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Here is the latest Caml Weekly News, for the week of November 13 to 20, 2007.

  1. Again: Findlib-1.2.1 released
  2. Eliminating existentials, finally
  3. OCaml runtime using too much memory in 64-bit Linux
  4. Private types

Again: Findlib-1.2.1 released


Gerd Stolpmann announced:
Sorry for that, 

findlib-1.2 contained a compatibility problem in the new camlp4 META 
file. Because of this it was not possible to parse source files with 
camlp4 that contained stream constructs, and a number of libraries did 
not compile. 

finddlib-1.2.1 fixes the problem.

Eliminating existentials, finally


Peng Zang asked and Oleg answered:
> Is there a way to create lists in which the elements may be of 
> differing types but which all have some set of operations defined 
> (eg. tostr) in common?  One can then imagine mapping over such lists 
> with "generic" versions of those common operations. 

First of all, if simple type classes, mentioned during the discussion, 
are desired, they can be easily obtained 

(alas, modulo the convenient inference and automatic dictionary 
construction). That is not the topic of this message however. We would 
like to show that in some (many?) circumstances, existentials can be 
just eliminated. 

Peng Zang continued: 

> Essentially we have ints, floats and bools.  All these types can be 
> shown.  It would be nice to be able to create a list of them [1; 2.0; 
> false] that you can then map a generalized show over. 

So, we want abstract values with the only non-trivial operation of 
converting them to strings. One may immediately ask: 
why not to convert them to strings to start with? So, instead of writing 
         [`Int 1; `Float 2.0; `Bool false] 
we can just 
        [string_of_int 1; string_of_float 2.0; string_of_bool false] 
That idea looks better in Haskell: first of all, since polymorphic 
equality is absent in Haskell, nothing breaks parametricity in 
safe Haskell and we lose nothing in expressiveness if we treat 
        forall a. Show a => a 
as Strings. Also, because of the default laziness of Haskell, the 
conversions to string are not performed unless needed. OTH, ML 
programmers have never been scared of thunks. Thus the idea is to 
represent an existential by a tuple of its observations, using thunks 
to delay computations. 

Here is a more complex example, of a counter, whose interface could be 
described as follows. 

module type COUNTER = sig 
  type t 
  val init : unit -> t 
  val observe : t -> int 
  val step : t -> t 

We see the producer, consumer/observer, and the transformer. Of course 
we cannot use modules of the above signature for our purposes 
since we cannot put modules into a list (cf: MoscowML and AliceML have 
first-class modules). We do note however that the above is equivalent 
to the following 

type counter = C of (unit -> int) * (unit -> counter);; 

Here are two different `constructors', with two different 
representations of the internal state (a pair of int, or a float). 

let counter1 = 
  (* internal function, unavailable outside *) 
  let rec make seed upper = 
    C ((fun () -> seed),(fun () -> 
      let seed = if seed >= upper then 0 else succ seed in make seed upper)) 
  in make 0 5;; 

(* use FP seed *) 
let counter2 = 
  (* internal function, unavailable outside *) 
  let observe seed = int_of_float (10.0 *. seed) in 
  let step seed = cos seed in 
  let rec make seed = C ((fun () -> observe seed), 
                         (fun () -> make (step seed))) 
  in make 0.0;; 

We can place them into a list 

let lst = [counter1; counter2];; 

and iterate over: 

let advance_all = (function C (_,adv) -> adv ());; 
let show_all = List.iter (function C (s,_) -> Printf.printf "%d\n" (s()));; 

let test = let () = show_all lst in 
           let () = show_all (advance_all (advance_all lst)) 
           in ();; 

We thus demonstrated a very old idea (whose realization in 1976 was 
the birth of Scheme) that closures are poor-man objects

The title betrays my hunch that co-algebraic implementations (using 
functions) typically require simpler types than the corresponding 
algebraic, data-type based implementations.

OCaml runtime using too much memory in 64-bit Linux


Adam Chlipala said:
I've encountered a problem where certain OCaml programs use orders of 
magnitude more RAM when compiled/run in 64-bit Linux instead of 32-bit 
Linux.  Some investigation led to the conclusion that the difference has 
to do with the size of OCaml page tables.  (Here I mean the page tables 
maintained by the OCaml runtime system, not any OS stuff.) 

