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Dynamically scoped variables in OCaml

Dynamic binding adds expressiveness; as Luc Moreau emphasized, it is, when used in moderation, quite useful: for parameterizing a function deep in the code without changing the interface of all callers; for propagating the environment information like the current working directory, printing-depth, etc. Dynamic binding is inescapable in mobile code or continuation-based web servers. Dynamic binding, in some restricted form, is already present in OCaml: exception handlers are dynamically scoped. This message announces the availability of general dynamic binding. This is joint work with Chung-chieh Shan and Amr Sabry.

Dynamic binding is implemented as a regular library, dependent on the delimited continuations library. No changes to the OCaml system and no code transformations are required; (parts of the) code that do not use dynamic variables incur no overhead and run at the same speed as before. Our dynamic variables are mutable; mutations however are visible only within the scope of the dlet statement where they occurred. It is also possible to obtain not only the latest binding to the dynamic variable, but also any of the shadowed bindings.

Because dynamic binding is implemented in terms of delimited continuations, the two features harmoniously interact. We can use dynamic variables in shift-based, cooperative threads, and support partial inheritance of the dynamic environment, with both shared and thread-private (mutable) dynamic variables.

Version
The current version is 1.1, Apr 10, 2006.
References
dynvar.txt [5K]
The announcement with a few examples
It was originally posted on the caml-list on Mon, 10 Apr 2006 18:25:29 -0700

dynvar.mli [2K]
The library interface
dynvar.ml [2K]
The library implementation

vdynvar.ml [6K]
The test code. The example at the end of that file demonstrates the partial inheritance of the dynamic environment among the parent and two cooperatively run threads.

Delimited Dynamic Binding
The ICFP 2006 paper justifying the implementation

Luc Moreau: A Syntactic Theory of Dynamic Binding. Higher-Order and Symbolic Computation, 11, 233-279 (1998)

Printing the outline of a pruned tree, using the extension to obtain shadowed dynamic bindings.

Delimited continuations in OCaml: required dependency

 

Resumable exceptions

Resumable exceptions are the strict generalization of regular exceptions, letting the exception raising form return a value and so the computation may continue. It's the exception handler that decides either to abort the exceptional computation or to resume it with a particular value. Resumable exceptions are made popular by Common Lisp, where they are widely used. Rainer Joswig's message, cited below, lists several real-life examples of resumable exceptions.

We show a conservative and elementary implementation of resumable exceptions in OCaml: the implementation is a self-contained 100% pure OCaml library; makes no changes to the OCaml system; supports the existing style of defining exceptions; is compatible with the ordinary exceptions; works in byte- or natively-compiled code; uses the most basic facilities of ML and so can easily be translated to SML.

We impose no extra restrictions on the resumable exception raising and handling forms. Like with ordinary exceptions, resumable ones may encapsulate values of arbitrary types; the same exception handler may process exceptions of many types -- and send resumption replies of many types. The raise form may appear within the guarded code at many places; different raise forms may resume with the values of different types. Furthermore, resumable exceptions are declared just like the ordinary ones, with the exception keyword. If the resumable exception handler never resumes, resumable exceptions act and feel precisely as the regular ones.

Version
The current version is 1.2, Jun 14, 2006.
References
resumable.txt [7K]
Motivation, design and an example of resumable exceptions
This announcement article was originally posted on the caml-list on Wed, 14 Jun 2006 15:54:03 -0700. This file also includes follow-ups, discussing syntactic sugar and the ways to implement resumable exceptions in a multi-threaded system.

resumable.ml [6K]
Complete implementation, interface documentation, explanation, and an illustrative example.

