I am trying to apply the free monad pattern as described in F# for fun and profit to implement data access (for Microsoft Azure Table Storage)
Example
Let's assume we have three database tables and three dao's Foo, Bar, Baz:
Foo Bar Baz
key | col key | col key | col
--------- --------- ---------
foo | 1 bar | 2 |
I want to select Foo with key="foo" and Bar with key="bar" to insert a Baz with key="baz" and col=3
Select<Foo> ("foo", fun foo -> Done foo)
>>= (fun foo -> Select<Bar> ("bar", fun bar -> Done bar)
>>= (fun bar -> Insert<Baz> ((Baz ("baz", foo.col + bar.col), fun () -> Done ()))))
Within the interpreter function
Select results in a function call that takes a key : string and returns an obj
Insert results in a function call that takes an obj and returns unit
Problem
I defined two operations Select and Insert in addition to Done to terminate the computation:
type StoreOp<'T> =
| Select of string * ('T -> StoreOp<'T>)
| Insert of 'T * (unit -> StoreOp<'T>)
| Done of 'T
In order to chain StoreOp's I am trying to implement the correct bind function:
let rec bindOp (f : 'T1 -> StoreOp<'T2>) (op : StoreOp<'T1>) : StoreOp<'T2> =
match op with
| Select (k, next) ->
Select (k, fun v -> bindOp f (next v))
| Insert (v, next) ->
Insert (v, fun () -> bindOp f (next ()))
| Done t ->
f t
let (>>=) = bindOp
However, the f# compiler correctly warns me that:
The type variable 'T1 has been constrained to be type 'T2
For this implementation of bindOp the type is fixed throughout the computation, so instead of:
Foo > Bar > unit
all I can express is:
Foo > Foo > Foo
How should I modify the definition of StoreOp and/or bindOp to work with different types throughout the computation?
As Fyodor mentioned in the comments, the problem is with the type declaration. If you wanted to make it compile at the price of sacrificing type safety, you could use obj in two places - this at least shows where the problem is:
type StoreOp<'T> =
| Select of string * (obj -> StoreOp<'T>)
| Insert of obj * (unit -> StoreOp<'T>)
| Done of 'T
I'm not entirely sure what the two operations are supposed to model - but I guess Select means you are reading something (with string key?) and Insert means that you are storing some value (and then continue with unit). So, here, the data you are storing/reading would be obj.
There are ways of making this type safe, but I think you'd get better answer if you explained what are you trying to achieve by using the monadic structure.
Without knowing more, I think using free monads will only make your code very messy and difficult to understand. F# is a functional-first language, which means that you can write data transformations in a nice functional style using immutable data types and use imperative programming to load your data and store your results. If you are working with table storage, why not just write the normal imperative code to read data from table storage, pass the results to a pure functional transformation and then store the results?
Related
So I have some (I'm assuming rather unusual) code which is for building Function Trees. Here's it is right now:
type FunctionTree<'Function> =
| BranchNode of seq<FunctionTree<'Function>>
| Leaf of (a:'Function -> unit) with
member __.Execute() = do a
The expression a:'Function -> unit is what makes the compiler throw a fit, giving me the error 'Anonymous type variables are not permitted in this declaration' and I have no idea why. I've tried adding a variable to the BranchNode, adding (yucky) double parentheses around the expression but nothing seems to have worked.
Answer to the compiler error question
This does not compile...
Leaf of (a:'Function -> unit)
...because discriminated field names can be added to the types of the DU cases, not to the types of the function types in a DU case. In contrast, this compiles...
Leaf of a: ('Function -> unit)
...because the field name a is being used to name the type (Function -> unit).
Additional discussion about the code
However, there is another issue. The member Execute that you are adding is not being added to the Leaf node, as your code implies. It is being added to the entire function tree. Consequently, you will not have access to the label a inside your implementation of Execute. Think of it like this...
type FunctionTree<'Function> =
| BranchNode of seq<FunctionTree<'Function>>
| Leaf of a: ('Function -> unit)
with member __.Execute() = do a
... with the member shifted to the left to clarify that it applies to the entire union, not just the leaf case. That explains why the above code now has a different compiler error... a is not defined. The field name a is used to clarify the instantiation of a Leaf case. The field name a is not available elsewhere.
let leaf = Leaf(a: myFunc)
Consequently, the label a is not available to your Execute member. You would need to do something like this...
with member x.Execute(input) =
match x with
| BranchNode(b) -> b |> Seq.iter(fun n -> n.Execute(input))
| Leaf(f) -> f(input) |> ignore
Notice in the above code that the x value is a FunctionTree.
