One problem with it is that your proposed syntax would break all existing code with records in it.

Yes, I just thought about that. One would need to write "destructor" instead of "field". if one wants to include the domain.

Thorsten

From: Jesper Cockx <***@sikanda.be<mailto:***@sikanda.be>>

Date: Wednesday, 7 March 2018 at 14:20

To: Thorsten Altenkirch <***@exmail.nottingham.ac.uk<mailto:***@exmail.nottingham.ac.uk>>

Cc: Agda mailing list <***@lists.chalmers.se<mailto:***@lists.chalmers.se>>

Subject: Re: [Agda] coinductively defined families

Probably you know you can already write this:

open import Agda.Builtin.Nat

open import Agda.Builtin.Equality

record Vec (A : Set) (n : Nat) : Set where

inductive

field

hd : â {m} â n â¡ suc m â A

tl : â {m} â n â¡ suc m â Vec A m

open Vec

[] : â {A} â Vec A 0

[] .hd ()

[] .tl ()

_â·_ : â {A n} â A â Vec A n â Vec A (suc n)

(x â· xs) .hd refl = x

(x â· xs) .tl refl = xs

but I agree that having syntax for indexed records would be a nice thing to have. One problem with it is that your proposed syntax would break all existing code with records in it.

I was actually thinking recently of going in the opposite direction and making indexed datatypes behave more like records, so you could have projections and eta-laws when there's only a single possible constructor for the given indices (as would be the case for vectors).

-- Jesper

On Wed, Mar 7, 2018 at 2:58 PM, Thorsten Altenkirch <***@nottingham.ac.uk<mailto:***@nottingham.ac.uk>> wrote:

Using coinductive types as records I can write

record Stream (A : Set) : Set where

coinductive

field

hd : A

tl : Stream A

and then use copatterns to define cons (after open Stream)

_â·_ : {A : Set} â A â Stream A â Stream A

hd (x â· xs) = x

tl (x â· xs) = xs

Actually I wouldn't mind writing

record Stream (A : Set) : Set where

coinductive

field

hd : Stream A â A

tl : Stream A â Stream A

as in inductive definitions we also write the codomain even though we know what it has to be. However, this is more interesting for families because we should be able to write

record Vec (A : Set) : â â Set where

coinductive

field

hd : â{n} â Vec A (suc n) â A

tl : â{n} â Vec A (suc n) â Vec A n

and we can derive [] and cons by copatterns:

[] : Vec A zero

[] ()

_â·_ : {A : Set} â A â Vec A n â Vec A (suc n)

hd (x â· xs) = x

tl (x â· xs) = xs

here [] is defined as a trivial copattern (no destructor applies). Actually in this case the inductive and the coinductive vectors are isomorphic. A more interesting use case would be to define coinductive vectors indexed by conatural numbers. And I have others. :-)

Maybe this has been discussed already? I haven't been able to go to AIMs for a while.

Thorsten

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