Both Racket’s object
and its (separate!) generic interface
offer single-dispatch object-oriented programming: the choice of
method body to execute depends on the type of just one of the
arguments given to the method, usually the first one.
In some cases, the first thing that a method will do is to decide
what to do next based on the type of a second argument. This is
called double dispatch, and it has a long history in
object-oriented programming languages—at least as far back as the
As an example, consider implementing addition for classes
representing numbers. A different method body would be needed
for each pair of representations of numbers.
I stumbled across the need for something like this when
implementing Operational Transformation (OT) for
in that code base is almost the double-dispatch macro from
this post; the difference is that for operational transformation,
the method concerned yields two results, and if the arguments
are switched on the way in, they must be switched on the way out.
Basic Double Dispatch
Here’s a basic double-dispatch macro:
It assumes that it will be used in a method where dispatch has
already been done on arg1, and that the next step is to inspect
arg2. It applies the pred?s in sequence until one of them
answers true, and then evaluates the corresponding body. If none
of the pred?s hold, it signals an error.
It’s often convenient to use it inside a class definition or
generic interface implementation with the following macros, which
simply define op to delegate immediately to double-dispatch.
The first is to be used with Racket’s object system, where the
first argument is bound implicitly to this and where predicates
should use Racket’s
function. The second is to be used with Racket’s generic interface
system, where both arguments are explicitly specified and
predicates are more general.
Commutative Double Dispatch
For commutative operations like addition, it’s common to see the
same code appear for adding an A to a B as for adding a B to an A.
The next macro automatically flips its arguments and tries again
to see if B’s method has support for A, if it can’t find support
for B within A’s method. That way, code for combining B with A
need only be supplied in one place. It uses a
to keep track of whether it’s currently trying out a flipped pair
Writing a simple wrapper works well for using
commutative-double-dispatch in a class definition:
but a wrapper for use with the generic interface system needs to
take care not to accidentally shadow the outer dispatch mechanism.
This macro uses
to make op* an alias of op that always does a full dispatch on
Let’s see the system in operation! First, using Racket’s object
system, and then using Racket’s generic interfaces.
We will first define two types of value foo and bar, each
responding to a single doubly-dispatched method, operator which
produces results according to the following table:
| foo | bar |
foo | foo | bar |
bar | bar | foo |
Then, we’ll extend the system to include a third type, zot,
which yields a zot when combined with any of the three types.
Double Dispatch with Classes
Some tests show that this is doing what we expect. Notice that we
get the right result when the first operand is a bar% and the
second a foo%, even though bar% only explicitly specified the
case for when the second operand is also a bar%. This shows the
automatic argument-flipping in operation.
Double Dispatch with Generic Interfaces
The tests show the same argument-flipping behavior as for the
object system above.
Extending The Example
First, we implement and test class zot%…
… and then implement and test struct zot.
Double dispatch is a useful addition to the object-oriented
programmer’s toolkit, and can be straightforwardly added to both
of Racket’s object systems using its macro facility.
This post was written as executable, literate Racket. You can
download the program from
Lack of system support for text yields massive code duplication.
Rather than having a system-wide, comprehensive model of text
representation, encoding, display, input, collation, and comparison,
each programming language and application must fend for itself.
Because it is difficult and time consuming to properly handle text,
developers tend to skimp on text support. Where a weakness is
identified, it must be repaired in each application individually
rather than at the system level. This is itself difficult and time
Finally, dealing only with byte sequences precludes consistent user
The user cannot simply work with a file containing text; they must
make a decision about which encoding to use. Woe betide them if they
A consistent approach would separate the question of text encodings
entirely from application-specific UIs. System UI for transcoding
would exist in one place, common to all applications.
A tiny fraction of the frustration this kind of thing causes is
recorded in Thunderbird’s
Notice that it took fourteen years to be fixed.
This Thunderbird change is just one example. Each and every
application suffers the same problems, and must have its text support
repaired, upgraded, and enhanced independently.
It’s not only a Unix problem. Windows and OS X are just as bad. They,
too, offer no higher-level model than byte sequences to their
applications. Even Android is a missed opportunity.
Learn from the past
Systems like Smalltalk, for all their flaws, offer a
higher-level model to programmers and users alike. In many cases, the
user never need learn about text encoding variations.
Instead, the system can separate text from its encoding.