Alternative implementation
We could continue going. However, I think the following may implement what you are aiming for:
type FunctionTree<'T> =
| BranchNode of seq<FunctionTree<'T>>
| LeafNode of ('T -> unit)
let rec evaluate input tree =
match tree with
| LeafNode(leaf) -> leaf(input)
| BranchNode(branch) -> branch |> Seq.iter (evaluate input)
BranchNode([
LeafNode(printfn "%d")
LeafNode(printfn "%A")
])
|> evaluate 42
I am trying to implement BST in F#. Since I am starting my journey with F# I wanted to ask for help.
I have simple a test;
[<Fact>]
let ``Data is retained`` () =
let treeData = create [4]
treeData |> data |> should equal 4
treeData |> left |> should equal None
treeData |> right |> should equal None
Tree type which uses discriminated unions
type Tree<'T> =
| Leaf
| Node of value: 'T * left: Tree<'T> * right: Tree<'T>
a recursive function which inserts data nodes into the tree
let rec insert newValue (targetTree: Tree<'T>) =
match targetTree with
| Leaf -> Node(newValue, Leaf, Leaf)
| Node (value, left, right) when newValue < value ->
let left' = insert newValue left
Node(value, left', right)
| Node (value, left, right) when newValue > value ->
let right' = insert newValue right
Node(value, left, right')
| _ -> targetTree
now I have problems with create function. I have this:
let create items =
List.fold insert Leaf items
and resulting error:
FS0001 Type mismatch. Expecting a
''a -> Tree<'a> -> 'a' but given a
''a -> Tree<'a> -> Tree<'a>' The types ''a' and 'Tree<'a>' cannot be unified.
The List.fold documentation shows its type signature as:
List.fold : ('State -> 'T -> 'State) -> 'State -> 'T list -> 'State
Let's unpack that. The first argument is a function of type 'State -> 'T -> 'State. That means it takes a state and an argument of type T, and returns a new state. Here, the state is your Tree type: starting at a basic Leaf, you're building up the tree step by step. Second argument to List.fold is the initial state (a Leaf in this case), and third argument is the list of items of type T to fold over.
Your second and third arguments are correct, but your first argument doesn't line up with the signature that List.fold is expecting. List.fold wants something of type 'State -> 'T -> 'State, which in your case would be Tree<'a> -> 'a -> Tree<'a>. That is, a function that takes the tree as its first parameter and a single item as its second parameter. But your insert function takes the parameters the other way around (the item as the first parameter, and the tree as the second parameter).
I'll pause here to note that your insert function is correct according to the style rules of idiomatic F#, and you should not change the order of its parameters. When writing functions that deal with collections, you always want to take the collection as the last parameter so that you can write something like tree |> insert 5. So I strongly suggest you don't change the order of the arguments your insert function takes.
So if you shouldn't change the order of arguments of your insert function, yet they're in the wrong order to use with List.fold, what do you do? Simple: you create an anonymous function with the arguments flipped around, so that you can use insert with List.fold:
let create items =
List.fold (fun tree item -> insert item tree) Leaf items
Now we'll go one step further and generalize this. It's actually pretty common in F# programming to find that your two-parameter function has the parameters the right way around for most things, but the wrong way around for one particular use case. To solve that problem, sometimes it's useful to create a general-purpose function called flip:
let flip f = fun a b -> f b a
Then you could just write your create function like this:
let create items =
List.fold (flip insert) Leaf items
Sometimes the use of flip can make code more confusing rather than less confusing, so I don't recommend using it all the time. (This is also why there isn't a flip function in the F# standard library: because it's not always the best solution. And because it's trivial to write yourself, its lack in the standard library is not a big deal). But sometimes using flip makes code simpler, and I think this is one of those cases.
P.S. The flip function could also have been written like this:
let flip f a b = f b a
This definition is identical to the let flip f = fun a b -> f b a definition I used in the main example. Do you know why?
