I have created a minimax function that determines the best possible move from a game state. Currently, it plays great except that it thinks that the opponent will always perfectly resulting in bad moves starting from gamestates (a possible board) like this:
X _ _
_ O _
_ _ _
Computer think that no matter what he does it will result in a tie, because the opponent will play perfectly. So he chooses the first move make a tie, resulting in this board:
X X _
_ O _
_ _ _
Where this move would've been better, when playing against a human opponent who makes mistakes.
X _ _
_ O _
_ _ X
How can I avoid this?
Related
I am trying to work out whether there is a particularly neat or efficient way of truncating a string after the final occurrence of a specific element. For my purposes, it is a monomorphized string list and the string I am looking for the final (highest index) occurrence of is known at compile-time, since I am only using it in one case.
The motivation for this is to find the nearest ancestor in a Unix directory system of the CWD whose name in its parent is a particular folder name. I.E., if I wanted to find the nearest ancestor called bin and I was running the executable from a CWD of /home/anon/bin/projects/sample/src/bin/foo/, then I would want to get back /home/anon/bin/projects/sample/src/bin
The current implementation I am using is the following:
let reverse_prune : tgt:string -> string -> string =
let rec drop_until x ys =
match ys with
| [] -> []
| y :: _ when x = y -> ys
| _ :: yt -> drop_until x yt
in
fun ~tgt path ->
String.split_on_char '/' path
|> List.rev |> drop_until tgt |> List.rev |> String.concat "/"
It isn't a particularly common or expensive code-path so there isn't actually a real need to optimize, but since I am still trying to learn practical OCaml techniques, I wanted to know if there was a cleaner way of doing this.
I also realize that it may technically be possible to avoid the string-splitting altogether and just operate on the raw CWD string without splitting it. I am, of course, welcome to such suggestions as well, but I am specifically curious if there is something that would replace the List.rev |> drop_until tgt |> List.rev snippet, rather than solve the overall problem in a different way.
I don't think this has anything to do with OCaml actually since I'd say the easiest way to do this is by using a regular expression:
let reverse_prune tgt path =
let re =
Str.regexp (Format.sprintf {|^[/a-zA-Z_-]*/%s\([/a-zA-Z_-]*\)$|} tgt)
in
Str.replace_first re {|\1|} path
let () =
reverse_prune "bin" "/home/anon/bin/projects/sample/src/bin/foo/"
|> Format.printf "%s#."
Is there a reason you want to reimplement regular expression searching in a string? If no, just use a solution like mine, I'd say.
If you want the part that comes before just change the group:
let reverse_prune tgt path =
let re =
Str.regexp (Format.sprintf {|^\([/a-zA-Z_-]*/\)%s[/a-zA-Z_-]*$|} tgt)
in
Str.replace_first re {|\1|} path
I was wondering what would be a good strategy to understand if pattern-matching in SML will proceed the Match warning.
Consider the following function:
fun f 7 (x,y) = x * 5.1 | f x (y,#"a") = y;
From first glance, it looks like it does not provide the Match warning. But if I'll run it, it will.
From my point of view, we handle all of the cases. which case we don't handle? even if f 7 (x,#"a") we know which case should be (first one).
My question is, how to decide that the function will output that waning.
Also, I would be glad for an answer why the following function is invalid:
fun f (x::xs) (y::ys) (z::zs) = y::xs::ys::zs;
without zs its valid. how does zs change it?
My question is, how to decide that the function will output that waning.
The compiler has an algorithm that decides this.
Either use the compiler and have it warn you, or use a similar heuristic in your head.
See Warnings for pattern matching by Luc Maranget (2007).
It covers the problem, algorithm and implementation of finding missing and duplicate patterns.
A useful heuristic: Line patterns up, e.g. like:
fun fact 0 = 1
| fact n = n * fact (n - 1)
and ask yourself: Is there any combination of values that is not addressed by exactly one case of the function? Each function case should address some specific, logical category of the input. Since your example isn't a practical example, this approach cannot be used, since there are no logical categories over the input.
And fact is a bit simple, since it's very easy to decide if it belongs to the categories 0 or n.
And yet, is the value ~1 correctly placed in one of these categories?
Here is a practical example of a function with problematic patterns:
fun hammingDistance [] [] = SOME 0
| hammingDistance (x::xs) (y::ys) =
if length xs <> length ys then NONE else
if x = y
then hammingDistance xs ys
else Option.map (fn d => d + 1) (hammingDistance xs ys)
It may seem that there are two logical cases: Either the lists are empty, or they're not:
The input lists are empty, in which case the first body is activated.
