How to visualize/draw automata in ocaml? - ocaml

I am doing composition of automata. So at the end of that, I want to draw the composed automata also. So are there any libraries for that in ocaml? or are there ocaml wrappers written for any graph visualization tool? I have googled for it but didn't get much for ocaml. Any comments on ocamlgraph? I will get more than 100 states in composed automata.

Use ocamlgraph -- it is a graph library that can generate a dot/graphviz file for you but can also do a lot of other stuff that maybe interesting for handling your automata.
The library can do fixpoints, spanning trees, graph search, find strongly connected components, etc., etc.
Here is a complete example of some directed graph with labeled edges + module for doing depth-first-search + module for creating dot-representations of it:
(* representation of a node -- must be hashable *)
module Node = struct
type t = int
let compare = Pervasives.compare
let hash = Hashtbl.hash
let equal = (=)
end
(* representation of an edge -- must be comparable *)
module Edge = struct
type t = string
let compare = Pervasives.compare
let equal = (=)
let default = ""
end
(* a functional/persistent graph *)
module G = Graph.Persistent.Digraph.ConcreteBidirectionalLabeled(Node)(Edge)
(* more modules available, e.g. graph traversal with depth-first-search *)
module D = Graph.Traverse.Dfs(G)
(* module for creating dot-files *)
module Dot = Graph.Graphviz.Dot(struct
include G (* use the graph module from above *)
let edge_attributes (a, e, b) = [`Label e; `Color 4711]
let default_edge_attributes _ = []
let get_subgraph _ = None
let vertex_attributes _ = [`Shape `Box]
let vertex_name v = string_of_int v
let default_vertex_attributes _ = []
let graph_attributes _ = []
end)
with that you can write your program; e.g. something like this:
(* work with the graph ... *)
let _ =
let g = G.empty in
let g = G.add_edge_e ...
...
let file = open_out_bin "mygraph.dot" in
let () = Dot.output_graph file g in
...
if D.has_cycle g then ... else ...

I would just write automata as text to file (in format suitable for graphviz) and then run graphviz against that file.

Related

ML: Is it possible to create a list of structures in SML?

I am a beginner to ML/Haskell and I am trying to create a list of structures.
Actually, I am developing a web application in Urweb (functional web programming language, a lot of features from ML and Haskell.) I am trying to create an interface to Tinymce (open source rich text editor, and it consists of all the plugin such as print, link). So to manage all plugins, I am composing in the form of structure and I need one data structure to hold all the structures (Plugins in my case) and at the end stage in can be used to initialize my editor.
For example:
val plugins = [print, link, img];
and elements inside list plugins such as print is a structure:
structure print = struct
type t = string
.
.
end
How can I achieve this?
The general answer is that No you cannot create a list of
structures, the same is true as well of signatures, and functors
however; if your plugin system is built in a way in which the entry types, and exit types of each plugin are the same across all plugins, you can build a kind of closure to a structure and embed that into a function.
you can then use functors, to build up the functions of your plugin system
We start out with the interface of each "plugin".
signature DANCER =
sig
type t;
val dancer : t
val tired : t -> bool
val dance : t -> t;
end
Followed by the interface through which our application interacts with the plugin.
datatype exhaustion = Exhausted;
signature DANCING_MANIA =
sig
val dance : unit -> exhaustion;
end
The implementation of the above DANCING_MANIA signature,
accepts a DANCER, and hides the differences between plugins/structures
functor Dancer (D : DANCER) : DANCING_MANIA =
struct
fun dance() =
let fun until_exhaustion (dancer) =
if not (D.tired dancer)
then until_exhaustion(D.dance(dancer))
else Exhausted;
in until_exhaustion(D.dancer) end
end
Finally we can implement some plugins, and throw them in a list.
structure Tony :> DANCER =
struct
type t = int;
val dancer = 5;
fun tired x = x <= 0;
fun dance x = (print "tony dance!\n"; x - 1);
end
structure Annette :> DANCER =
struct
type t = real;
val dancer = 1.0;
fun tired x = x <= 0.0;
fun dance x = (print "annette dance!\n"; x - 0.2);
end
structure TonyDance = Dancer(Tony);
structure AnnetteDance = Dancer(Annette);
val dancers = [TonyDance.dance, AnnetteDance.dance];
fun danceOff (x::xs) = let val _ = x(); in danceOff(xs) end
| danceOff ([]) = ();
val _ = danceOff(dancers);
So, the idea is that while you cannot create a list of structures,
you can create a list of things, that each contain a different structure,
as long as the exposed types are uniform.

