How to extract data from F# list - f#

Following up my previous question, I'm slowly getting the hang of FParsec (though I do find it particularly hard to grok).
My next newbie F# question is, how do I extract data from the list the parser creates?
For example, I loaded the sample code from the previous question into a module called Parser.fs, and added a very simple unit test in a separate module (with the appropriate references). I'm using XUnit:
open Xunit
[<Fact>]
let Parse_1_ShouldReturnListContaining1 () =
let interim = Parser.parse("1")
Assert.False(List.isEmpty(interim))
let head = interim.Head // I realise that I have only one item in the list this time
Assert.Equal("1", ???)
Interactively, when I execute parse "1" the response is:
val it : Element list = [Number "1"]
and by tweaking the list of valid operators, I can run parse "1+1" to get:
val it : Element list = [Number "1"; Operator "+"; Number "1"]
What do I need to put in place of my ??? in the snippet above? And how do I check that it is a Number, rather than an Operator, etc.?

F# types (including lists) implement structural equality. This means that if you compare two lists that contain some F# types using =, it will return true when the types have the same length and contain elements with the same properties.
Assuming that the Element type is a discriminated union defined in F# (and is not an object type), you should be able to write just:
Assert.Equal(interim, [Number "1"; Operator "+"; Number "1"])
If you wanted to implement the equality yourself, then you could use pattern matching;
let expected = [Number "1"]
match interim, expected with
| Number a, Number b when a = b -> true
| _ -> false

Related

Extending Query Expressions

Are there any documents or examples out there on how one can extend/add new keywords to query expressions? Is this even possible?
For example, I'd like to add a lead/lag operator.
In addition to the query builder for the Rx Framework mentioned by #pad, there is also a talk by Wonseok Chae from the F# team about Computation Expressions that includes query expressions. I'm not sure if the meeting was recorded, but there are very detailed slides with a cool example on query syntax for generating .NET IL code.
The source code of the standard F# query builder is probably the best resource for finding out what types of operations are supported and how to annotate them with attributes.
The key attributes that you'll probably need are demonstrated by the where clause:
[<CustomOperation("where",MaintainsVariableSpace=true,AllowIntoPattern=true)>]
member Where :
: source:QuerySource<'T,'Q> *
[<ProjectionParameter>] predicate:('T -> bool) -> QuerySource<'T,'Q>
The CustomOperation attribute defines the name of the operation. The (quite important) parameter MaintainsVariableSpace allows you to say that the operation returns the same type of values as it takes as the input. In that case, the variables defined earlier are still available after the operation. For example:
query { for p in db.Products do
let name = p.ProductName
where (p.UnitPrice.Value > 100.0M)
select name }
Here, the variables p and name are still accessible after where because where only filters the input, but it does not transform the values in the list.
Finally, the ProjectionParameter allows you to say that p.UnitValue > 100.0M should actually be turned into a function that takes the context (available variables) and evaluates this expression. If you do not specify this attribute, then the operation just gets the value of the argument as in:
query { for p in .. do
take 10 }
Here, the argument 10 is just a simple expression that cannot use values in p.
Pretty cool feature for the language. Just implemented the reverse to query QuerySource.
Simple example, but just a demonstration.
module QueryExtensions
type ExtendedQueryBuilder() =
inherit Linq.QueryBuilder()
/// Defines an operation 'reverse' that reverses the sequence
[<CustomOperation("reverse", MaintainsVariableSpace = true)>]
member __.Reverse (source : Linq.QuerySource<'T,System.Collections.IEnumerable>) =
let reversed = source.Source |> List.ofSeq |> List.rev
new Linq.QuerySource<'T,System.Collections.IEnumerable>(reversed)
let query = ExtendedQueryBuilder()
And now it being used.
let a = [1 .. 100]
let specialReverse =
query {
for i in a do
select i
reverse
}

How to declare an immutable graph with circular references?

