[isabelle-dev] Problem with code generation for non-executable types

[Andreas Lochbihler]

Hi Johannes,

>      Then the dictionary construction for type constructors does not
>      work in ML! The type signature would be the following:
>
>        val test_prod : ('a * 'b) filter
>
>      Which apparently is not allow in ML.
This is the famous value restriction (which I also regularly run into). The standard 
solution is to add a unit closure, because functions may be polymorphic in ML.

Andreas

> 2.  If your type class contains non-computable data, i.e.
>
>        instantiation bool :: test_class
>        begin
>
>        definition "test = if P = NP then top else bot"
>
>        instance proof qed
>        end
>
>      You get a non-terminating program at the time point when the
>      dictionary for bool :: test_class is constructed. When the
>      code equation is hidden with [code del] one gets a exception!
>
> 3.  Our current solution is to introduce code_datatype Abs_filter
>      Rep_filter [code del] and define for each uniformity:
>
>        uniformity = Abs_filter (%P. Code.abort (STR''FAILED'') (Rep_filter test P))
>
>      @Florian: is the an alternative solution?
>
>
> - Johannes
>
> PS: Here is a short, concrete example:
>
> theory Scratch
>    imports Complex_Main
> begin
>
> class test_class =
>    fixes test :: "'a filter"
>
> instantiation prod :: (test_class, test_class) test_class
> begin
>
> definition [code del]: "test = (test ×⇩F test :: ('a × 'b) filter)"
>
> instance proof qed
> end
>
> instantiation unit :: test_class
> begin
>
> definition [code del]:
>    "(test :: unit filter) = bot"
>
> instance proof qed
> end
>
> definition "test2 (x::'a::test_class) = (Suc 0)"
> definition "test3 = test2 ((), ())"
>
> value [code] "test3"
>
> section ‹Solution›
>
> code_datatype Abs_filter
> declare [[code abort: Rep_filter]]
>
> lemma test_Abort: "test = Abs_filter (λP. Code.abort (STR ''test'')
> (λx. Rep_filter test P))"
>    unfolding Code.abort_def Rep_filter_inverse ..
>
> declare test_Abort[where 'a="'a::test_class * 'b :: test_class", code]
> declare test_Abort[where 'a=unit, code]
>
> end
>
>
>
>
>
>
> Am Freitag, den 08.01.2016, 09:56 +0100 schrieb Johannes Hölzl:
>> Hi,
>>
>> I want to introduce uniform spaces in HOL, for this I need to
>> introduce
>> a type class of the form (see the attached bundle):
>>
>>    class uniformity =
>>      fixes uniformity :: "('a × 'a) filter"
>>
>> Note that uniformity is a filter and not a function.
>>
>> which sits between topological spaces and metric spaces, i.e. every
>> metric type is also in the following type classes:
>>
>>    class open_uniformity = "open" + uniformity +
>>      assumes open_uniformity: "⋀U. open U ⟷ (∀x∈U. eventually (λ(x',
>> y). x' = x ⟶ y ∈ U) uniformity)"
>>
>>    class uniformity_dist = dist + uniformity +
>>      assumes uniformity_dist: "uniformity = (INF e:{0 <..}. principal
>> {(x, y). dist x y < e})"
>>
>> Everything works fine until Affinite_Arithmetic, there in
>> Intersection.thy the code generation fails with the following ML
>> error:
>>
>>    Error: Type mismatch in type constraint.
>>       Value: {uniformity = uniformity_proda} : {uniformity: 'a}
>>       Constraint: ('a * 'b) uniformity
>>       Reason:
>>          Can't unify 'a to (('a * 'b) * ('a * 'b)) filter
>>             (Type variable is free in surrounding scope)
>>    {uniformity = uniformity_proda} : ('a * 'b) uniformity
>>    At (line 1619 of "generated code")
>>    Exception- Fail "Static Errors" raised
>>
>> I assume this is a strange interaction btw code_abort and the fact
>> that
>> uniformity is a filter (datatype 'a filter = _EMPTY) and not a
>> function.
>>
>> Does anybody know how to avoid such kind of errors? Do I need to
>> sprinkle more [code del] or code_abort annotations?
>>
>>   - Johannes
>>
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>> le-dev
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