做一个N维走在纯粹的功能ML?
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20-08-2019 - |
题
我们的想法是多个维度走过去,每一个定义为范围
(* lower_bound, upper_bound, number_of_steps *)
type range = real * real * int
所以类似功能的 fun foo y x
强>或 fun foo z y x
强>可以应用于整个正方形X Y或立方体X ý* Z。
SML / NJ不喜欢低于我实现:
test2.sml:7.5-22.6 Error: right-hand-side of clause doesn't agree with function result type [circularity]
expression: (real -> 'Z) -> unit
result type: 'Z -> 'Y
in declaration:
walk = (fn arg => (fn <pat> => <exp>))
下面的代码:
fun walk [] _ = ()
| walk (r::rs) f =
let
val (k0, k1, n) = r
val delta = k1 - k0
val step = delta / real n
fun loop 0 _ = ()
| loop i k =
let in
walk rs (f k) ; (* Note (f k) "eats" the first argument.
I guess SML doesn't like having the
type of walk change in the middle of its
definition *)
loop (i - 1) (k + step)
end
in
loop n k0
end
fun do2D y x = (* ... *) ()
fun do3D z y x = (* ... *) ()
val x_axis = (0.0, 1.0, 10)
val y_axis = (0.0, 1.0, 10)
val z_axis = (0.0, 1.0, 10)
val _ = walk [y_axis, x_axis] do2D
val _ = walk [z_axis, y_axis, x_axis] do3D
就是这种结构的可能?
任何指针欢迎。
解决方案
在ML的类型系统是walk
表达
val walk : range list -> (real -> real -> unit) -> unit
val walk : range list -> (real -> real -> real -> unit) -> unit
在相同的一个值不可能与两个在ML那些类型存在。
我们可以很容易地产生的值的每个所期望的类型的,虽然。
type range = real * real * int
signature WALK =
sig
type apply
val walk : range list -> apply -> unit
end
structure Walk0 : WALK =
struct
type apply = unit
fun walk _ _ = ()
end
functor WALKF (Walk : WALK) : WALK =
struct
type apply = real -> Walk.apply
fun walk ((low, high, steps)::rs) f =
let fun loop i =
if i > steps then () else
let val x = low + (high - low) * real i / real steps
in (Walk.walk rs (f x); loop (i + 1)) end
in loop 0 end
end
struture Walk1 = WALKF(Walk0)
struture Walk2 = WALKF(Walk1)
struture Walk3 = WALKF(Walk2)
通过此,将具有期望类型存在以下的值。
val Walk0.walk : range list -> unit -> unit
val Walk1.walk : range list -> (real -> unit) -> unit
val Walk2.walk : range list -> (real -> real -> unit) -> unit
val Walk3.walk : range list -> (real -> real -> real -> unit) -> unit
然后你只需要编写
val _ = Walk2.walk [y_axis, x_axis] do2D
val _ = Walk3.walk [z_axis, y_axis, x_axis] do3D
要使用相同的walk
每一个维度,您需要使用相同的类型,为每个维度。
fun walk nil f = f nil
| walk ((low, high, steps)::rs) f =
let fun loop i =
if i > steps then () else
let val x = low + (high - low) * real i / real steps
in (walk rs (fn xs -> f (x::xs)); loop (i + 1)) end
in loop 0 end
由于该类型被改变成
val walk : range list -> (real list -> unit) -> unit
您的使用情况也有可能改变到
fun do2D [y,x] = (* ... *) ()
fun do3D [z,y,x] = (* ... *) ()
其他提示
fun walk lst f = let
fun aux rev_prefix [] = f (rev rev_prefix)
| aux rev_prefix (r::rs) = let
val (k0, k1, n) = r
val delta = k1 - k0
val step = delta / real n
fun loop 0 _ = ()
| loop i k = (
aux (k+step :: rev_prefix) rs;
loop (i - 1) (k + step)
)
in
loop n k0
end
in
aux [] lst
end
fun do2D [x,y] = print (Real.toString x ^ "\t" ^
Real.toString y ^ "\n")
fun do3D [x,y,z] = print (Real.toString x ^ "\t" ^
Real.toString y ^ "\t" ^
Real.toString z ^ "\n")
val x_axis = (0.0, 1.0, 10)
val y_axis = (0.0, 1.0, 10)
val z_axis = (0.0, 1.0, 10)
val () = walk [y_axis, x_axis] do2D
val () = walk [z_axis, y_axis, x_axis] do3D
找到的参数可变数目此实施的。不知道它适用,但它看起来很丑陋。
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