A program that should be using just a few megabytes of RAM ends up using 
200+ MB to store a page table.  It seems that a C macro is defined by 
default on 64-bit Linux to use mmap() instead of malloc().  Ironically, 
a comment says that this was done to avoid being given blocks of memory 
that are very far apart from each other, forcing the creation of overly 
large page tables.  It's ironic because that is exactly the problem that 
is showing up now with mmap().  It ends up called twice for the program 
I'm looking at, and the two addresses it returns are far enough apart to 
lead to creation of a 200 MB page table. 

Has anyone else experienced this problem?  Would the runtime system need 
to be changed to avoid it?
After several other reports, Xavier Leroy answered:
Concerning this issue with large page tables on 64-bit architectures, 
I opened a problem report on the bug-tracking system to help gather 
more information.  I'd like to ask all members of this list that 
reported the problem to kindly visit 

and add the required information as a note.  That will help 
pinpointing the problem. 

Some more explanation on what's going on.  The Caml run-time system 
needs to keep track of which memory areas belong to the major heap, 
and uses a page table for this purpose, with a dense representation 
(an array of bytes).  If the major heap areas are closely spaced, this 
table is very small compared with the size of the heap itself. 
However, if these areas are widely spaced in the addressing space, the 
table can get big. 

For 32-bit platforms, this isn't much of a problem since the maximum 
size of the page table is 1 megabytes.  For 64-bit platforms, the sky 
is the limit, however.  So far, the only 64-bit platform where this 
has been a problem in the past is Linux with glibc, where blocks 
allocated by malloc() can come either from sbrk() or mmap(), two areas 
that are spaced several *exa*bytes apart.  We worked around the 
problem by allocating all major heap areas directly with mmap(), 
obtaining closely spaced addresses. 

Apparently, this trick is no longer working on some systems, but I 
need to understand better which ones exactly.  (I suspect some Linux 
distros that applied address randomization patches to the stock Linux 
kernel.)  So, please provide feedback in the BTS. 

If the problem is confirmed, there are several ways to go about it. 
One is to implement the page table with a sparse data structure, 
e.g. a hash table.  However, the major GC and some primitives like 
polymorphic equality perform *lots* of page table lookups, so a 
performance hit is to be expected.  The other is to revise OCaml's 
data representations so that the GC and polymorphic primitives no 
longer need to know which pointers fall in the major heap.  This seems 
possible in principle, but will take quite a bit of work and break a 
lot of badly written C/OCaml interface code.  You've been warned :-)

Private types


The editor said:
This thread was very big and covered many discussions about some language 
features. Here are two messages from Pierre Weis discussing in detail private 
Pierre Weis said:
In the next version of the compiler, you will have an extension to the 
definition of types with private construction functions (aka ``private'' 
types) that just fulfills your programming concern: in addition to usual 
private sum and record private type definitions, you can now define a type 
abbreviation which is private to the implementation part of a module (see 
note 1). 

Since the values of a private type are concrete, it is much easier for the 
programmer to use the values of the type abbreviation. 

Using the new private type abbreviation feature, you can write for instance: 
type row = int;; 
let make i = 
  if i < 0 then failwith "Row: cannot create a negative row" else 
let from i = i;; 

type row = private int;; 

val make : int -> row;; 
val from : row -> int;; 

This solution does not require any additional tagging or boxing, only the 
usage of injection/projection function for the type. As for usual private 
types, the injection function is handy to provide useful invariants (in the 
row type example case, we get ``a row value is always a positive integer''). 

In addition, the private abbreviation is publicly exposed in the interface 
file. Hence, the compiler knows about it: it can (and effectively does) 
optimize the programs that use values of type row in the same way as if the 
type row were defined as a regular public abbreviation. 

Last but not least, being an instance of the identity function, the from 
projection function is somewhat generic: we can dream to suppress the burden 
of having to write it for each private type definition, if we find a way to 
have it automatically associated to the new private type by the compiler. 

Best regards, 

Note 1: this is a generalization for regular type abbreviations of the 
polymorphic variants private type definitions that Jacques Garrigue already 
introduced to provide polymorphic variants (and object) types with private 
row variables.
Alain Frisch asked and Pierre Weis answered:
> > - a value of type row is in fact a concrete integer (it is not hidden in 
> > any way),

> But you cannot apply integer operations to it, so it is not a normal 
> concrete integer, right?

