[Agda] rewrite on the right?
Martin Stone Davis
martin.stone.davis at gmail.com
Fri Feb 19 01:21:41 CET 2016
My "Reright" is buggy-by-design. I'm working on a much better version. More
to come.
--
Martin Stone Davis
Postal/Residential:
1223 Ferry St
Apt 5
Eugene, OR 97401
Talk / Text / Voicemail: (310) 699-3578 <3106993578>
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Website: martinstonedavis.com
On Fri, Feb 12, 2016 at 11:43 PM, Martin Stone Davis <
martin.stone.davis at gmail.com> wrote:
> Thanks to all for those suggestions. I wound-up writing it from scratch,
> which was helpful in my learning reflection in agda.
>
> "Reright" is now available on my fork
> <https://github.com/m0davis/agda-prelude> of agda-prelude. Some (very
> messy) sample code is here
> <https://github.com/m0davis/agda-prelude/blob/master/test/Reright.agda>.
> Due to issue #1833 <https://github.com/agda/agda/issues/1833>, a
> parameter needs to be supplied to the macro, counting (roughly speaking)
> the number of arguments on the lhs.
>
> --
> Martin Stone Davis
>
> Postal/Residential:
> 1223 Ferry St
> Apt 5
> Eugene, OR 97401
> Talk / Text / Voicemail: (310) 699-3578 <3106993578>
> Electronic Mail: martin.stone.davis at gmail.com
> Website: martinstonedavis.com
>
> On Fri, Jan 22, 2016 at 4:51 AM, Victor Miraldo <victor.cacciari at gmail.com
> > wrote:
>
>> Hello,
>>
>> I did implement a library for doing exactly that as my Msc thesis. My
>> code is not up-to-date with the new API for reflection aswell,
>> and, in fact, this new API provides a lot of interesting oportunities to
>> improve it. If you're using a "not so recent" version of Agda
>> it might be worth to check it out.
>>
>> https://github.com/VictorCMiraldo/agda-rw
>>
>> Cheers,
>> Victor
>>
>> On Wed, Jan 20, 2016 at 6:59 PM, Jesper Cockx <Jesper at sikanda.be> wrote:
>>
>>> I implemented a simple rewrite tactic using the reflection in Agda back
>>> in 2014, see https://lists.chalmers.se/pipermail/agda/2014/007032.html.
>>> The code is not up-to-date with the new reflection API (and you could now
>>> probably make something that has a much nicer syntax anyway, using the new
>>> macro system) but it shows that there is nothing preventing you to do this
>>> using reflection. So I would say there is no need to implement something as
>>> a language extension if it is already possible as a library.
>>>
>>> cheers,
>>> Jesper
>>>
>>> On Wed, Jan 20, 2016 at 6:33 PM, Andrea Vezzosi <sanzhiyan at gmail.com>
>>> wrote:
>>>
>>>> Yes, having rewrite on the right would be very nice.
>>>>
>>>> It'd have to generate an helper like you did manually, that's how
>>>> rewrite on the left is implemented too, so it might not make sense as
>>>> an expression because it mangles the context, maybe it can have the
>>>> same status as the macros of reflection.
>>>>
>>>> In your case you cannot really get away with just a subst, however you
>>>> can get somewhere if you have proven that get commutes with subst, so
>>>> you can fill the open goal here:
>>>>
>>>> (λ { gbx≡gax → trans gbx≡gax (trans (cong (subst V a≡b) gax≡gay) ?) })
>>>>
>>>> Best,
>>>> Andrea
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> On Wed, Jan 20, 2016 at 1:39 AM, Martin Stone Davis
>>>> <martin.stone.davis at gmail.com> wrote:
>>>> > I've found myself wishing that 'rewrite' or with-abstractions were
>>>> invokable
>>>> > from lambda expressions. A (contrived) case in point is as follows,
>>>> where a
>>>> > helper function is used to complete 'foo'. NB, I realize that, in
>>>> this case,
>>>> > I could have simply used a with-abstraction (as in 'bar'), but there
>>>> are
>>>> > other cases (not shown here) where one of the variables being
>>>> ≟-compared
>>>> > only exists on the rhs, thus requiring a call to 'case_of_'.