Rainer Joswig's message with several examples of usefulness of resumable exceptions. It is posted on `Lambda the Ultimate' on June 15, 2006.
< http://lambda-the-ultimate.org/node/1544#comment-18632 >

 

Persistent twice-delimited continuations

The new version of the delimcc library of first-class delimited continuations for byte-code OCaml now supports serializing and storing of captured continuations. The stored continuation can be invoked in the same or a different process running the same executable. The persistence feature supports process checkpointing, migration -- and specifically CGI programming on any, unmodified web server, e.g., Apache. Serialized continuations are twice delimited -- both in `control' and in `data'; the latter makes them compact and possible. The delimcc library is a pure library; it makes no changes to the OCaml system and has no effect on the code that does not capture delimited continuations.

One may think that making captured continuations persistent is trivial: after all, OCaml already supports marshaling of values including closures. If one actually tries to marshal a captured delimited continuation, one quickly discovers that the naive marshaling fails with the error on attempting to serialize an abstract data type. One may even discover that the troublesome abstract data type is _chan. The captured delimited continuation (a piece of stack along with administrative data) refers to heap data structures created by delimcc and other OCaml libraries; some of these data structures are closures, which contain module's environment and may refer to standard OCaml functions like prerr. That function is a closure over the channel stderr, which is non-serializable. This points out the first problem: if we serialize all the data reachable from the captured continuation, we may end up marshaling a large part of the heap and the global environment. This is not only inefficient but also lethal, as we are liable to encounter channels and other non-serializable data structures.

There is a more serious problem however. If we serialize all data reachable from the captured delimited continuation, we also serialize two pieces of global state used by the delimcc library itself. When the stored continuation is deserialized, a fresh copy of these global data is created, referenced from within the restored continuation. Thus the whole program will have two copies of delimcc global data: one for use in the main program and one for use by the deserialized continuation. Although such an isolation may be desirable in many cases, it is precisely wrong in our case: the captured and the host continuations do not have the common view of the system and cannot work together. It may be instructive to contemplate process checkpointing offered by some operating systems (see also `undump' typically used by Emacs and TeX). When checkpointing a process, we wish to save the continuation of the process only (rather than the continuation of the scheduler that created the process, and the rest of the OS continuation). We also wish to save data associated with the process, for example, the process control block and the description of allocated memory and other resources. Control blocks of all processes are typically linked in; when saving the control block of one process, we definitely do not wish to save everything that is reachable from it. When saving the state of a process in a checkpoint, we do not usually save the state of the file system -- or even of all files used by the process. First of all, that is impractical. Mainly, it is sometimes wrong. For example, a process might write to a log file, e.g., syslog. We specifically do not wish to save the contents of the syslog along with the process image. We want the restored process append to the system log rather than replace it!

Of course resuming a suspended process after modifying its input files may also be wrong. It is a hard question of what should be saved by value and what should be saved by reference only. It is clear however that both mechanisms are needed. The serialization code of the delimcc library does offer both mechanisms. The inspiration comes from the fact that OCaml's own marshaling function, when handling closures, serializes OCaml code by reference. The delimcc library extends this approach to data. The library supports the registration of data (which currently must be closures in the old heap) in a global array. When serializing a continuation, the library traverses it and replaces all references to registered closures with indices in the global array; we then invoke OCaml's own serialization routine to marshal the result. After that, we undo the replacement of closures with indices. Such value mangling is not without precedent: to detect sharing, OCaml's own marshaling routine too mangles the input value. The use of the global array is akin to the implementation of cross-staged persistence in MetaOCaml.

Version
The current version is 1.7, April 2008.
References
Delimited continuations in OCaml
The description of the delimcc library
The persistent twice-delimited continuations have been demonstrated at the Continuation Fest 2008 (April 13, Tokyo, Japan) and described in the message to the Caml-List posted on Sun, 27 Apr 2008 17:53:36 -0700 (PDT).

Persistent delimited continuations for CGI programming with nested transactions
The salient application of persistent delimited continuations is the library for writing CGI scripts as if they were interactive console applications using read and printf. The above library implements the minimal CGI programming framework with form validation. The library also supports nested transactions. The captured continuations are relatively compact: the essentially empty captured continuation takes 491 bytes when serialized. Serialized continuations of the unoptimized blog application have the typical size of 10K (depending on the size of the posts); bzip can compress them to one third of the original size.