The input lists are not empty, in which case they have different or equal length.
If they have different lengths, NONE.
If they have equal lengths, compute the distance.
There's a subtle bug, of course, because the first list can be empty while the second one isn't, and the second list can be empty while the first one isn't. And if this is the case, the second body is never hit, and the distinction between different / equal lengths is never made. Because the task of categorizing is split between pattern matching and if-then-else with precedence to pattern matching.
What I do personally to catch problems like these preemptively is to think like this:
When I'm pattern matching on a list (just for example), I have to cover two constructors (1. [], 2. ::), and when I'm pattern matching on two lists, I have to cover the Cartesian product of its constructors (1. [], [], 2. [], ::, 3. ::, [], and 4. ::, ::).
I can count only two patterns/bodies, and none of them aim to cover more than one of my four cases, so I know that I'm missing some.
If there had been a case with variables, I have to ask how many of my common cases it covers, e.g.
fun hammingDistance (x::xs) (y::ys) =
if x = y
then hammingDistance xs ys
else Option.map (fn d => d + 1) (hammingDistance xs ys)
| hammingDistance [] [] = SOME 0
| hammingDistance _xs _ys = NONE
Here there's only three patterns/bodies, but the last one is a catch-all; _xs and _ys match all possible lists, empty or non-empty, except if they're matched by one of the previous patterns first. So this third case accounts for both of 2. [], :: and 3. ::, [].
So I can't simply count each pattern/body once. Some may account for more than one class of input if they contain very general patterns via pattern variables. And some may account for less of the total input space if they contain overly specific patterns via multiple constructors. E.g.
fun pairs (x::y::rest) = (x, y) :: pairs rest
| pairs [] = []
Here x::y::rest is so specific that I'm not covering the case of exactly one element.
I've been using the library FsVerbalExpressions to write some functions. I'm having a hard time trying to build a regEx programmatically.
For example, if I have a string "Int. Bus. Mach", I can remove periods and whitespaces and end up with the array
let splitString = [|"Int"; "Bus"; "Mach"|]
What I'd like to do is build a regular expression from splitString so that its result is:
let hardCoded =
VerbEx()
|> startOfLine
|> then' "Int"
|> anything
|> whiteSpace
|> then' "Bus"
|> anything
|> whiteSpace
|> then' "Mach"
hardCoded;;
val it : VerbEx =
^(Int)(.*)\s(Bus)(.*)\s(Mach) {MatchTimeout = -00:00:00.0010000;
Regex = ^(Int)(.*)\s(Bus)(.*)\s(Mach);
RegexOptions = None;
RightToLeft = false;}
My problem is that I don't know how to build this programmatically so that, if the original string is "This is a much bigger string", the entire regEx is built from code rather than hard coded. I can create individual regular expressions with
let test =
splitString
|> Array.map (fun thing -> VerbEx()
|> then' thing)
|> Array.toList
but this is a list of VerbEx() rather than a single VerbEx() above.
Does anyone know how I could build a regEx with FsVerbalExpressions programmatically?
Thanks in advance for your help!
Think about it like this: you need to start with some initial value, VerbEx() |> startOfLine, and then apply to it repeating patterns that have the general shape of anything |> whitespace |> then' word.
You can also think about it in inductive terms: you're producing a series of values, where each value is expressed as previousValue |> anything |> whitespace |> then' word - that is, each next value in the series is previous value with some change applied to it. The very last element of such series is your final answer.
Such operation - producing a series of values, where each value is expressed as a modification of the previous one, - is traditionally called fold. And sure enough, F# has standard library functions for performing this operation:
let applyChange previousValue word =
previousValue |> anything |> whitespace |> then' word
let initialValue = VerbEx() |> startOfLine
let finalAnswer = splitString |> Array.fold applyChange initialValue
Or you can roll that all together:
let finalAnswer =
splitString
|> Array.fold
(fun previousValue word -> previousValue |> anything |> whitespace |> then' word)
(VerbEx() |> startOfLine)
// But pattern matching also makes it easy.
def penultimateRecursive[A](ls: List[A]): A = ls match {
case h :: _ :: Nil => h
case _ :: tail => penultimateRecursive(tail)
case _ => throw new NoSuchElementException
}
Can someone comment what this is doing line by line?