>>>> >
>>>> > Is there a way to 'subst' my way out of the need for foo-helper?
>>>> >
>>>> > module RewriteOnRight where
>>>> > open import Data.Product using (∃ ; _,_)
>>>> > open import Relation.Nullary using (Dec ; yes ; no)
>>>> > open import Function using (case_of_)
>>>> > open import Relation.Nullary.Negation using (contradiction)
>>>> > open import Relation.Binary using (IsDecEquivalence)
>>>> > open import Relation.Binary.PropositionalEquality using (_≡_ ;
>>>> subst ;
>>>> > trans ; refl)
>>>> >
>>>> > postulate
>>>> > K : Set
>>>> > V : K → Set
>>>> > M : Set
>>>> > _∈_ : K → M → Set
>>>> > get : ∀ {k : K} {m : M} → k ∈ m → V k
>>>> > isDecEquivalence/K : IsDecEquivalence {A = K} _≡_
>>>> >
>>>> > open IsDecEquivalence isDecEquivalence/K using (_≟_ ; sym)
>>>> >
>>>> > foo-helper :
>>>> > ∀ {x : M}
>>>> > {y : M}
>>>> > {a : K}
>>>> > {b : K}
>>>> > {a∈x : a ∈ x}
>>>> > {b∈x : b ∈ x}
>>>> > {a∈y : a ∈ y}
>>>> > (gax≡gay : get a∈x ≡ get a∈y)
>>>> > (a≡b : a ≡ b)
>>>> > (gbx≡gax : get b∈x ≡ subst V a≡b (get a∈x))
>>>> > → get b∈x ≡ get (subst (λ k → k ∈ y) a≡b a∈y)
>>>> > foo-helper gax≡gay a≡b gbx≡gax rewrite a≡b = trans gbx≡gax gax≡gay
>>>> >
>>>> > foo : ∀ {x : M}
>>>> > {y : M}
>>>> > (a : K)
>>>> > (b : K)
>>>> > {a∈x : a ∈ x}
>>>> > {b∈x : b ∈ x}
>>>> > {a∈y : a ∈ y}
>>>> > (gax≡gay : get a∈x ≡ get a∈y)
>>>> > → Dec (∃ λ (a≡b : a ≡ b) → (gbx≡gax : get b∈x ≡ subst V a≡b
>>>> (get
>>>> > a∈x)) → get b∈x ≡ get (subst (λ k → k ∈ y) a≡b a∈y))
>>>> > foo a b gax≡gay = case a ≟ b of λ
>>>> > { (yes a≡b) → yes (a≡b , (λ {gbx≡gax → foo-helper gax≡gay a≡b
>>>> gbx≡gax}))
>>>> > ; (no a≢b) → no (λ { (a≡b , _) → contradiction a≡b a≢b })
>>>> > }
>>>> >
>>>> > bar : ∀ {x : M}
>>>> > {y : M}
>>>> > (a : K)
>>>> > (b : K)
>>>> > {a∈x : a ∈ x}
>>>> > (b∈x : b ∈ x)
>>>> > {a∈y : a ∈ y}
>>>> > (gax≡gay : get a∈x ≡ get a∈y)
>>>> > → Dec (∃ λ (a≡b : a ≡ b) → (gbx≡gax : get b∈x ≡ subst V a≡b
>>>> (get
>>>> > a∈x)) → get b∈x ≡ get (subst (λ k → k ∈ y) a≡b a∈y))
>>>> > bar a b _ _ with a ≟ b
>>>> > bar _ ._ b∈x gax≡gay | yes refl = yes (refl , (λ {gbx≡gax → trans
>>>> gbx≡gax
>>>> > gax≡gay}))
>>>> > bar _ _ _ _ | no a≢b = no (λ { (a≡b , _) → contradiction
>>>> a≡b a≢b
>>>> > })
>>>> >
>>>> > --
>>>> > Martin Stone Davis
>>>> >
>>>> > Postal/Residential:
>>>> > 1223 Ferry St
>>>> > Apt 5
>>>> > Eugene, OR 97401
>>>> > Talk / Text / Voicemail: (310) 699-3578
>>>> > Electronic Mail: martin.stone.davis at gmail.com
>>>> > Website: martinstonedavis.com
>>>> >
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