Right: a value of type row has type row ... not type int!

> Can you show an example where replacing all "type t = private ..." 
> definitions by "type t" changes a well-typed program into an ill-typed 
> one?   I understand that if private types create real subtypes (w.r.t. 
> :>) then they are different than abstract types, but otherwise, I don't 
> see the difference for the type-checker.

May be, I must recall what are private types in the first place: private
types has been designed to implement quotient data structure.

(***  Warning.

Wao: after re-reading this message I realize that it is really long.

You can skip it, if you already know something about mathematical quotient
structures, private types for record and variant, relational types and the
mocac compiler!


What is a quotient ?

 Here quotient has to be understood in the mathematical sense of the term:
given a set S and an equivalence relation R, you consider the set S/R of the
equivalence classes modulo the relation R. S/R is named the quotient
structure of S by R. Quotient structures are fundamental in mathematics and
there properties have been largely studied, in particular to find the
relationship between operations defined on S and operations on S/R: which
operations on S can be extended to operations on S/R ? Which properties of
operations on S are still valid for there extension on S/R ? and so on.

Simple examples of quotient structures can be found everywhere in maths, for
instance consider the equivalence relation R on pairs of integer values
defined as

 z_1 equiv z_2 if and only if z_1 and z_2 are both odd or are both even
(in Caml terms
 z_1 equiv z_2 if and only if (z_1 mod 2) = (z_2 mod 2))

The set Z/R is named Z/2Z and it inherits properties of operations on Z: it
is an abelian group (and more).

A wonderful example of such inheritance of interesting properties by
inheritance of operations thanks to a definition by a quotient structure is
the hierarchy of sets of numbers: starting with N (the set of natural
numbers) we define Z (the set of relative integer numbers) as a quotient of
NxN), then Q (the rational numbers) as a quotient of ZxZ*, R (the set of real
numbers) as a quotient of Q^N (the sets of sequences of rational numbers), C
(the set of complex numbers) as a quotient of R[X] (the set of polynomials
with one unknown and real coefficients). Note here that at each step of the
hierarchy the quotient structure is richer (has more properties and/or more
elements) than the original structure: first we have a monoide, then a group
and a ring, then a field, then a complete field and so on.

Why quotient structures ?

So quotient structures are a fundamental tool to express mathematical
structures and properties. Exactly as mathematical functions, relations and
sets. As you may have noticed, programming languages are extremely related to
maths (due to their purely logical bases) even if, in some cases, the zealots
of the language at hand try to hide the mathematical fundation into a strange
anthropomorphic discurse to describe their favorite language features.

In the end, the computer programing languages try hard to incorporate
powerful features from mathematics, because these features have been polished
by mathematicians for centuries. As a consequence of this work, we know
facts, properties and theorems about the mathematical features and this is an
extremely valuable benefit.

Now, what is the next frontier ? What can we steal more to mathematics for the
benefit of our favorite programming language ?

If we review the most powerful tools of mathematicians, we found that
functions have been borrowed (hello functional programming, lambda-calculus
and friends :)), relations have been borrowed (data bases, hash tables,
association lists), sets have been more or less borrowed (hello setle,
pascal, and set definition facilities from various libraries of various
languages...). More or less, we have all those basic features.

From the mathematical set construction tools, we have got in Caml:

- the cartesian product of sets (the * binary type constructor, the record
  type definitions),
- the disjunct union of sets (the | of polymorphic variants, the sum (or
  variant) type definitions).

Unfortunately, we have no powerful way to define a quotient data
structure. That what private type definitions have been designed to do.

What do we need for a quotient data structure ?

In the first place, we need the ``true'' thing, the real feature that is
indeed used in maths. Roughly speaking this means to assimilate the quotient
set S/R to a subset of S.

