Question

我已经在Agda中编写了流数据类型和一个头操作。现在我想检查头部操作是否正确。

所以我将输入流作为1 :: 2 :: 3 ::。。。但是agda不接受这个作为流。

所以我的问题是如何定义流??

请帮忙。

Answer 1

有几种可能性。

使用Data.Stream模块，您可以像这样定义无限序列1 2 3 1 2 3 1 2 3 ...：

open import Data.Stream
open import Coinduction

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

使用Data.Colist模块，您可以定义有限和无限序列：

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))

您还可以将Stream数据类型定义为coinductive记录：

{-# 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

然而，复制品与Agda的其余部分（从发行说明中取得）不能很好地发挥作用：

 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.

如何使用agda中的流？

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