Thorsten Altenkirch

2018-03-07 13:58:12 UTC

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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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

This message and any attachment are intended solely for the addressee

and may contain confidential information. If you have received this

message in error, please contact the sender and delete the email and

attachment.

Any views or opinions expressed by the author of this email do not

necessarily reflect the views of the University of Nottingham. Email

communications with the University of Nottingham may be monitored

where permitted by law.