 

Listing toplevel bindings

We show how to list all top-level bindings defined since the start of the OCaml toplevel session. We can list the names and the types of the bindings. We can also print the values of top-level bindings of a specific type. There is no need to recompile anything. However, we need the OCaml installation directory with the object files left after the making of the toplevel. If we are willing to remake the toplevel, the installation directory is no longer required.

After the preparation step or the alternative preparation step described below, we enter or #use, in the toplevel, the code print-toplevel-bindings.ml. We define a few sample bindings:

     # let x = 1;;
     # let x = 2;;
     # let y = 10;;
After that, evaluating
     # print_bindings Format.std_formatter (get_value_bindings (!Toploop.toplevel_env));;
will print all the top-level bindings defined since the start of the toplevel session:
     binding: get_value_bindings/79
       val get_value_bindings : Env.t -> (Ident.t * Types.value_description) list
     binding: print_bindings/107
       val print_bindings :
         Format.formatter -> (Ident.t * Types.value_description) list -> unit
     binding: type_to_str/177  val type_to_str : Types.type_expr -> string
     binding: print_int_toplevel/179
       val print_int_toplevel :
         Format.formatter -> (Ident.t * Types.value_description) list -> unit
     binding: x/186   val x : int
     binding: x/187   val x : int
     binding: y/188   val y : int
     Done
For each binding, its name and type are printed. We see that the type environment keeps track of all the previous definitions of a name. Because x was defined twice, there are two entries in the type environment: x/186 and x/187. The counters are the timestamp.

We can also print the values associated with the bindings of one particular type, for example, int:

     # print_int_toplevel Format.std_formatter (get_value_bindings (!Toploop.toplevel_env));;
which gives the following output:
     binding: x/186  value: 2
     binding: x/187  value: 2
     binding: y/188  value: 10
     Done
If a variable is defined several times, the top-level value environment keeps the last associated value, however. The function print_int_toplevel cannot, generally, be polymorphic -- unless we are willing to assume responsibility that our type representation string matches the desired type -- or we are willing to use MetaOCaml.
Version
The current version is 1.1, Sep 26, 2006.
References
Caml-list discussion thread Listing toplevel bindings started by John Harrison. Sep 26-27, 2006.

Preparation step
This step requires the OCaml installation directory with the object files left after the building of the toplevel. First, we need to retrieve
gprint_toplevel.ml [2K]
and adjust the paths in the #directory directives to point to our OCaml installation directory. We start the OCaml toplevel and execute all #directory and the #load directives in that file up to, but not including the loading of genprintval.cmo . Please do not change the order of the load directives! It took about half an hour to find the right order....

Alternative preparation step
On the discussion thread, Jonathan Roewen suggested an alternative. It requires rebuilding of the toplevel; the OCaml distribution is no longer needed then. We need to skip the expunge step after the toplevel is built: grep for expunge in the base Makefile. That step erases the mentioning of many internal components from toplevel's module dictionary. Therefore, these OCaml system modules act as if they are not loaded. We need these module for the present application however.

print-toplevel-bindings.ml [2K]
The implementation file. It was posted on the above discussion thread on Tue, 26 Sep 2006 01:01:20 -0700 (PDT)

 

Non-deterministic choice amb

The amb operator, first introduced by John McCarthy and well described by Dorai Sitaram in the context of Scheme, takes zero or more expressions (thunks) and nondeterministically returns the value of one of them. This implies that at least one of amb's expressions must yield a value, that is, does not fail. If amb has no expressions to evaluate or all of them fail, amb itself fails. One may think that amb is easily implementable by taking a list of thunks and evaluating the thunks in some order within the try block. The value of the thunk finishing without raising an exception is returned. However, that simple implementation is wrong. It is not enough that amb's chosen expression itself evaluates successfully. The chosen expression must be such that its value causes the whole program finish without errors, if at all possible. The amb operator must `anticipate' how the value of the chosen expression will be used in the rest of the computation. Therefore, amb is called an angelic nondeterministic choice operator.

