在haskell列表理解中跨列表应用乘法

Question

haskell noob 在这里。我正在做Learn you a Haskell 并遇到了这个问题：

[ x*y | x <- [2,5,10], y <- [8,10,11]]

我改写如下

[ x*y | x <- [[1,2,3], [2,3,4]], y <- [[4,5,6],[5,6,7]] ]

编译器对我咆哮可能是因为我试图将一个列表与另一个列表相乘。但是，如果我想递归地将 x 和 y 的每个子列表相乘，我该怎么做？

这是我得到的错误：

No instance for (Num [t0]) arising from a use of `*'
    Possible fix: add an instance declaration for (Num [t0])
    In the expression: x * y

更新

到目前为止，我已经到达这里：

[ [a*b | a <- x, b <- y] | x <- [[1,2,3],[2,3,4]], y <- [[4,5,6], [5,6,7]] ]

但这仍然返回一个列表列表。在 Haskell 中扁平化列表的优雅方式是什么？

Answer 1

在 GHCI 中试试这个：

Prelude> let combinate xs ys = [ x*y | x<-xs, y<-ys ]
Prelude> concat [ combinate x y | x <- [[1,2,3], [2,3,4]], y <- [[4,5,6],[5,6,7]] ]
[4,5,6,8,10,12,12,15,18,5,6,7,10,12,14,15,18,21,8,10,12,12,15,18,16,20,24,10,12,14,15,18,21,20,24,28]

Answer 2

所以让我们尝试几种方法。我将使用 ghci 来说明一些例子：

% ghci
GHCi, version 7.8.2: http://www.haskell.org/ghc/  :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer-gmp ... linking ... done.
Loading package base ... linking ... done.
λ [ x*y | x <- [2,5,10], y <- [8,10,11]]
[16,20,22,40,50,55,80,100,110]
λ -- so let's abstract that to a function
λ let multList xs ys = [ x*y | x <- xs, y <- ys ]
λ multList [2,5,10] [8,10,11]
[16,20,22,40,50,55,80,100,110]
λ -- let's try a simpler example
λ multList [1] [1]
[1]
λ -- now let's see if we can get your code working
λ -- (I tweaked the variable names, but that's just cosmetic)
λ [ xs*ys | xs <- [[1,2,3], [2,3,4]], ys <- [[4,5,6],[5,6,7]] ]

<interactive>:13:1:
    No instance for (Num [t0]) arising from a use of ‘it’
    In a stmt of an interactive GHCi command: print it
λ -- yup, that's the error alright
λ -- let's skip multiplying. what else can we do with xs and ys?
λ -- well, we could create the pair (xs,ys)
λ [ (xs,ys) | xs <- [[1,2,3], [2,3,4]], ys <- [[4,5,6],[5,6,7]] ]
[([1,2,3],[4,5,6]),([1,2,3],[5,6,7]),([2,3,4],[4,5,6]),([2,3,4],[5,6,7])]
λ -- that's each pair of sublists, but we want to compute the products of each element
λ -- fortunately, that's exactly what multList does!
λ :t multList
multList :: Num t => [t] -> [t] -> [t]
λ [ multList xs ys | xs <- [[1,2,3], [2,3,4]], ys <- [[4,5,6],[5,6,7]] ]
[[4,5,6,8,10,12,12,15,18],[5,6,7,10,12,14,15,18,21],[8,10,12,12,15,18,16,20,24],[10,12,14,15,18,21,20,24,28]]
λ -- so that creates four sublists, one for each pair of lists.
λ -- what if we want to flatten that out?
λ -- well, we could just use `concat`
λ :t concat
concat :: [[a]] -> [a]
λ concat [ multList xs ys | xs <- [[1,2,3], [2,3,4]], ys <- [[4,5,6],[5,6,7]] ]
[4,5,6,8,10,12,12,15,18,5,6,7,10,12,14,15,18,21,8,10,12,12,15,18,16,20,24,10,12,14,15,18,21,20,24,28]
λ -- alternately, we could try to inline our definition of `multList` and see where that gets us
λ [ [ x*y | x <- xs, y <- ys ] | xs <- [[1,2,3], [2,3,4]], ys <- [[4,5,6],[5,6,7]] ]
[[4,5,6,8,10,12,12,15,18],[5,6,7,10,12,14,15,18,21],[8,10,12,12,15,18,16,20,24],[10,12,14,15,18,21,20,24,28]]
λ -- nothing yet, but see how we've got two list comprehensions?
λ -- let's combine them into one!
λ [ x*y | xs <- [[1,2,3], [2,3,4]], ys <- [[4,5,6],[5,6,7]], x <- xs, y <- ys ]
[4,5,6,8,10,12,12,15,18,5,6,7,10,12,14,15,18,21,8,10,12,12,15,18,16,20,24,10,12,14,15,18,21,20,24,28]
λ -- hey, that worked!