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
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.
caml-liston Mon, 10 Apr 2006 18:25:29 -0700
The library interface
The library implementation
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
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,
exception keyword. If
the resumable exception handler never resumes, resumable exceptions
act and feel precisely as the regular ones.
caml-liston 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.
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 >
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
_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
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.
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
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.
After the preparation step or the alternative preparation step
described below, we enter or
#use, in the toplevel, the
print-toplevel-bindings.ml. We define a few sample
# 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 DoneFor 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
xwas defined twice, there are two entries in the type environment:
x/187. The counters are the timestamp.
We can also print the values associated with the bindings of
one particular type, for example,
# 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 DoneIf a variable is defined several times, the top-level value environment keeps the last associated value, however. The function
print_int_toplevelcannot, 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.
This step requires the OCaml installation directory with the object files left after the building of the toplevel. First, we need to retrieve
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.
The implementation file. It was posted on the above discussion thread on Tue, 26 Sep 2006 01:01:20 -0700 (PDT)
amboperator, 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
ambhas no expressions to evaluate or all of them fail,
ambitself fails. One may think that
ambis easily implementable by taking a list of thunks and evaluating the thunks in some order within the
tryblock. 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
amboperator 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
ambinside 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,
implementable in terms of
call/cc, as well explained by
Dorai Sitaram. OCaml has more appropriate delimited control operators,
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
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,
ambis equivalent to
MonadPlus. Even though we are interested in the first result of the entire
MonadPluscomputation, along the way we have to keep track of many possible worlds. That is, we need something like a
Listmonad rather than a
Maybemonad (the latter should not even be regarded as
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 >
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
We implement a simplified version of the numeric
Num typeclass, called
Numb, and use it to write
a polymorphic function
summ to sum a list of any
Numb-ers. For clarity, we develop code both in Haskell
and OCaml. It is instructive to compare the inferred types of the
summ function, in Haskell and OCaml. They are, respectively:
summ :: (Numb a) => [a] -> a val summ : 'a numb -> 'a list -> 'a = <fun>The only difference is in the shape of the arrow:
(Numb a =>)vs.
('a numb ->). In both Haskell and OCaml, the function
summis bounded polymorphic: it applies to lists of values of any type, provided that we have the evidence, or the `dictionary', that the type is in the class
Numb. We must pass that evidence, the witness of the
Numbconstraint, as the first argument of
summ. The OCaml type of
summis revealing about the nature of bounded polymorphism. An unbounded polymorphic function such as
id : 'a -> 'acorresponds to the universally quantified proposition
forall a. a -> a. The function
summcorresponds to the proposition
(List(a) -> a)quantified only over a part of the domain of discourse. That part is decided by the predicate
Numb(a). In other words, we assert
List(a) -> aonly when
Numb(a). The whole proposition reads
forall a. Numb(a) -> (List(a) -> a)-- which is literally the type of
summmodulo stylistic differences.
Although the OCaml implementation is a faithful translation of Haskell code, the explicit use of dictionary passing is quite an annoyance. Since the translation replaces double arrow with a single arrow, we have to explicitly pass the dictionary argument to all bounded polymorphic functions in OCaml. In Haskell, these arguments are (most of the time) inferred.
Implementing Haskell's constructor classes -- classes parameterized on type constructors -- require the use of the module system of OCaml.
Numtypeclass in OCaml, in comparison with Haskell. This article was originally posted on the
caml-liston Thu, 8 Mar 2007 23:36:58 -0800 (PST)
P. J. Stuckey and M. Sulzmann: A theory of overloading
ACM Transactions on Programming Languages and Systems (TOPLAS), 27(6):1-54, 2005.
Translucent applicative functors in Haskell:
contrasting the module system of OCaml with Haskell typeclasses.
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
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
loopis properly tail-recursive (NB: the body of a
tryblock is not in a tail position) and avoids any administrative data structures. Alas, the typechecker does not accept the exception declaration, which says that
Doneshould 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
Doneto have the same type as the result of the polymorphic function
fold_file. We should have declared the exception inside
fold_file. Surprisingly, that can be done:
Delimcc.promptis 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
resultis 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.
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 >
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 * BListor, 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
(unit,bool*'self) eithermatches 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.
The complete OCaml code and the tests
val fprint : Format.formatter -> ('a,'b) code -> stringis 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
fprintreturns 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.
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 optionThe 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
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.
caml-liston Sun, 16 Apr 2006 19:09:10 -0700
oleg-at-pobox.com or oleg-at-okmij.org
Your comments, problem reports, questions are very welcome!
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