Andrej Bauer gave the following example on the discussion thread:

     if (amb [(fun _ -> false); (fun _ -> true)]) then
        7
     else failwith "failure"
This program, he explained, should return 7: ``the amb inside the conditional should "know" (be told by an angel) that the right choice is the second element of the list because it leads to 7, whereas choosing the first one leads to failure.''

Therefore, we need the ability to examine (or speculatively execute) the rest of the computation. In Scheme, amb is implementable in terms of call/cc, as well explained by Dorai Sitaram. OCaml has more appropriate delimited control operators, which implement amb in two lines of code. We also need a `toplevel function', to tell us if the overall computation succeeded. One may think of it as St. Peter at the gate. For now, we take a computation that raises no exception as successful. In general, even non-termination within a branch can be dealt with intelligently (cf. `cooperative' threading which must yield from time to time). Andrej Bauer's test now looks in full as

     let test1 () =
       let v = 
         if (amb [(fun _ -> false); (fun _ -> true)]) then
           7
         else failwith "Sinner!"
       in Printf.printf "the result: %d\n" v;;
     let test1r = toplevel test1;; (* "the result: 7" *)
Speculatively evaluating amb's expressions or the rest of the computation may incur effects, such as mutation or IO. We can deal with them using one of the standard transaction implementation techniques: prohibit effects, log the updates, log the state at the beginning to roll back to, use zipper for functional `mutations'.

Here is a more advanced test, requiring a three-step-ahead clairvoyance from amb:

     let numbers = List.map (fun n -> (fun () -> n)) [1;2;3;4;5];;
     let pyth () =
       let (v1,v2,v3) =
         let i = amb numbers in
         let j = amb numbers in
         let k = amb numbers in
         if i*i + j*j = k*k then (i,j,k) else failwith "too bad"
       in Printf.printf "the result: (%d,%d,%d)\n" v1 v2 v3;;
     
     let pythr = toplevel pyth;; (* the result: (3,4,5) *)
In monadic terms, amb is equivalent to msum in MonadPlus. Even though we are interested in the first result of the entire MonadPlus computation, along the way we have to keep track of many possible worlds. That is, we need something like a List monad rather than a Maybe monad (the latter should not even be regarded as MonadPlus).
Version
The current version is 1.1, Feb 10, 2007.
References
Caml-list discussion thread Amb started by Jonathan Bryant. February 09-10, 2007.

Dorai Sitaram: Teach Yourself Scheme in Fixnum Days. 1998-2004. Chapter 14. Nondeterminism.
< http://www.ccs.neu.edu/home/dorai/t-y-scheme/t-y-scheme-Z-H-16.html#node_chap_14 >

amb.ml [3K]
Commented OCaml implementation
It was posted on the above discussion thread on Sat, 10 Feb 2007 03:15:56 -0800 (PST)

Zipper File system and transactional storage

 

Local globally-quantified exceptions

SML has local exception declarations. Furthermore, it lets us define a polymorphic function whose body declares a local exception with the type tied to that of the whole function. For example:
     fun 'a embed () = let exception E of 'a
                           fun project (e: t): 'a option =  ...
At first sight, that SML feature seems impossible in OCaml (prior to OCaml 3.12). Although we can declare local exceptions in OCaml via local structures, before OCaml 3.12 we could not use type variables quantified outside the structure: a structure limits the scope of all of its type variables. We show that local globally-quantified exceptions are macro-expressible in all versions of OCaml and demonstrate two translations. The first one relies on multi-prompt delimited continuations, whose implementation leads to the second translation. The latter represents a polymorphic exception mere by a parameter-less exception and one reference cell.