I have been working with some f# parsers and some streaming software and I find myself using this pattern more and more. I find it to be a natural alternative to sequences and it has some natural advantages.
here are some example functions using the type.
type foldedSequence<'a> =
| Empty
| Value of ' a * (unit -> 'a foldedSequence)
let rec createFoldedSequence fn state =
match fn state with
| None -> Empty
| Some(value, nextState) ->
Value(value, (fun () -> unfold fn nextState))
let rec filter predicate =
function
| Empty -> Empty
| Value(value, nextValue) ->
let next() = filter predicate(nextValue())
if predicate value then Value(value, next)
else next()
let toSeq<'t> =
Seq.unfold<'t foldedSequence, 't>(function
| Empty -> None
| Value(value, nextValue) -> Some(value, nextValue()))
It has been very helpful I would like to know if it has a name so I can research some tips and tricks for it
To add to the existing answers, I think Haskellers might call a generalised version of this this a list monad transformer. The idea is that your type definition looks almost like ordinary F# list except that there is some additional aspect to it. You can imagine writing this as:
type ListTransformer<'T> =
| Empty
| Value of 'T * M<ListTransformer<'T>>
By supplying specific M, you can define a number of things:
M<'T> = 'T gives you the ordinary F# list type
M<'T> = unit -> 'T gives you your sequence that can be evaluated lazily
M<'T> = Lazy<'T> gives you LazyList (which caches already evaluated elements)
M<'T> = Async<'T> gives you asynchronous sequences
It is also worth noting that in this definition LazyTransformer<'T> is not itself a delayed/lazy/async value. This can cause problems in some cases - e.g. when you need to perform some async operation to decide whether the stream is empty - and so a better definition is:
type ListTransformer<'T> = M<ListTransformerInner<'T>>
and ListTransformerInner<'T> =
| Empty
| Value of 'T * ListTransformer<'T>
This sounds like LazyList which used to be in the "powerpack" and I think now lives here:
http://fsprojects.github.io/FSharpx.Collections/reference/fsharpx-collections-lazylist-1.html
https://github.com/fsprojects/FSharpx.Collections/blob/master/src/FSharpx.Collections/LazyList.fs
Your type is close to how an iteratee would be defined, and since you already mention streaming, this might be the concept you're looking for.
Iteratee IO is an approach to lazy IO outlined by Oleg Kiselyov. Apart from Haskell, implementations exist for major functional languages, including F# (as part of FSharpx.Extras).
This is how FSharpx defines an Iteratee:
type Iteratee<'Chunk,'T> =
| Done of 'T * Stream<'Chunk>
| Error of exn
| Continue of (Stream<'Chunk> -> Iteratee<'Chunk,'T>)
See also this blog post: Iteratee in F# - part 1. Note that there doesn't seem to be a part 2.
If the answer to this is "you are going about it all wrong", by all means let me know a more proper way. I had code which was structured like this:
type Res<'T> =
| E of (DC -> 'T)
| V of 'T
Now this type was primarily used directly, with a lot of inline code that did manual per-case binding, which is a lot of boilerplate I am trying to get rid of, so I figured I turn it into a computation expression. It wasn't too hard to get map, bind and apply right.
State was carried along through DC but this was cumbersome to get right, so I changed it to the following, which is a common signature I see in discussions with the state monad.
type Res<'T> =
| E of (DC -> DC * 'T)
| V of 'T
Then I decided to take it to the next level and introduce the Delayed monad (or Eventually or whatever its name is). So I changed my type as follows, making it recursive:
type Res<'T> =
| E of (DC -> DC * Res<'T>)
| V of 'T
I tried some variants of the following, but keep getting:
The resulting type would be infinite when unifying ''a' and 'Res<'a> -> Res<'b>'
(usually happens when I do not invoke the return, i.e. the Res.E <| below)
Or I can't seem to get my types right, the following (understandably) throws a type error, but I'm having a blind spot fixing it:
This expression was expected to have type 'Res<'a>' but here has type 'DC * Res<'a>'.
let rec bind k res =
match res with
| Res.V v -> k v // not delayed, should it be?
| Res.E e ->
Res.E <| fun dc -> bind k (e dc) // here's my error, on 'e dc'
//(fun dc -> dc, bind f (e dc))
bind k res
I understand that the signature should be ('a -> Res<'b>) -> Res<'a> -> XRes<'b>. The problem comes from getting the recursion right, at least in my head. I'm not even sure why I am feeding the result to Res.E, as in my understanding, the k continuation should already return this type anyway.