 In the previous definition of quotient structures, there is a careful
distinction between the base set S and the quotient set S/R. In fact, there
always exists a canonical injection from S to S/R, and if we choose a
canonical representant in each equivalence class of S/R, we get another
canonical injection from S/R to S, so that S/R can be considered as a subset
of S (the story is a bit more complex but that's the idea). This
injection/projection trickery is intensively used in maths; for instance, in
the hierarchy of number sets, we say and consider that N is a subset of Z
that itself is a subset of Q, a subset of R, a subset of C. Rigourously, we
should say for instance, there is a subset of Z that is canonically
isomorphic to N; in fact, we abusively assimilate N to this subset of Z;
hence, we say that N is ``included'' in Z, when we should say ``the image of
N by the canonical isomorphism from N to Z'' is included in Z; then, we go
one step further in the assimilation of N to a subset of Z, by denoting the
same, the elements of N and there image in Z; for instance, ``the neutral
element of the multiplication in Z'' and the successor of 0 in N is denoted
``1''; and we now can say that 1 belongs to Z. Note here that, in the first
place, ``the neutral element of the multiplication in Z'' is an equivalence
class (as all elements in Z are). So it is a set. More exactly, the ``neutral
element of the multiplication in Z'' is the infinite set of pairs of natural
numbers (n, m) such that n - m = 1 (here ``-'' is an operation in N and ``1''
is the successor of the natural number ``0'', so that n - m = 1 is a
shorthand for n = succ m). The assimilation between N and its isomorphic
image allows to use 1 as the denotation of this infinite set of pairs of
natural numbers.

We understand why the mathematicians always write after having designed a
quotient structure: ``thanks to this isomorphism, and if no confusion may
arise, we always assimilate S to its canonical injection in S/R''.

This assimilation is what private type definitions allow.

How do we define a quotient data structure ?

The mathematical problem:
- we have a set S and an equivalence relation R on SxS,
- we construct the quotient S/R.
- we state afterwards:
  ``if no confusion may arise, we always assimilate S to its canonical
    injection in S/R''.

The programming problem:
- we have a data structure S (defined by a type s) and a relation R on SxS
  (defined by a function r from s * s to bool).
- we construct a data structure that represents S/R.
- we have afterwards:
  ``No confusion may arise, we always assimilate S to its canonical injection
    in S/R''.

The private data type solution:
- the data structure S is defined as any Caml data structure and the
  relation R is implemented by the canonical injection(s) from S to S/R.
- the canonical projection from S/R to S is automatic.
- S (defined by s) is assimilated to S/R (which is then also s!).

We defined S/R as a subset of S, the set of canonical representants of
equivalence classes of S/R.

More exactly, the canonical injection from S to S/R maps each element of S to
its equivalent class in S/R; if we assimilate each equivalence class to its
canonical representant (an element of S), the canonical injection maps each
element of S to the canonical representant of its equivalence class. Hence
the canonical injection has type S -> S.

An example treated without private types:

Let's take a simple example:

S is the following data structure that implements a mathematical (free) structure
generated by the constant 0, the unary symbol succ, and the binary symbol +.

type peano = 
   | Zero
   | Succ of peano
   | Plus of peano * peano

R is the (equivalence) relation that expresses that
- 0 is the neutral element for + (for all x in S, 0 + x = x and x + 0 = x),
- + is associative (for all x, y, z in S³, (x + (y + z)) = ((x + y) + z)).

The canonical injection is a function from peano -> peano that maps each value
in S (the type peano) to the canonical representant of its class in S/R (an
element of S (the type peano)):

let rec make = function
  | Zero -> Zero
  | Plus (Succ n, p) -> Succ (make (Plus (n, p)))
  | Plus (Zero, p) -> p
  | Plus (p, Zero) -> p
  | Plus (Plus (x, y), z) -> make (Plus (x, make (Plus (y, z))))
  | Succ p -> Succ p

(This function may be wrong but you see the idea :))

So, if you want to represent S/R for peano in Caml you must:
- (1) define the type peano
- (2) always use the make function to create a value in S/R
- (3) not to confuse S and S/R in your head (I mean in your programs)

Private data types permits (1), ensures (2), and helps for (3) concerning the
head part and ensures (3) for programs by means of compile-time type errors.

The same example with private types:

To define a private data type you must define a module.
- in the implementation, you define the carrier S and its canonical injection.
- in the interface, you export the carrier and the injection.