The caml-list thread referenced below gave a good motivation for locally polymorphic exceptions: writing an efficient library function fold_file of the following interface:

     module type FoldFile = sig
      val fold_file : in_channel ->         (* file      *)
                      (in_channel -> 'a) -> (* read_func *)
                      ('a -> 'b -> 'b)   -> (* combiner  *)
                      'b ->                 (* seed      *)
                      'b
     end;;
We can use this general folding over a file to, for example, count the number of lines in a file:
     module TestFold(F:FoldFile) = struct
      let line_count filename = (* string->int *)
        let f = open_in filename in
        let counter _ count = count + 1 in
        F.fold_file f input_line counter 0
      let test = line_count "/etc/motd"
     end;;
The following tentative implementation has been outlined on ocaml-list:
     module Attempt0 = struct
       exception Done of 'a
       let fold_file file read_func elem_func seed =
        let rec loop prev_val =
          let input = try read_func file
                      with End_of_file -> raise (Done prev_val) in
          let combined_val = elem_func input prev_val in
          loop combined_val
        in
        try loop seed with Done x -> x
     end;;
The loop is properly tail-recursive (NB: the body of a try block is not in a tail position) and avoids any administrative data structures. Alas, the typechecker does not accept the exception declaration, which says that Done should carry a value of all types. There is no such value in OCaml, and if it were, it wouldn't be useful. That was not our intention anyway: we want the value of Done to have the same type as the result of the polymorphic function fold_file. We should have declared the exception insidefold_file. Surprisingly, that can be done: Delimcc.prompt is precisely this type of `local exceptions'. We need only a slight and local adjustment to the above code to make it compile. This is our first translation.
     open Delimcc   let abort p v = take_subcont p (fun sk () -> v);;
     
     module AttemptA : FoldFile = struct
       let fold_file file read_func elem_func seed =
        let result = new_prompt () in (* here is our local exn declaration *)
        let rec loop prev_val =
          let input = try read_func file
                      with End_of_file -> abort result prev_val in
          let combined_val = elem_func input prev_val in
          loop combined_val
        in
        push_prompt result (fun () -> loop seed)
     end;;
     
     let module TestA = TestFold(AttemptA) in TestA.test;; (* - : int = 24 *)

The analogy between exceptions and delimited continuations is profound: local exceptions are commonly used to implement multi-prompt delimited continuations in SML. We see the converse is also true. Furthermore, delimited continuations in OCaml are implemented in terms of exceptions. Abort is essentially raise. If we `inline' the gist of the delimited continuation library we arrive at our second translation. The result requires no libraries and works with both byte-code and native compiler.

     module AttemptR : FoldFile = struct
       exception Done
       let fold_file file read_func elem_func seed =
        let result = ref None in (* here is our local exn declaration *)
        let rec loop prev_val =
          let input = try read_func file
                      with End_of_file -> result := Some prev_val; raise Done in
          let combined_val = elem_func input prev_val in
          loop combined_val
        in
        try loop seed with Done -> (match !result with Some x -> x
                                      | _ -> failwith "impossible!")
     end;;
     let module TestR = TestFold(AttemptR) in TestR.test;; (* - : int = 24 *)
The code is still properly tail-recursive and deforested. In contrast to other imperative implementations of fold_file, ours is almost pure: the reference cell result is written to and immediately after read from only once during the whole folding -- namely, at the very end. The bulk of the iteration is functional. A mutable cell is the trick behind typing of multi-prompt delimited continuations. One may even say that if a type system supports reference cells, it shall support multi-prompt delimited continuations -- and vice versa.
Version
The current version is 1.2, Oct 4, 2007.
References
Yin-so Chen, Olivier Roussel, kirillkh, et al. best and fastest way to read lines from a file? Caml-list discussion thread. October 1-2, 2007.

Caml-list discussion thread Locally-polymorphic exceptions October 3-4, 2007.
Of special note is the PML implementation posted by Christophe Raffalli.

The MLton team. UniversalType Source for the SML example of local exceptions
< http://mlton.org/UniversalType >

 

Type-directed memoization

Memoization of a function is recording and reusing already computed associations between the argument and the result of the function. The associations are recorded in a memo table, which can be constructed generically, with the type determined automatically from the type of function's argument. The paper ``Fun with type functions'' (Sections 3.1 and 3.2) describes one such generic construction in Haskell, using type functions, and refers to other constructions. Essentially the same approach leads to generic finite maps, see Section 3.3 of the paper.

