How to work with stream in agda?

Question

I have written the stream data type and one head operation in Agda. Now i want to check whether head operation is correct or not.

So i take my input stream as 1 :: 2 :: 3 :: . . . But agda does not accept this as a stream.

So my question is how to define stream ??

Please help.

to define a list i wrote like this ex : List N ex = 1::(2::(3::[])). But not able to define stream like this. — ajayv, Feb 27 '15 at 16:44

score 1 · Answer 1 · answered Feb 27 '15 at 17:33

There are several possibilities.

Using the Data.Stream module you can define an infinite sequence 1 2 3 1 2 3 1 2 3 ... like this:

open import Data.Stream
open import Coinduction

stream : Stream ℕ
stream = 1 ∷ ♯ (2 ∷ ♯ (3 ∷ ♯ stream))

Using the Data.Colist module you can define both finite and infinite sequences:

open import Data.Colist
open import Coinduction

colist-fin : Colist ℕ
colist-fin = 1 ∷ ♯ (2 ∷ ♯ (3 ∷ ♯ []))

colist-inf : Colist ℕ
colist-inf = 1 ∷ ♯ (2 ∷ ♯ (3 ∷ ♯ colist-inf))

And you can also define the Stream datatype as a coinductive record:

{-# OPTIONS --copatterns #-}

record Stream {α} (A : Set α) : Set α where
  coinductive
  constructor _∷_
  field
    head : A
    tail : Stream A
open Stream

zeros : Stream ℕ
head zeros = 0
tail zeros = zeros

However copatterns do not play well with the rest of Agda (taken from release notes):

 Copatterns are yet experimental and the following does not work:
* Copatterns and 'with' clauses.
* Compilation of copatterns to Haskell, JS, or Epic.
* Projections generated by
open R {{...}}
are not handled properly on lhss yet.
* Conversion checking is slower in the presence of copatterns,
since stuck definitions of record type do no longer count
as neutral, since they can become unstuck by applying a projection.
Thus, comparing two neutrals currently requires comparing all
they projections, which repeats a lot of work.

How to work with stream in agda?

1 Answers1