I have the following SML code that I wrote for a class:
fun lookup (cmp: 'a * 'a -> order) (x: 'a, t: 'a tree) : 'a option =
case t of
Empty => NONE
| Node(l,y,r) =>
case cmp(x,y) of
EQUAL => SOME y
| LESS => lookup (cmp) (x,r)
| GREATER => lookup (cmp) (x,l)
In testing this with:
val SOME 3 = lookup Int.compare (3, Node(Empty,3,Empty));
And getting the following error back:
stdIn:153.1-166.12 Error: operator and operand don't agree [tycon mismatch]
operator domain: int * int ?.tree
operand: int * int tree
in expression:
(lookup Int.compare) (3,Node (Empty,3,Empty))
What does the ?. mean?
This is usually to do with restricted visibility across modules. What does your 'tree' definition look like? You might need to tell the compiler that your 'tree' type in one module is the same as the one in another module.
Related
So what I want to do is to convert a string into an int and do some error catching on it. I would also like to know where I would put what I want it to do after it fails if it does.
I know how to convert, but I am not sure how to catch it and where the code will jump to after the error
I believe the method for converting it Int.fromString(x)
Thank you.
SML has two approaches to error handling. One, based on raise to raise errors and handle to catch the error, is somewhat similar to how error handling works in languages like Python or Java. It is effective, but the resulting code tends to lose some of its functional flavor. The other method is based on the notion of options. Since the return type of Int.fromString is
string -> int option
it makes the most sense to use the option-based approach.
An int option is either SOME n, where n is and integer, or it is NONE. The function Int.fromString returns the latter if it fails in its attempt to convert the string to an integer. The function which calls Int.fromString can explicitly test for NONE and use the valOf to extract the value in the case that the return value is of the form SOME n. Alternatively, and somewhat more idiomatically, you can use pattern matching in a case expression. Here is a toy example:
fun squareString s =
case Int.fromString(s) of
SOME n => Int.toString (n * n) |
NONE => s ^ " isn't an integer";
This function has type string -> string. Typical output:
- squareString "4";
val it = "16" : string
- squareString "Bob";
val it = "Bob isn't an integer" : string
Note that the clause which starts NONE => is basically an error handler. If the function that you are defining isn't able to handle such errors, it could pass the buck. For example:
fun squareString s =
case Int.fromString(s) of
SOME n => SOME (Int.toString (n * n))|
NONE => NONE;
This has type string -> string option with output now looking like:
- squareString "4";
val it = SOME "16" : string option
- squareString "Bob";
val it = NONE : string option
This would make it the responsibility of the caller to figure out what to do with the option.
The approach to error handling that John explains is elaborated in the StackOverflow question 'Unpacking' the data in an SML DataType without a case statement. The use-case there is a bit different, since it also involves syntax trees, but the same convenience applies for smaller cases:
fun squareString s = Int.fromString s >>= (fn i => SOME (i*i))
Assuming you defined the >>= operator as:
infix 3 >>=
fun NONE >>= _ = NONE
| (SOME a) >>= f = f a
The drawback of using 'a option for error handling is that you have to take into account, every single time you use a function that has this return type, whether it errored. This is not unreasonable. It's like mandatory null-checking. But it comes at the cost of not being able to easily compose your functions (using e.g. the o operator) and a lot of nested case-ofs:
fun inputSqrt s =
case TextIO.inputLine TextIO.stdIn of
NONE => NONE
| SOME s => case Real.fromString s of
NONE => NONE
| SOME x => SOME (Math.sqrt x) handle Domain => NONE
A workaround is that you can build this constant error handling into your function composition operator, as long as all your functions share the same way of expressing errors, e.g. using 'a option:
fun safeSqrt x = SOME (Math.sqrt x) handle Domain => NONE
fun inputSqrt () =
TextIO.inputLine TextIO.stdIn >>=
(fn s => Real.fromString s >>=
(fn x => safeSqrt x))
Or even shorter by applying Eta conversion:
fun inputSqrt () = TextIO.inputLine TextIO.stdIn >>= Real.fromString >>= safeSqrt
This function could fail either because of a lack of input, or because the input didn't convert to a real, or because it was negative. Naturally, this error handling isn't smart enough to say what the error was, so you might want to extend your functions from using an 'a option to using an ('a, 'b) either:
datatype ('a, 'b) either = Left of 'a | Right of 'b
infix 3 >>=
fun (Left msg) >>= _ = Left msg
| (Right a) >>= f = f a
fun try (SOME x) _ = Right x
| try NONE msg = Left msg
fun inputLine () =
try (TextIO.inputLine TextIO.stdIn) "Could not read from stdIn."
fun realFromString s =
try (Real.fromString s) "Could not derive real from string."