How to reduce code clutter in this function?

The function tally below is really simple: it takes a string s as argument, splits it on non-alphanumeric characters, and tallies the numbers of the resulting "words", case-insensitively.
open Core.Std
let tally s =
let get m k =
match Map.find m k with
| None -> 0
| Some n -> n
in
let upd m k = Map.add m ~key:k ~data:(1 + get m k) in
let re = Str.regexp "[^a-zA-Z0-9]+" in
let ws = List.map (Str.split re s) ~f:String.lowercase in
List.fold_left ws ~init:String.Map.empty ~f:upd
I think this function is harder to read than it should be due to clutter. I wish I could write something closer to this (where I've indulged in some "fantasy syntax"):
(* NOT VALID SYNTAX -- DO NOT COPY !!! *)
open Core.Std
let tally s =
let get m k =
match find m k with
| None -> 0
| Some n -> n ,
upd m k = add m k (1 + get m k) ,
re = regexp "[^a-zA-Z0-9]+" ,
ws = map (split re s) lowercase
in fold_left ws empty upd
The changes I did above fall primarily into three groups:
get rid of the repeated let ... in's, consolidated all the bindings (into a ,-separated sequence; this, AFAIK, is not valid OCaml);
got rid of the ~foo:-type noise in function calls;
got rid of the prefixes Str., List., etc.
Can I achieve similar effects using valid OCaml syntax?
Readability is difficult to achieve, it highly depends on the reader's abilities and familiarity with the code. I'll focus simply on the syntax transformations, but you could perhaps refactor the code in a more compact form, if this is what you are really looking for.
To remove the module qualifiers, simply open them beforehand:
open Str
open Map
open List
You must open them in that order to make sure the List values you are using there are still reachable, and not scope-overridden by the Map ones.
For labelled parameters, you may omit the labels if for each function call you provide all the parameters of the function in the function signature order.
To reduce the number of let...in constructs, you have several options:
Use a set of rec definitions:
let tally s =
let rec get m k =
match find m k with
| None -> 0
| Some n -> n
and upd m k = add m k (1 + get m k)
and re = regexp "[^a-zA-Z0-9]+"
and ws = map lowercase (split re s)
in fold_left ws empty upd
Make multiple definitions at once:
let tally s =
let get, upd, ws =
let re = regexp "[^a-zA-Z0-9]+" in
fun m k ->
match find m k with
| None -> 0
| Some n -> n,
fun g m k -> add m k (1 + g m k),
map lowercase (split re s)
in fold_left ws empty (upd get)
Use a module to group your definitions:
let tally s =
let module M = struct
let get m k =
match find m k with
| None -> 0
| Some n -> n
let upd m k = add m k (1 + get m k)
let re = regexp "[^a-zA-Z0-9]+"
let ws = map lowercase (split re s)
end in fold_left ws empty M.upd
The later is reminiscent of the Sml syntax, and perhaps better suited to proper optimization by the compiler, but it only get rid of the in keywords.
Please note that since I am not familiar with the Core Api, I might have written incorrect code.
If you have a sequence of computations on the same value, then in OCaml there is a |> operator, that takes a value from the left, and applies in to the function on the right. This can help you to "get rid of" let and in. What concerning labeled arguments, then you can get rid of them by falling back to a vanilla standard library, and make your code smaller, but less readable. Anyway, there is a small piece of sugar with labeled arguments, you can always write f ~key ~data instead of f ~key:key ~data:data. And, finally, module names can be removed either by local open syntax (let open List in ...) or by locally shorcutting it to a smaller names (let module L = List in).
Anyway, I would like to show you a code, that contains less clutter, to my opinion:
open Core.Std
open Re2.Std
open Re2.Infix
module Words = String.Map
let tally s =
Re2.split ~/"\\PL" s |>
List.map ~f:(fun s -> String.uppercase s, ()) |>
Words.of_alist_multi |>
Words.map ~f:List.length