I want to declare a graph of all states where the edges represent contiguous states. I think what I am trying to do might be called "tying the knot" (not sure about that though). It's not working like I expected, and I have a couple of questions.
First, I want a State type that has a string name and a list of contiguous states. But this declaration gives compiler error "...immediate cyclic reference...":
type State = string * (State list)
This way works:
type State(name:string, contigs: (State list)) =
let name = name
let contigs = contigs
But it's really not a requirement to name the members. A tuple is fine. How can I make that terse syntax work?
Second, the following code attempts to declare what should be three graphs of contiguous states (HI and AK are graphs consisting of a single node, all the remaining states constitute the last graph), followed by a list of all nodes. (For brevity I've only actually declared a handful of states here):
let rec hi = State("hi", [])
and mo = State("mo", [il ia])
and il = State("il", [mo])
and ia = State("ia", [mo])
and states = [hi,mo,il,ia]
This gives a variety of errors though including "mo will eventually be evaluated as part of it's own definition" and "expression was expected to have type 'a->'b but here has type State". I thought the 'rec' and 'and' keywords would allow this to work. Can I define this self referencing graph? If so, how?
The problem is your data structure and using invalid list element delimiters (should be semicolon). This works: (see edit)
type State =
| State of string * State list
let rec hi = State("hi", [])
and mo = State("mo", [il; ia])
and il = State("il", [mo])
and ia = State("ia", [mo])
let states = [hi; mo; il; ia]
Recursive references will be materialized as thunks (lazy). So you could, with a bit more typing do the same thing yourself with mutable lazys--just FYI--what you have is idiomatic.
EDIT
Intellisense didn't have a problem with it, but the compiler says
Recursive values cannot appear directly as a construction of the type 'List`1' within a recursive binding. This feature has been removed from the F# language. Consider using a record instead.
You can fix this by using seq instead of list.
type State =
| State of string * State seq
let rec hi = State("hi", [])
and mo = State("mo", seq { yield il; yield ia })
and il = State("il", seq { yield mo })
and ia = State("ia", seq { yield mo })
let states = [hi; mo; il; ia]
Although what Daniel says is correct I would contest the assertion that it is "idiomatic" because that does not produce a very useful data structure for representing graphs in the general case. Specifically, it only permits the addition of new vertices and edges from them but not adding or removing edges between existing vertices. In particular, this basically means your graph must be statically defined as a constant in your source code so you cannot load such a graph from disk easily.
The idiomatic purely functional representation of a graph is to replace dereferences with dictionary lookups. For example, represent the graph as a Map from vertices to Sets of vertices to which there are edges:
> let g =
Map["hi", set[]; "mo", set["il"; "ia"]; "il", set["mo"]; "ia", set["mo"]];;
val g : Map<string,Set<string>> =
map
[("hi", set []); ("ia", set ["mo"]); ("il", set ["mo"]);
("mo", set ["ia"; "il"])]
For example, you can lookup the vertices directly reachable via edges from mo like this:
> g.["mo"];;
val it : Set<string> = set ["ia"; "il"]
This is easier to debug than the mutable representation but it has significant disadvantages:
Lookup in a purely functional dictionary like Map is at least 200× slower than dereferencing a pointer for traversing graphs (according to a quick test here).
The garbage collector no longer reclaims unreachable subgraphs for you. The imperative solution is to use a weak dictionary but there are no known purely functional weak dictionaries.
So this is only feasible if performance and leaks will not be a problem. This is most commonly the case when your graphs are small or static.

Transform an Abstract Syntax Tree (AST) in F#

I am trying to design an AST for a decision logic table. One of the things I would like to be able to do with the discriminated union that represents my AST is transform parts of it for different reasons. For clarity I will give you an example
Decision Logic Table
# VAR = 10 ;Y;
The above can be read as there is one rule and the condition VAR = 10 enters this rule with a Y entry.
Abstract Syntax Tree Definition (simplified for this example)
type expression =
| Value of double
| Variable of string
| Equality of expression * expression
type entry =
| Entry of string
type entries =
| Entries of entry list
type conditional =
| ConditionEntries of expression * entries
type condition
| Condition of expression * string
type rule =
| Rule of condition list
Rendered (before transform)
ConditionEntries(
Equality(
Variable("VAR"),
Value(10.0)),
Entries(["Y"]))
Rendered (after transform)
Rule(
Condition(
Equality(
Variable("VAR"),
Value(10.0)
),
Entry("Y")
)
)
Now what I would like to do is transform the above tree to expand the rules that are represented in the entries. My thinking was I could use a recursive function and pattern-matching to do this but I am having a little trouble wrapping my head around it right now.
I guess in essence what I am trying to do is whenever I see a ConditionEntries node, I want to emit a new Rule for every string in the Entries list where the Condition is combined with the Entry. Does that make any sense?
Thanks in advance for any advice.
p.s. I haven't quite tried to compile the above example, so please forgive any grammatical errors.
Hmm, based on your AST, which is awfully broken up, here is a tranform function which produces the output from input you desire (though it's not recursive, just uses List.map with some pattern matching. expression is your only recursive type but it doesn't look like you want to process it recursively?):
let ex1 =
ConditionEntries(
Equality(
Variable("VAR"),
Value(10.0)),
Entries([Entry("Y")]))
let ex2 =
ConditionEntries(
Equality(
Variable("VAR"),
Value(10.0)),
Entries([Entry("X");Entry("Y");Entry("Z")]))
let transform ces =
match ces with
| ConditionEntries(x, Entries(entries)) ->
entries
|> List.map (function Entry(entry) -> Condition(x, entry))
//FSI output:
> transform ex1;;
val it : condition list =
[Condition (Equality (Variable "VAR",Value 10.0),"Y")]
> transform ex2;;
val it : condition list =
[Condition (Equality (Variable "VAR",Value 10.0),"X");
Condition (Equality (Variable "VAR",Value 10.0),"Y");
Condition (Equality (Variable "VAR",Value 10.0),"Z")]