Is the [A] a generic like in c# we would do ?
h doesn't seem to be defined?
I think the major part of the algo is the recursive call:
case _ :: tail => penultimateRecursive(tail)
There doesnt' seem to be a check for 2 items in the list, and then taking the 1st item to get the 2nd last, confused!
The keys to understanding the pattern match are to realize that x :: y will only match a list with a single item x followed by the rest of the list y (which could be just Nil, or could be many elements), and that _ means "there needs to be something here, but we won't bother naming it". (And that the matches occur in order, and that lists end with Nil.)
You're correct that [A] is a generic type.
So, the first line:
case h :: _ :: Nil => h
says, if our list looks like (conceptually) Node(h) -> Node(whatever) -> Nil, then we return h. This is exactly a two-element list with the first item selected. Note that Nil does not match any arbitrary tail of the list; it matches only the end-of-list item Nil. This is because of a rule that Scala uses to distinguish the two: lower case variables are treated as wildcards that are to have the appropriate value filled in, while upper case variables are treated as constants to match. (If you must match a lower-case name, you can if surround it by backticks.)
Okay, now suppose it's not a two-element list. Then if it's not empty, it will match
case _ :: tail => penultimateRecursive(tail)
so if we haven't got a two-element list, we throw away the first item and try again. Finally, if we somehow never ended up with a two-element list, we get to
case _ => throw new NoSuchElementException
and we're done. (This could also be case Nil, actually, since this is the only possibility that doesn't match the other two entries.)
A is a type variable, meaning the function is defined generically for any type A.
h is bound by the pattern matching: the first case states, if there are exactly two elements, then call the first h and return it.
There doesnt' seem to be a check for 2 items in the list
There is: h :: _ :: Nil means "an element h, followed by any element, followed by no more elements." Nil isn't an element, it's the end of the list.
and then taking the 1st item to get the 2nd last
Taking the first of a two-element list means taking the penultimate. If the list has fewer or more elements than two, the other two cases apply.
larsmans and Rex have covered your questions, but see Chapter 9 for more details on '::' http://www.scala-lang.org/docu/files/ScalaByExample.pdf
The first line means that any list element h will be returned if h is followed by another one and a Nil pointer (at the end of the list). The actual element following to h is not important, that's why you use _ to specify that there is an element but you don't care about its value.
If the first case does not match, the second case will invoke recursion if the list has a head element and a tail of at least one element.
Lastly you bail out on lists consisting only a single element. Once again, you don't have to care about the actual value of the elements value.
I found this useful article on using Active Patterns with Regular Expressions:
http://www.markhneedham.com/blog/2009/05/10/f-regular-expressionsactive-patterns/
The original code snippet used in the article was this:
open System.Text.RegularExpressions
let (|Match|_|) pattern input =
let m = Regex.Match(input, pattern) in
if m.Success then Some (List.tl [ for g in m.Groups -> g.Value ]) else None
let ContainsUrl value =
match value with
| Match "(http:\/\/\S+)" result -> Some(result.Head)
| _ -> None
Which would let you know if at least one url was found and what that url was (if I understood the snippet correctly)
Then in the comment section Joel suggested this modification:
Alternative, since a given group may
or may not be a successful match:
List.tail [ for g in m.Groups -> if g.Success then Some g.Value else None ]
Or maybe you give labels to your
groups and you want to access them by
name:
(re.GetGroupNames()
|> Seq.map (fun n -> (n, m.Groups.[n]))
|> Seq.filter (fun (n, g) -> g.Success)
|> Seq.map (fun (n, g) -> (n, g.Value))
|> Map.ofSeq)
After trying to combine all of this I came up with the following code:
let testString = "http://www.bob.com http://www.b.com http://www.bob.com http://www.bill.com"
let (|Match|_|) pattern input =
let re = new Regex(pattern)
let m = re.Match(input) in
if m.Success then Some ((re.GetGroupNames()
|> Seq.map (fun n -> (n, m.Groups.[n]))
|> Seq.filter (fun (n, g) -> g.Success)
|> Seq.map (fun (n, g) -> (n, g.Value))
|> Map.ofSeq)) else None
let GroupMatches stringToSearch =
match stringToSearch with
| Match "(http:\/\/\S+)" result -> printfn "%A" result
| _ -> ()
GroupMatches testString;;
When I run my code in an interactive session this is what is output:
map [("0", "http://www.bob.com"); ("1", "http://www.bob.com")]
The result I am trying to achieve would look something like this:
map [("http://www.bob.com", 2); ("http://www.b.com", 1); ("http://www.bill.com", 1);]
Basically a mapping of each unique match found followed by the count of the number of times that specific matching string was found in the text.