convert a few 2-tuples to a list of lists

this is a question about ocaml lists and tuples. I have some 2-tuples of numbers (either integers or floats) and I want to convert it to a list of lists (with 2 elements). Assuming that I have defined a num type Int of int | Float of float, the conversion should give the following:
((1,1.0),(0.4,1),(0,0)) => [[Int 1;Float 1.0];[Float 0.4; Int 1];[Int 0;Int 0]]
or more precisely
let a = (1,1.0) and b = (0.4,1) and c = (0,0) in
myconversion (a,b,c) ;;
=> [[Int 1;Float 1.0];[Float 0.4; Int 1];[Int 0;Int 0]]
the point being the values a, b, c... are defined in several places in the source files (by people who use different signatures for their tuples).
The difficulty here is that I don't know the types of the elements of the 2-tuples (int or float, that varies depending on the tuple).
Your input data can't be represented in OCaml as you describe it. OCaml is strongly typed. For example, your example input list is an invalid value in OCaml:
# [(1,1.0);(0.4,1);(0,0)];;
Error: This expression has type float but an expression was expected of type
int
So what you describe as the essence of your problem (not knowing the types) is in fact not possible. You'll have to use some other method of representing the input. For example, you could just use floats for everything. Or you could use pairs of strings.
Update
The answer for the rewritten question is the same. In OCaml it's not possible not to know the type of something statically; i.e., at the time you're writing the program (unless it can be any type at all). It's not possible (or necessary) to query the type of something at runtime. So your question doesn't have an answer (at least as far as I can see).
For OCaml, you have to think with the type system rather than against it. After a while you start to really like it (or at least that's how it worked for me). I'd start by writing down the type you want your function myconverstion to have.
Update 2
I'll repeat my advice to treat your inputs as strings. Assuming you've parsed your input up into pairs of strings, here's some code that does what you want:
let myconversion coords =
let c1 s =
if String.contains s '.' then
Float (float_of_string s)
else
Int (int_of_string s)
in
let cp (a, b) = [c1 a; c1 b] in
List.map cp coords
Here's how it works for your input (reinterpreted as strings):
# myconversion [("1", "1.0"); ("0.4", "1"); ("0", "0")];;
- : fi list list = [[Int 1; Float 1.]; [Float 0.4; Int 1]; [Int 0; Int 0]]
Update 3
Here's some (crude) code that parses a file of numbers into coordinates represented as pairs of strings. It should work as long as the tuples in the input are well formed.
let coords fname =
let ic = open_in fname in
let len = in_channel_length ic in
let buf = Buffer.create 128 in
let () = Buffer.add_channel buf ic len in
let () = close_in ic in
let s = Buffer.contents buf in
let nums = Str.(split (regexp "[^0-9.]+") s) in
let rec mkcoords sofar = function
| [] | [_] -> List.rev sofar
| a :: b :: rest -> mkcoords ((a, b) :: sofar) rest
in
mkcoords [] nums
There are two distinct problems in your setup:
you don't know the type of the tuples parameters
you want to pass them as a single n-ary tuple
For problem 2, you would have to write a function for that type specifically, whereas you could mimic a type level list type by nesting couple of tuples:
myconversion a,(b,c) ;;
The reason is that with that setup, you could write a recursive polymorphic function on the type level list:
val myconversion : type a b. (a,b) -> num list
There would still be a problem on the last element though.
So, assuming that you could pass a sequence to your conversion function, and have it process elements of that sequence one by one, you would still need to find a way of selecting the proper function of pair conversion from the tuple type: that's basically ad-hoc polymorphism, ie. you would need to be able to overload a function on its parameters' types(1). Unfortunately, OCaml doesn't support that out of the box.
One possibility would be perhaps (I have no experience doing that) to implement an extension which would extract the type information of a given expression, and generate the correct code to process it in your own code.
A flexible technique consists in having that extension generate an algebraic description of the tuples types, and use that description as an equality witness in the code which will process the tuples:
type _ w =
| U : (unit * unit) w
| IF : 'a w -> ((int * float) * 'a) w
| FI : 'a w -> ((float * int) * 'a) w
(* other constructors if necessary *)
(* data *)
let a = 1,1.0
let b = 2.0, 2
let c = 3.0, 3
let d = 4, 4.0
let l = a,(b, (c,(d,((),()))))
(* witness *)
let w = IF (FI (FI (IF U)))
(* the type parameter of w should be the same as l type *)
let rec conv : type a b. (a * b) w -> (a * b) -> num list = fun w (x, xs) ->
match w with
U -> []
| IF w' -> let i,f = x in (Int I)::(Float f)::(conv w' xs)
(* etc *)
Here, we encode the type level nil list as (unit * unit) w.
A coalgebraic approach would require to register function overloads to the conversion function polymorphic signature within the extension, and let it pick the right one from the function overload dictionary.
There's a discussion on that topic on the LtU site.
Thanks to everybody who answered. I finally found a solution, using a bit of magic:
# type num = Int of int | Float of float;;
# let to_num x = if Obj.is_int (Obj.repr x) then
Int (Obj.magic (Obj.repr x) : int)
else
Float ((Obj.magic (Obj.repr x) : float));;
# let pair_to_num (a,b) = [to_num a; to_num b];;
# let myconversion (a,b,c) = [pair_to_num a; pair_to_num b; pair_to_num c];;
and the test:
# myconversion ((1,1.0),(0.4,1),(0,0));;
- : num list list = [[Int 1; Float 1.]; [Float 0.4; Int 1]; [Int 0; Int 0]]
# myconversion ((0,0),(1,1.0),(0.4,1));;
- : num list list = [[Int 0; Int 0]; [Int 1; Float 1.]; [Float 0.4; Int 1]]
Magic, the order does not matter and the type is recorded! I can then follow didier's idea to get rid of the pair of superfluous parentheses.