Also, I currently have the return as follows (following Steve Horsfield):
let result v = Res.V v
But also noticed in some posts (notably the hilarious Frankenfunctor) this:
let result v = Res.E <| fun dc -> dc, Res.V v
Maybe I am following a pattern I shouldn't have, but it seemed a good idea at the time, especially in trying to refactor zillions of boilerplate code and replace it with computation expressions, but perhaps I should stick to the direct evaluation, it fit in my head ;).
But I feel like I'm close... Any ideas?
I'm not quite sure what the meaning of this monad would be, but
Ok, after thinking about it a bit and reading the question's header :- ), I do understand what it means, and I can see how to build bind for it.
Your mistake is that the function wrapped in Res.E should return a tuple, but you're having it return just Res<'b> by recursively calling bind. And to mirror that, you're passing the result of e to recursive bind call in place of Res<'b> parameter, while e actually returns a tuple.
To do this correctly, you need to destructure the result of e, then pass second part to recursive bind call, and pair its result with the first part:
let rec bind (k: 'a -> 'b Res) (res: 'a Res) : 'b Res =
match res with
| V a -> k a
| E e ->
E <| fun dc ->
let dc', res' = e dc
dc', bind k res'
The terminal case, I don't believe should be also delayed. That is, I don't see a reason for it. As far as I understand, the interpretation of the V x case should be "a computation that doesn't change state and returns x", in which case making it delayed doesn't add anything but an extra lambda-expression.
Have a look at this F#/OCaml code:
type AllPossible =
| A of int
| B of int*int
| ...
| Z of ...
let foo x =
....
match x with
| A(value) | B(value,_) -> (* LINE 1 *)
(* do something with the first (or only, in the case of A) value *)
...
(* now do something that is different in the case of B *)
let possibleData =
match x with
| A(a) -> bar1(a)
| B(a,b) -> bar2(a+b)
| _ -> raise Exception (* the problem - read below *)
(* work with possibleData *)
...
| Z -> ...
So what is the problem?
In function foo, we pattern match against a big list of types.
Some of the types share functionality - e.g. they have common
work to do, so we use "|A | B ->" in LINE 1, above.
We read the only integer (in the case of A), or the first integer
(in the case of B) and do something with it.
Next, we want to do something that is completely different, depending
on whether we work on A or B (i.e. call bar1 or bar2).
We now have to pattern match again, and here's the problem: In this
nested pattern match, unless we add a 'catchAll' rule (i.e. '_'),
the compiler complains that we are missing cases - i.e. it doesn't
take into account that only A and B can happen here.
But if we add the catchAll rule, then we have a far worse problem:
if at some point we add more types in the list of LINE1
(i.e. in the line '|A | B ->' ... then the compiler will NOT help
us in the nested match - the '_' will catch them, and a bug will
be detected at RUNTIME. One of the most important powers of
pattern matching - i.e. detecting such errors at compile-time - is lost.
Is there a better way to write this kind of code, without having
to repeat whatever work is shared amongst A and B in two separate
rules for A and B? (or putting the A-and-B common work in a function
solely created for the purpose of "local code sharing" between A and B?)
EDIT: Note that one could argue that the F# compiler's behaviour is buggy in this case -
it should be able to detect that there's no need for matching beyond A and B
in the nested match.
If the datatype is set in stone - I would also prefer local function.
Otherwise, in OCaml you could also enjoy open (aka polymorphic) variants :
type t = [`A | `B | `C]
let f = function
| (`A | `B as x) ->
let s = match x with `A -> "a" | `B -> "b" in
print_endline s
| `C -> print_endline "ugh"
I would just put the common logic in a local function, should be both faster and more readable. Matches nested that way is pretty hard to follow, and putting the common logic in a local function allows you to ditch the extra matching in favour of something that'll get inlined anyway.
Hmm looks like you need to design the data type a bit differently such as:
type AorB =
| A of int
| B of int * int
type AllPossible =
| AB of AorB
| C of int
.... other values
let foo x =
match x with
| AB(v) ->
match v with
| A(i) -> () //Do whatever need for A
| B(i,v) -> () // Do whatever need for B
| _ -> ()
Perhaps the better solution is that rather than
type All =
|A of int
|B of int*int
you have
type All =
|AorB of int * (int Option)
If you bind the data in different ways later on you might be better off using an active pattern rather than a type, but the result would be basically the same
I don't really agree that this should be seen as a bug - although it would definitely be convenient if the case was handled by the compiler.
The C# compiler doesn't complain to the following and you wouldn't expect it to:
var b = true;
if (b)
if (!b)
Console.WriteLine("Can never be reached");