The type checker will ensure transparent projection from the quotient to the
carrier and mandatory use of the canonical projection to build a value in

interface peano.mli
type peano = private
   | Zero
   | Succ of peano
   | Plus of peano * peano

val zero : peano;;
val succ : peano -> peano;;
val plus : peano * peano -> peano;;

type peano =
   | Zero
   | Succ of peano
   | Plus of peano * peano

let rec make = function

let zero = make Zero;;
let succ p = make (Succ p);;
let plus (n, m) = make (Plus (n, m));;

(See note (1) for a discussion on the design of this example.)

What is given by private types:

- You cannot create a value of S/R if you do not use the canonical injection
  # Zero;;
  Cannot create values of the private type peano

- As a consequence, values in S (i.e. S/R) are always canonical:
  # let one = succ zero;;
  val one : M.peano = Succ Zero
  # let three = plus (one, succ (plus (one, zero)));;
  val three : M.peano = Succ (Succ (Succ Zero))

- Projection is automatic
  # let rec int_of_peano = function
      | Zero -> 0
      | Succ n -> 1 + int_of_peano n
      | Plus (n, p) -> int_of_peano n + int_of_peano p
  val int_of_peano : M.peano -> int = <fun>
  # int_of_peano three;;
  - : int = 3

What about private abbreviations ?

Private abbreviation definitions are a natural extension of private data type
definitions to abbreviation type definitions. The same notions are carried
out mutatis-mutandis:

- we have a data structure S (defined by a type s) and a relation R on SxS
  (defined by a function r from s * s to bool).
- we construct a data structure that represents S/R.
- we have afterwards:
  ``No confusion may arise, we always assimilate S to its canonical injection
    in S/R''.

In the case of abbreviations:

- the data structure S/R is defined by a type s (which is an abbreviation) and
  a relation defined by a function,
- the canonical injection should be defined in the implementation file of the
  private data type module,
- we always assimilate S to its canonical injection in S/R.

In pratice, as for usual private types (for which the constructive part of
the data type is not available outside the implementation), the type abbreviation
is not known outside the implementation (it is really private to its
implementation). This prevents the construction of values of S/R without
using the canonical injection.

Th noticeable difference is the projection function: it cannot be fully
implicit (otherwise, as you said Alain, the assimilation will turn to complete
confusion: we would have S identical to S/R, hence row=int and no difference
between a regular abbreviation definition and a private abbreviation
definition). If not implicit, the injection function should granted to be the
identity function (something that we would get for free, if we allow
projection via sub-typing coercion).

In short: abstract data types provide values that cannot be inspected nor
safely manipulated without using the functions provided by the module that
defines the abstract data type. In contrast, private data types are
explicitely concrete and you can freely write any algorithm you need. A good
test is printing: you can always write a function to print values of a
private type, it is up to the implementor of an abstract type to give you the
necessary primitives to access the components of the abstracted values.

Automatic generation of the canonical injection:

You may have realized that writing the canonical injection can be a real

The moca compiler (see helps you to write the
canonical injection by generating one for you, provided you can express the
injection at hand via a set of predefined algebraic relations (and/or rewrite
rules you specify) attached to the constructors of the private type. Private
types with constructors having algebraic relations are named relational
types. Moca generated canonical injections for relation types.

For instance, you would write the peano example as the following peano.mlm

type peano = private
   | Zero
   | Succ of peano
   | Plus of peano * peano
     neutral (Zero)
     rule Plus (Succ n, p) -> Succ (Plus (n, p))

The mocac compiler will generate the interface and implementation of the
peano module for you, including the necessary canonical injection function.

Best regards,

Pierre Weis

INRIA Rocquencourt,

Note (1):
- we can't just export the canonical injection since you could not build any
  value of the type without previously defined values!
- we provide specialized versions of the canonical injection function
  introducing the convention that the lowercase name of a value constructor is
  the name of its associated canonical injection.
- we do not export the plasin true canonical injection since it would be more
  confusing than useful.

Using folding to read the cwn in vim 6+

Here is a quick trick to help you read this CWN if you are viewing it using vim (version 6 or greater).

:set foldmethod=expr
:set foldexpr=getline(v:lnum)=~'^=\\{78}$'?'&lt;1':1

If you know of a better way, please let me know.

Old cwn

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Alan Schmitt