fun safeSqrt x =
try (SOME (Math.sqrt x) handle Domain => NONE) "Square root of negative number"
fun inputSqrt () =
inputLine () >>= realFromString >>= safeSqrt
And trying this out:
- inputSqrt ();
9
> val it = Right 3.0 : (string, real) either
- inputSqrt ();
~42
> val it = Left "Square root of negative number" : (string, real) either
- inputSqrt ();
Hello
> val it = Left "Could not derive real from string." : (string, real) either
- (TextIO.closeIn TextIO.stdIn; inputSqrt ());
> val it = Left "Could not read from stdIn." : (string, real) either
Excuse my potential misuse of terminology, I'm still not very comfortable with OCaml.
We have a functor with the following (abridged) signature:
module type FUNCTORA = sig
type input
type output
type key
type inter
val my_function : input list -> (key * output) list Deferred.t
end
Next, we implement it as such. MYAPP has the same types as above.
module MyFunctor (App : MyAPP) : FUNCTORA = struct
type input = App.input
type output = App.output
type key = App.key
type inter App.value
let my_function lst = ...
end
When trying to compile the implementation, we get this error:
Error: Signature mismatch:
...
Values do not match:
val my_function :
App.input list ->
(App.key * App.output) list Async_kernel.Deferred.t
is not included in
val my_function :
input list -> (key * output) list Async.Std.Deferred.t
It doesn't consider input to include App.input etc, even though we set them to be the same type. How can we get this to type check?
If I make the following changes:
MyAPP => FUNCTORA (* Since you say they are the same *)
type inter App.value => type inter = App.inter (* Syntax/name error *)
Deferred.t => option (* To limit dependence on other modules *)
Then your code compiles for me.
Possibly the problem is with Deferred.t. There are two distinct looking types in the error message.
So I have this list of tuples(n=2), witch I'm supposed to "unzip" and by that create a new list like so: for list of tuples like this val it = (1,"one") :: (2,"two") :: nil : (int,string) alterlist, the unzip function will create a list like so [(1,2),("one", "two")].
This is what I got so far:
datatype ('a, 'b) alterlist = nil | :: of ('a*'b) * ('a, 'b) alterlist;
infixr 5 ::
fun build4(x, one, y, two) = (x,one)::((y,two)::nil);
fun unzip(alterlist) =
let
fun extract([], i) = []
| extract((x,y)::xs, i) = if i=0 then x::extract(xs, i)
else y::extract(xs, i);
in
(extract(alterlist, 0))::(extract(alterlist, 1))
end;
But I get a bunch of errors:
stdIn:48.6-50.26 Error: parameter or result constraints of clauses don't agree [tycon mismatch]
this clause: ('Z,'Y) alterlist * 'X -> 'W
previous clauses: 'V list * 'U -> 'W
in declaration:
extract =
(fn (nil,i) => nil
| (<pat> :: <pat>,i) =>
if <exp> = <exp> then <exp> :: <exp> else <exp> :: <exp>)
stdIn:49.41-49.58 Error: operator and operand don't agree [tycon mismatch]
operator domain: 'Z list * 'Y
operand: ('X,'W) alterlist * int
in expression:
extract (xs,i)
stdIn:50.9-50.26 Error: operator and operand don't agree [tycon mismatch]
operator domain: 'Z list * 'Y
operand: (_ * _,'X) alterlist * int
in expression:
extract (xs,i)
stdIn:48.6-50.26 Error: right-hand-side of clause doesn't agree with function result type [tycon mismatch]
expression: (_,_) alterlist
result type: 'Z list
in declaration:
extract =
(fn (nil,i) => nil
| (<pat> :: <pat>,i) =>
if <exp> = <exp> then <exp> :: <exp> else <exp> :: <exp>)
And being that I'm new to ml I have very little idea what causes it. Would greatly appreciate help!
My advice is first do it without the infix operator because it is a little bit confusing.
First solve it without and add it later.
Here is a solution without the infix:
datatype ('a,'b)alterlist = Nil
| element of 'a*('b,'a)alterlist;
fun unzip (Nil : ('a,'b)alterlist ) = ([],[])
| unzip (ablist : ('a,'b)alterlist) =
let
fun extract Nil = []
| extract (element (curr, Nil)) = curr::[]
| extract (element (curr, element(_,rest))) = curr::(extract rest)
val element (_, balist) = ablist
in
(extract ablist, extract balist)
end;
So for example a list like this: ["a", 1, "b", 2] would be created by:
element ("a", element (1, element ("b", element (2, Nil))));
Giving you:
val it = element ("a",element (1,element #)) : (string,int) alterlist
* The # is just to indicate the list is longer than is displayed.
