>) on Int be given a compositional
semantics, i.e. a semantics as [[Int]] -> [[Int]] -> [[Bool]], where [[Int]]
= MachineInfo -> Z and [[Bool]] = {bottom,false,true} (with the usual
ordering)?

  - Conal

On Mon, Mar 23, 2009 at 9:34 AM, Jake McArthur <jake at pikewerks.com> wrote:

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> Conal Elliott wrote:
> | The question I'm asking is this: Assuming compositional semantics, can
> | [[Bool]] be this simple & customary three-value domain in the presence
> | of an implementation-dependent [[Int]] (given that Int expressions can
> | play a non-trivial role in Bool expressions)?
>
> As I understand it, your question might be reworded like this: If we can
> compose values of type (MachineInfo -> Int) to create a value of type
> (MachineInfo -> Bool), does that mean Bool is dependent on MachineInfo?
> To simplify the question, I would like to rephrase it further to ask
> whether the ability to construct any value of type (MachineInfo -> Bool)
> means that Bool is dependent on MachineInfo. My (uneducated) reaction is
> that this does not mean that Bool is dependent on MachineInfo any more
> than the ability to construct a value of type (forall a. a -> Bool)
> means that Bool is dependent on everything.
>
> - - Jake
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