If you think I'm going down the wrong path here please feel free to suggest a completely different approach. I'm somewhat new to both Active Patterns and Regular Expressions so I have no idea where to even begin in trying to fix this.
I also came up with this which is basically what I would do in C# translated to F#.
let testString = "http://www.bob.com http://www.b.com http://www.bob.com http://www.bill.com"
let matches =
let matchDictionary = new Dictionary<string,int>()
for mtch in (Regex.Matches(testString, "(http:\/\/\S+)")) do
for m in mtch.Captures do
if(matchDictionary.ContainsKey(m.Value)) then
matchDictionary.Item(m.Value) <- matchDictionary.Item(m.Value) + 1
else
matchDictionary.Add(m.Value, 1)
matchDictionary
Which returns this when run:
val matches : Dictionary = dict [("http://www.bob.com", 2); ("http://www.b.com", 1); ("http://www.bill.com", 1)]
This is basically the result I am looking for, but I'm trying to learn the functional way to do this, and I think that should include active patterns. Feel free to try to "functionalize" this if it makes more sense than my first attempt.
Thanks in advance,
Bob
Interesting stuff, I think everything you are exploring here is valid. (Partial) active patterns for regular expression matching work very well indeed. Especially when you have a string which you want to match against multiple alternative cases. The only thing I'd suggest with the more complex regex active patterns is that you give them more descriptive names, possibly building up a collection of different regex active patterns with differing purposes.
As for your C# to F# example, you can have functional solution just fine without active patterns, e.g.
let testString = "http://www.bob.com http://www.b.com http://www.bob.com http://www.bill.com"
let matches input =
Regex.Matches(input, "(http:\/\/\S+)")
|> Seq.cast<Match>
|> Seq.groupBy (fun m -> m.Value)
|> Seq.map (fun (value, groups) -> value, (groups |> Seq.length))
//FSI output:
> matches testString;;
val it : seq<string * int> =
seq
[("http://www.bob.com", 2); ("http://www.b.com", 1);
("http://www.bill.com", 1)]
Update
The reason why this particular example works fine without active patterns is because 1) you are only testing one pattern, 2) you are dynamically processing the matches.
For a real world example of active patterns, let's consider a case where 1) we are testing multiple regexes, 2) we are testing for one regex match with multiple groups. For these scenarios, I use the following two active patterns, which are a bit more general than the first Match active pattern you showed (I do not discard first group in the match, and I return a list of the Group objects, not just their values -- one uses the compiled regex option for static regex patterns, one uses the interpreted regex option for dynamic regex patterns). Because the .NET regex API is so feature filled, what you return from your active pattern is really up to what you find useful. But returning a list of something is good, because then you can pattern match on that list.
let (|InterpretedMatch|_|) pattern input =
if input = null then None
else
let m = Regex.Match(input, pattern)
if m.Success then Some [for x in m.Groups -> x]
else None
///Match the pattern using a cached compiled Regex
let (|CompiledMatch|_|) pattern input =
if input = null then None
else
let m = Regex.Match(input, pattern, RegexOptions.Compiled)
if m.Success then Some [for x in m.Groups -> x]
else None
Notice also how these active patterns consider null a non-match, instead of throwing an exception.
OK, so let's say we want to parse names. We have the following requirements:
Must have first and last name
May have middle name
First, optional middle, and last name are separated by a single blank space in that order
Each part of the name may consist of any combination of at least one or more letters or numbers
Input may be malformed
First we'll define the following record:
type Name = {First:string; Middle:option<string>; Last:string}
Then we can use our regex active pattern quite effectively in a function for parsing a name:
let parseName name =
match name with
| CompiledMatch #"^(\w+) (\w+) (\w+)$" [_; first; middle; last] ->
Some({First=first.Value; Middle=Some(middle.Value); Last=last.Value})
| CompiledMatch #"^(\w+) (\w+)$" [_; first; last] ->
Some({First=first.Value; Middle=None; Last=last.Value})
| _ ->
None
Notice one of the key advantages we gain here, which is the case with pattern matching in general, is that we are able to simultaneously test that an input matches the regex pattern, and decompose the returned list of groups if it does.