Writing F# code to parse "2 + 2" into code

Extremely just-started-yesterday new to F#.
What I want: To write code that parses the string "2 + 2" into (using as an example code from the tutorial project) Expr.Add(Expr.Num 2, Expr.Num 2) for evaluation. Some help to at least point me in the right direction or tell me it's too complex for my first F# project. (This is how I learn things: By bashing my head against stuff that's hard)
What I have: My best guess at code to extract the numbers. Probably horribly off base. Also, a lack of clue.
let script = "2 + 2";
let rec scriptParse xs =
match xs with
| [] -> (double)0
| y::ys -> (double)y
let split = (script.Split([|' '|]))
let f x = (split[x]) // "This code is not a function and cannot be applied."
let list = [ for x in 0..script.Length -> f x ]
let result = scriptParse
Thanks.
The immediate issue that you're running into is that split is an array of strings. To access an element of this array, the syntax is split.[x], not split[x] (which would apply split to the singleton list [x], assuming it were a function).
Here are a few other issues:
Your definition of list is probably wrong: x ranges up to the length of script, not the length of the array split. If you want to convert an array or other sequence to a list you can just use List.ofSeq or Seq.toList instead of an explicit list comprehension [...].
Your "casts" to double are a bit odd - that's not the right syntax for performing conversions in F#, although it will work in this case. double is a function, so the parentheses are unnecessary and what you are doing is really calling double 0 and double y. You should just use 0.0 for the first case, and in the second case, it's unclear what you are converting from.
In general, it would probably be better to do a bit more design up front to decide what your overall strategy will be, since it's not clear to me that you'll be able to piece together a working parser based on your current approach. There are several well known techniques for writing a parser - are you trying to use a particular approach?

How to create a recursive data structure value in (functional) F#?

How can a value of type:
type Tree =
| Node of int * Tree list
have a value that references itself generated in a functional way?
The resulting value should be equal to x in the following Python code, for a suitable definition of Tree:
x = Tree()
x.tlist = [x]
Edit: Obviously more explanation is necessary. I am trying to learn F# and functional programming, so I chose to implement the cover tree which I have programmed before in other languages. The relevant thing here is that the points of each level are a subset of those of the level below. The structure conceptually goes to level -infinity.
In imperative languages a node has a list of children which includes itself. I know that this can be done imperatively in F#. And no, it doesn't create an infinite loop given the cover tree algorithm.
Tomas's answer suggests two possible ways to create recursive data structures in F#. A third possibility is to take advantage of the fact that record fields support direct recursion (when used in the same assembly that the record is defined in). For instance, the following code works without any problem:
type 'a lst = Nil | NonEmpty of 'a nelst
and 'a nelst = { head : 'a; tail : 'a lst }
let rec infList = NonEmpty { head = 1; tail = infList }
Using this list type instead of the built-in one, we can make your code work:
type Tree = Node of int * Tree lst
let rec x = Node(1, NonEmpty { head = x; tail = Nil })
You cannot do this directly if the recursive reference is not delayed (e.g. wrapped in a function or lazy value). I think the motivation is that there is no way to create the value with immediate references "at once", so this would be awkward from the theoretical point of view.
However, F# supports recursive values - you can use those if the recursive reference is delayed (the F# compiler will then generate some code that initializes the data structure and fills in the recursive references). The easiest way is to wrap the refernece inside a lazy value (function would work too):
type Tree =
| Node of int * Lazy<Tree list>
// Note you need 'let rec' here!
let rec t = Node(0, lazy [t; t;])
Another option is to write this using mutation. Then you also need to make your data structure mutable. You can for example store ref<Tree> instead of Tree:
type Tree =
| Node of int * ref<Tree> list
// empty node that is used only for initializataion
let empty = Node(0, [])
// create two references that will be mutated after creation
let a, b = ref empty, ref empty
// create a new node
let t = Node(0, [a; b])
// replace empty node with recursive reference
a := t; b := t
As James mentioned, if you're not allowed to do this, you can have some nice properties such as that any program that walks the data structure will terminate (because the data-structrue is limited and cannot be recursive). So, you'll need to be a bit more careful with recursive values :-)

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