And then if you would try unzip it;
You would get:
val it = (["a","b"],[1,2]) : string list * int list
As you would like.
Now try to change element into a :: infix operator.
Good luck!
I have a module StringMap built by the functor Map.Make given a type String:
module StringMap = Map.Make(String)
Besides the ordinary operations provided by Map, I would like to add more definitions in this module, for instance, my_own_function, such that I could call StringMap.my_own_function. Does anyone know where I should define this kind of functions and their signature?
You can use the include keyword inside a new module to add all the same functions. This was also extended to the signature in OCaml 3.12.
module StringMap =
struct
include Map.Make(String)
end
If you want to access the structure of the map, you'll have to add some Obj.magic or the %identity special external function. The redefinition of the type must be exact since no type checking is happening,
module Make (Ord : Map.OrderedType) =
struct
include Map.Make(Ord)
type 'a impl = Empty
| Node of 'a impl * key * 'a * 'a impl * int
external impl_of_t : 'a t -> 'a impl = "%identity"
external t_of_impl : 'a impl -> 'a t = "%identity"
let cardinal map =
let rec cardinal = function
| Empty -> 0
| Node(l,_,_,r,_) -> cardinal l + 1 + cardinal r
in
cardinal (impl_of_t map)
end
I have two module types:
module type ORDERED =
sig
type t
val eq : t * t -> bool
val lt : t * t -> bool
val leq : t * t -> bool
end
module type STACK =
sig
exception Empty
type 'a t
val empty : 'a t
val isEmpty : 'a t -> bool
val cons : 'a * 'a t -> 'a t
val head : 'a t -> 'a
val tail : 'a t -> 'a t
val length : 'a t -> int
end
I want to write a functor which "lifts" the order relation from the basic ORDERED type to STACKs of that type. That can be done by saying that, for example, two stacks of elements will be equal if all its individual elements are equal. And that stacks s1 and s2 are s.t. s1 < s2 if the first of each of their elements, e1 and e2, are also s.t. e1 < e2, etc.
Now, if don't commit to explicitly defining the type in the module type, I will have to write something like this (or won't I?):
module StackLift (O : ORDERED) (S : STACK) : ORDERED =
struct
type t = O.t S.t
let rec eq (x,y) =
if S.isEmpty x
then if S.isEmpty y
then true
else false
else if S.isEmpty y
then false
else if O.eq (S.head x,S.head y)
then eq (S.tail x, S.tail y)
else false
(* etc for lt and leq *)
end
which is a very clumsy way of doing what pattern matching serves so well. An alternative would be to impose the definition of type STACK.t using explicit constructors, but that would tie my general module somewhat to a particular implementation, which I don't want to do.
Question: can I define something different above so that I can still use pattern matching while at the same time keeping the generality of the module types?
As an alternative or supplement to the other access functions, the module can provide a view function that returns a variant type to use in pattern matching.
type ('a, 's) stack_view = Nil | Cons of 'a * 's
module type STACK =
sig
val view : 'a t -> ('a , 'a t) stack_view
...
end
module StackLift (O : ORDERED) (S : STACK) : ORDERED =
struct
let rec eq (x, y) =
match S.view x, S.view y with
Cons (x, xs), Cons (y, ys) -> O.eq (x, y) && eq (xs, ys)
| Nil, Nil -> true
| _ -> false
...
end
Any stack with a head and tail function can have a view function too, regardless of the underlying data structure.
I believe you've answered your own question. A module type in ocaml is an interface which you cannot look behind. Otherwise, there's no point. You cannot keep the generality of the interface while exposing details of the implementation. The only thing you can use is what's been exposed through the interface.
My answer to your question is yes, there might be something you can do to your definition of stack, that would make the type of a stack a little more complex, thereby making it match a different pattern than just a single value, like (val,val) for instance. However, you've got a fine definition of a stack to work with, and adding more type-fluff is probably a bad idea.
Some suggestions with regards to your definitions:
Rename the following functions: cons => push, head => peek, tail => pop_. I would also add a function val pop : 'a t -> 'a * 'a t, in order to combine head and tail into one function, as well as to mirror cons. Your current naming scheme seems to imply that a list is backing your stack, which is a mental leak of the implementation :D.
Why do eq, lt, and leq take a pair as the first parameter? In constraining the type of eq to be val eq : 'a t * 'a t -> 'a t, you're forcing the programmer that uses your interface to keep around one side of the equality predicate until they've got the other side, before finally applying the function. Unless you have a very good reason, I would use the default curried form of the function, since it provides a little more freedom to the user (val eq : 'a t -> 'a t -> 'a t). The freedom comes in that they can partially apply eq and pass the function around instead of the value and function together.