Linear types in OCaml

Rust has a linear type system. Is there any (good) way to simulate this in OCaml? E.g., when using ocaml-lua, I want to make sure some functions are called only when Lua is in a specific state (table on top of stack, etc).
Edit: Here's a recent paper about resource polymorphism relevant to the question: https://arxiv.org/abs/1803.02796
Edit 2: There are also a number of articles about session types in OCaml available, including syntax extensions to provide some syntactic sugar.
As suggested by John Rivers, you can use a monadic style to represent
"effectful" computation in a way that hides the linear constraint in
the effect API. Below is one example where a type ('a, 'st) t is
used to represent computation using a file handle (whose identity is
implicit/unspoken to guarantee that it cannot be duplicated), will
product a result of type 'a and leave the file handle in the state
'st (a phantom type being either "open" or "close"). You have to use
the run of the monad¹ to actually do anything, and its type ensure
that the file handles are correctly closed after use.
module File : sig
type ('a, 'st) t
type open_st = Open
type close_st = Close
val bind : ('a, 's1) t -> ('a -> ('b, 's2) t) -> ('b, 's2) t
val open_ : string -> (unit, open_st) t
val read : (string, open_st) t
val close : (unit, close_st) t
val run : ('a, close_st) t -> 'a
end = struct
type ('a, 'st) t = unit -> 'a
type open_st = Open
type close_st = Close
let run m = m ()
let bind m f = fun () ->
let x = run m in
run (f x)
let close = fun () ->
print_endline "[lib] close"
let read = fun () ->
let result = "toto" in
print_endline ("[lib] read " ^ result);
result
let open_ path = fun () ->
print_endline ("[lib] open " ^ path)
end
let test =
let open File in
let (>>=) = bind in
run begin
open_ "/tmp/foo" >>= fun () ->
read >>= fun content ->
print_endline ("[user] read " ^ content);
close
end
(* starting with OCaml 4.13, you can use binding operators:
( let* ) instead of ( >>= ) *)
let test =
let open File in
let ( let* ) = bind in
run begin
let* () = open_ "/tmp/foo" in
let* content = read in
print_endline ("[user] read " ^ content);
close
end
Of course, this is only meant to give you a taste of the style of
API. For more serious uses, see Oleg's monadic
regions examples.
You may also be interested in the research programming language
Mezzo, which aims to
be a variant of ML with finer-grained control of state (and related
effectful patterns) through a linear typing discipline with separated
resources. Note that it is only a research experiment for now, not
actually aimed at users. ATS is also relevant,
though finally less ML-like. Rust may actually be a reasonable
"practical" counterpart to these experiments.
¹: it is actually not a monad because it has no return/unit combinator, but the point is to force type-controlled sequencing as the monadic bind operator does. It could have a map, though.

Convert 'a list to a Set?

