F＃：递归函数：测试元素是否是给定列表的成员

Question

I'm trying to figure out how to code this.

Implement in F# a function that tests whether an element is a member of a given list. Here is the type I want.

val memberof : 'a * 'a list -> bool when 'a : equality

Here are examples of the function in action.

memberof 1 [1;2;3];; error FS0003: This value is not a function and cannot be applied

memberof (1,[1;2;3]);; val it : bool = true

memberof (1, []);; val it : bool = false

memberof (1,[2;3;4]);; val it : bool = false

heres what i've put together...

let rec memberof l =
    match (l:float) with
    | a.Item(l) -> l -> bool + (memberof l)

or

let rec memberof l =
    match (l:float list) with
    | [] -> false
    | (a:float)::b -> (a)=(memberof b)->bool

Answer 1

let rec memberof (l : float list) (item : float) : bool =
    match l with
    | hd::tl when hd = item -> true
    | hd::tl -> memberof tl item
    | [] -> false

or

let rec memberof (l : float list) (item : float) : bool =
    match l with
    | hd::tl ->
        if hd = item then
            true
        else
            memberof tl item
    | [] -> false

or

let rec memberof (l : float list) (item : float) : bool =
     match l with 
     | [] -> false 
     | hd :: tl -> 
         hd = item
         || memberof tl item

Test cases

let test001 = memberof [1.0; 2.0; 3.0] 0.0    
printfn "test001: %A" test001   

let test002 = memberof [1.0; 2.0; 3.0] 1.0  
printfn "test002: %A" test002   

let test003 = memberof [1.0; 2.0; 3.0] 2.0  
printfn "test003: %A" test003 

let test004 = memberof [1.0; 2.0; 3.0] 3.0  
printfn "test004: %A" test004   

let test005 = memberof [] 0.0    
printfn "test005: %A" test005 

Which outputs

val test001 : bool = false
val test002 : bool = true
val test003 : bool = true
val test004 : bool = true
val test005 : bool = false

The problem with

let rec memberof l =
    match (l:float list) with
    | [] -> false
    | (a:float)::b -> (a)=(memberof b)->bool

is that

| (a:float)::b -> (a)=(memberof b)->bool

is pulling the list apart correctly with

 (a:float)::b

however

 (a)=(memberof b)->bool

is not right.

With recursive functions over a list you want to pull off the head of the list and process the head. Then you want to call the function again, this time passing the tail of the list as the new list variable, eg

memberof tl item

Since this is a predicate , we only need to stop once we reach a desired true or false. In this example when true is found the function can end, so no need to call memberof for the remainder of the list.

For the particular signature you requested

val memberof : item:'a * list:'a list -> bool when 'a : equality

let rec memberof ((item : 'a), (list : 'a list)) : bool when 'T : equality =
    match list with
    | hd::tl ->
        if hd = item then
            true
        else
            memberof (item, tl)
    | [] -> false