We implement the type-directed memoization from the paper in OCaml. Quite a few adjustments had to be made. First of all, OCaml does not have type families, or even type classes. We use type-indexed--value approach pioneered by Zhe Yang. Second, whereas Haskell relied on laziness, we explicitly use reference cells for recording the computed results. Finally, recursive types require an additional level of indirection via the reference cell. The trick is not unlike the eta-expansion that converts the ordinary fixpoint combinator to the applicative one: We have to delay the computation of the fixpoint until we receive the argument for the fixpointed function. Still, the computed fixpoint should be shared among all applications of the memoized function.

Here is a simple example: memoizing functions on boolean lists. A boolean list has a recursive type (recursive sum of product), which can be written as:

     BList = 1 + Bool * BList
or, with the explicit fixpoint,
     blist = mu self.(unit + bool * self)
In OCaml, we write it as follows:
     module BLST =
        FIX(struct type 'self t = (unit,bool*'self) either
                   let mdt self = md_sum md_unit (md_prod md_bool self) end)
     
     let nil      = BLST.Fix (Left ())
     let cons h t = BLST.Fix (Right (h,t))
The type expression for the type of BLST, (unit,bool*'self) either matches the mathematical notation. Mainly, the expression md_sum md_unit (md_prod md_bool self) that computes the memoizer for the functions on boolean lists from the memoizers for unit, booleans and memoizer combinators, too, matches the mathematical notation for the recursive type of boolean lists. Our memo tables are indeed type-directed.
Version
The current version is January 2009.
References
Fun with type functions
Joint work with Simon Peyton Jones and Chung-chieh Shan
< http://research.microsoft.com/en-us/um/people/simonpj/papers/assoc-types/fun-with-type-funs/typefun.pdf >
< http://haskell.org/haskellwiki/Simonpj/Talk:FunWithTypeFuns >
< http://research.microsoft.com/en-us/um/people/simonpj/papers/assoc-types/fun-with-type-funs/fun-with-type-funs.zip >

memo_type_directed.ml [6K]
The complete OCaml code and the tests

 

Generic print function

The facility that prints results and types of expressions evaluated at the top-level was available anywhere in the program -- in bytecode- or natively compiled programs. Generic printing is a, perhaps unintentional, `side-effect' of the old (pre N100) MetaOCaml -- of the fact that a code value is not merely AST; the code value also captures the type and the type environment of variables and other values.
     val fprint : Format.formatter -> ('a,'b) code -> string
is the core function which takes a code value of any type, and pretty-prints it on the given formatter. The printed result is exactly the same as that by the top-level value printing. The function fprint returns the representation of the expression's type, as a string. The latter is arguably a frill, but it was easy to do, so just as well.

For example,

     let pr_type et = Format.printf "\n%s@." et
     let () =
       let x = Some ([|(10,true);(11,false)| ]) in
       pr_type (print .<x>.)
prints the following two lines:
     Some [|(10, true); (11, false)| ]
     (int * bool) array option
The first line is the value, and the latter (printed by pr_type) is the type. There was no need to define any custom printer for the value or its components. A more involved example is given at the end of the announcement article referenced below.

Informally, an OCaml function of the type 'a-> ... corresponds to the Haskell function a -> .... OTH, an OCaml function of the type ('a,'b) code -> ... corresponds to Haskell's Typeable b => b -> .... The latter enables generic programming, similar to Haskell's `Scrap Your Boilerplate' (Laemmel and Peyton-Jones).

The version N100 of MetaOCaml has simplified the representation of code values. Types are no longer included. Therefore, the described generic printing no longer works.

Version
The current version is January 2011.
References
gprint.txt [8K]
Motivation, design and examples of generic print
This announcement article was originally posted on the caml-list on Sun, 16 Apr 2006 19:09:10 -0700


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