Is it really true that OCaml doesn't have a function which converts from a list to a set?
If that is the case, is it possible to make a generic function list_to_set? I've tried to make a polymorphic set without luck.
Fundamental problem: Lists can contain elements of any types. Sets (assuming you mean the Set module of the standard library), in contrary, rely on a element comparison operation to remain balanced trees. You cannot hope to convert a t list to a set if you don't have a comparison operation on t.
Practical problem: the Set module of the standard library is functorized: it takes as input a module representing your element type and its comparison operation, and produces as output a module representing the set. Making this work with the simple parametric polymoprhism of lists is a bit sport.
To do this, the easiest way is to wrap your set_of_list function in a functor, so that it is itself parametrized by a comparison function.
module SetOfList (E : Set.OrderedType) = struct
module S = Set.Make(E)
let set_of_list li =
List.fold_left (fun set elem -> S.add elem set) S.empty li
end
You can then use for example with the String module, which provides a suitable compare function.
module SoL = SetOfList(String);;
SoL.S.cardinal (SoL.set_of_list ["foo"; "bar"; "baz"]);; (* returns 3 *)
It is also possible to use different implementation of sets which are non-functorized, such as Batteries and Extlib 'PSet' implementation (documentation). The functorized design is advised because it has better typing guarantees -- you can't mix sets of the same element type using different comparison operations.
NB: of course, if you already have a given set module, instantiated form the Set.Make functor, you don't need all this; but you conversion function won't be polymorphic. For example assume I have the StringSet module defined in my code:
module StringSet = Set.Make(String)
Then I can write stringset_of_list easily, using StringSet.add and StringSet.empty:
let stringset_of_list li =
List.fold_left (fun set elem -> StringSet.add elem set) StringSet.empty li
In case you're not familiar with folds, here is a direct, non tail-recursive recursive version:
let rec stringset_of_list = function
| [] -> StringSet.empty
| hd::tl -> StringSet.add hd (stringset_of_list tl)
Ocaml 3.12 has extensions (7,13 Explicit naming of type variables and 7,14 First-class modules) that make it possible to instantiate and pass around modules for polymorphic values.
In this example, the make_set function returns a Set module for a given comparison function and the build_demo function constructs a set given a module and a list of values:
let make_set (type a) compare =
let module Ord = struct
type t = a
let compare = compare
end
in (module Set.Make (Ord) : Set.S with type elt = a)
let build_demo (type a) set_module xs =
let module S = (val set_module : Set.S with type elt = a) in
let set = List.fold_right S.add xs S.empty in
Printf.printf "%b\n" (S.cardinal set = List.length xs)
let demo (type a) xs = build_demo (make_set compare) xs
let _ = begin demo ['a', 'b', 'c']; demo [1, 2, 3]; end
This doesn't fully solve the problem, though, because the compiler doesn't allow the return value to have a type that depends on the module argument:
let list_to_set (type a) set_module xs =
let module S = (val set_module : Set.S with type elt = a) in
List.fold_right S.add xs S.empty
Error: This `let module' expression has type S.t
In this type, the locally bound module name S escapes its scope
A possible work-around is to return a collection of functions that operate on the hidden set value:
let list_to_add_mem_set (type a) set_module xs =
let module S = (val set_module : Set.S with type elt = a) in
let set = ref (List.fold_right S.add xs S.empty) in
let add x = set := S.add x !set in
let mem x = S.mem x !set in
(add, mem)
If you don't mind a very crude approach, you can use the polymorphic hash table interface. A hash table with an element type of unit is just a set.
# let set_of_list l =
let res = Hashtbl.create (List.length l)
in let () = List.iter (fun x -> Hashtbl.add res x ()) l
in res;;
val set_of_list : 'a list -> ('a, unit) Hashtbl.t = <fun>
# let a = set_of_list [3;5;7];;
val a : (int, unit) Hashtbl.t = <abstr>
# let b = set_of_list ["yes";"no"];;
val b : (string, unit) Hashtbl.t = <abstr>
# Hashtbl.mem a 5;;
- : bool = true
# Hashtbl.mem a 6;;
- : bool = false
# Hashtbl.mem b "no";;
- : bool = true
If you just need to test membership, this might be good enough. If you wanted other set operations (like union and intersection) this isn't a very nice solution. And it's definitely not very elegant from a typing standpoint.
Just extend the original type, as shown in
http://www.ffconsultancy.com/ocaml/benefits/modules.html
for the List module:
module StringSet = Set.Make (* define basic type *)
(struct
type t = string
let compare = Pervasives.compare
end)
module StringSet = struct (* extend type with more operations *)
include StringSet
let of_list l =
List.fold_left
(fun s e -> StringSet.add e s)
StringSet.empty l
end;;
Using the core library you could do something like:
let list_to_set l =
List.fold l ~init:(Set.empty ~comparator:Comparator.Poly.comparator)
~f:Set.add |> Set.to_list
So for example:
list_to_set [4;6;3;6;3;4;3;8;2]
-> [2; 3; 4; 6; 8]
Or:
list_to_set ["d";"g";"d";"a"]
-> ["a"; "d"; "g"]