Specific denotations for pure types
Conal Elliott
conal at conal.net
Mon Mar 23 12:42:16 EDT 2009
And my own answer is "no". Otherwise, dodgy would have value true, false,
or bottom, rather than the value true-or-false-depending-on-the-machine.
On Mon, Mar 23, 2009 at 9:39 AM, Conal Elliott <conal at conal.net> wrote:
> 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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>
>
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