为什么不能解决`n`和`plus n 0`之间的约束？

Question

我正在尝试在 REPL 上重新加载包含以下 Idris 2 函数的源文件：

||| Apply a function across all elements of a vector.
||| @function The function to apply.
||| @input_vector The vector whose elements will be given as an argument to the function.
my_vect_map : (function : a -> b) -> (input_vector : Vect n a) -> Vect n b
my_vect_map function Nil = Nil
my_vect_map function (head :: tail) =
  (my_vect_map' ((function head) :: Nil) tail) where
    my_vect_map' : (accumulator : Vect length_b b) -> Vect length_a a -> Vect (length_b + length_a) b
    my_vect_map' accumulator Nil = accumulator
    my_vect_map' accumulator (head' :: tail') =
      my_vect_map' (accumulator ++ ((function head') :: Nil)) tail'

但是它无法进行类型检查并出现错误：

Error: While processing right hand side of my_vect_map. While processing right hand side
of my_vect_map,my_vect_map'. Can't solve constraint
between: length_b (implicitly bound at page_75_section_3_2_exercises_solutions.idr:89:5--89:47) and plus length_b 0.

page_75_section_3_2_exercises_solutions.idr:89:36--89:47
    |
 89 |     my_vect_map' accumulator Nil = accumulator
    |                                    ^^^^^^^^^^^

Error(s) building file page_75_section_3_2_exercises_solutions.idr

为什么类型检查器无法解决 length_b 和 plus length_b 0 之间的约束？我做错了什么，我该如何纠正？我尝试手动完成一些示例，似乎可行：

my_vect_map id [] => Nil => []

my_vect_map id ['a'] => my_vect_map id ('a' :: Nil) => my_vect_map' ((id 'a') :: Nil) Nil => my_vect_map' ('a' :: Nil) Nil => ('a' :: Nil) => ['a']
                                                                                                          ^length_b=1  ^length_a=0            ^length=1=length_b+length_a

my_vect_map id ['a', 'b'] => my_vect_map id ('a' :: ('b' :: Nil)) => my_vect_map' ((id 'a') :: Nil) ('b' :: Nil) => my_vect_map' ('a' :: Nil) ('b' :: Nil) => my_vect_map' (('a' :: Nil) ++ ((id 'b') :: Nil)) Nil => my_vect_map' (('a' :: Nil) ++ ('b' :: Nil)) Nil => my_vect_map' ('a' :: ('b' :: Nil)) Nil => ('a' :: ('b' :: Nil)) => ['a', 'b']
                                                                                                                                 ^length_b=1  ^length_a=1                                                                                                                             ^length_b=2           ^length_a=0                     ^length=2=length_b+length_a

此外，我如何让类型检查器意识到 length_b + length_a 等于 n（因为我认为我没有设法将这种关系编码到函数中）？

Answer 1

你可以用Data.Nat中的rewrite rule plusZeroRightNeutral来证明n + 0 = n。

不过您可能需要重新考虑一下这个函数。

您可以非常简单地创建矢量图：

my_vect_map : (a -> b) -> Vect n a -> Vect n b
my_vect_map fn [] = []
my_vect_map fn (x :: xs) = fn x :: my_vect_map fn xs

编辑

这是 map 的尾递归版本：

mutual
  rhs : {m : Nat} -> (a -> b) -> a -> Vect m b -> Vect len a -> Vect (plus m (S len)) b
  rhs f x acc xs = rewrite sym $ plusSuccRightSucc m len in my_vect_map' f (f x :: acc) xs

  my_vect_map' : {m : Nat} -> (a -> b) -> Vect m b -> Vect n a -> Vect (m + n) b
  my_vect_map' f acc [] = rewrite plusZeroRightNeutral m in acc
  my_vect_map' f acc (x :: xs) = rhs f x acc xs

my_vect_map : (a -> b) -> Vect n a -> Vect n b
my_vect_map f = reverse . my_vect_map' f []

rhs的唯一目的是暴露len，xs的大小。

我们还使用 {} 将类型变量引入值级别的范围。

希望对您有所帮助。

为什么不能解决`n`和`plus n 0`之间的约束？

Why can't the constraint between `n` and `plus n 0` be solved?

types

identity

tail-recursion

dependent-type

idris