Where encoding is relevant to the user, there can be a single place
to work with it. Contrast this with the many places encoding leaks
into application UIs today, just one of which is shown in the
Thunderbird example above.
It’s not just text
Text is just one example. Pictures are another. You can probably think
Our operating systems do not support sharing of high-level
abstractions of data between documents or applications.
An operating system with a mechanism for doing so would take a great
burden off both programmers and users.
Let’s start thinking about what a better modern operating system
would look like.
Programming language designers often need to experiment with syntax
directly is out of the question if we want our experiments to escape
Ohm is “a library and domain-specific language for parsing and
language preprocessor. I’ll build a simple compiler for ES5 extended
with a new kind of for loop, using Ohm and the ES5 grammar
included with it.
All the code in this post is available in a Github repo.
Our toy extension: “for five”
We will add a “for five” statement to ES5, which will let us write
programs like this:
The new construct simply runs its body five times in a row, binding a
loop variable in the body. Running the program above through our
Extending the ES5 grammar
We write our extension to the ES5 grammar in a new file for5.ohm as
Let’s take this a piece at a time. First of all, the declaration For5
<: ES5 tells Ohm that the new grammar should be called For5, and
that it inherits from a grammar called ES5. Next,
extends the existing ES5 grammar’s
nonterminal with a new production that will be called
Finally, we define two new nonterminals as convenient shorthands for
parsing the two new keywords, and augment the existing
There are three interesting points to be made about keywords:
First of all, making something a keyword rules it out as an
identifier. In our extended language, writing var five = 5 is a
syntax error. Define new keywords with care!
We make sure to reject input tokens that have our new keywords as a
prefix by defining them as their literal text followed by
anything that cannot be parsed as a part of an identifier,
~identifierPart. That way, the compiler doesn’t get confused by,
say, fivetimes or five_more, which remain valid identifiers.
By making sure to extend keyword, tooling such as syntax
highlighters can automatically take advantage of our extension, if
they are given our extended grammar.
Translating source code using the new grammar
First, require the ohm-js NPM module and its included ES5 grammar:
Next, load our extended grammar from its definition in for5.ohm, and
compile it. When we compile the grammar, we pass in a namespace that
makes the ES5 grammar available under the name our grammar expects,
Finally, we define the translation from our extended language to plain
ES5. To do this, we extend a semantic function, modifiedSource,
adding a method for each new production rule. Ohm automatically uses
defaults for rules not mentioned in our extension.
Each parameter to the IterationStatement_for5_named method is a
syntax tree node corresponding positionally to one of the tokens in
the definition of the parsing rule. Accessing the asES5 attribute of
a syntax tree node computes its translated source code. This is done
with recursive calls to the modifiedSource attribute where required.
Our compiler is, at this point, complete. To use it, we need code to
feed it input and print the results:
This style of syntactic extension is quite coarse-grained: we must
translate whole compilation units at once, and must specify our
extensions separately from the code making use of them. There is no
way of adding a local syntax extension scoped precisely to a block
of code that needs it (known to Schemers as
style of syntax extension than the one explored in this post.
Mention of sweet.js leads me to the thorny topic of
hygiene. Ohm is a
parsing toolkit. It lets you define new concrete syntax, but doesn’t
know anything about scope, or about how you intend to use identifiers.
After all, it can be used for languages that don’t necessarily even
have identifiers. So when we write extensions in the style I’ve
presented here, we must write our translations carefully to avoid
unwanted capture of identifiers. This is a tradeoff: the broad
generality of Ohm’s parsing in exchange for less automation in
Ohm’s extensible grammars let us extend any part of the language, not
just statements or expressions. We can specify new comment syntax, new
string syntax, new formal argument list syntax, and so on. Because Ohm
is based on
parsing expression grammars,
Altering or extending a language’s lexical syntax is just as easy as
altering its grammar.
We have defined an Ohm-based compiler for an extension to ES5
syntax, using only a few lines of code. Each new production rule
requires, roughly, one line of grammar definition, and a short method
defining its translation into simpler constructs.
You can try out this little compiler, and maybe experiment with your
own extensions, by cloning its Github repo.
I ran some very quick-and-dirty informal experiments on my Acer C720
laptop, which is running a 64-bit Debian system and has 2GB RAM and a
two-core Celeron 2955U at 1.40GHz.
I measured approximate alist and hash table performance for
fixnum keys, using eq? as the lookup predicate (so assq, hasheq) (fixnum program)
length-64 byte vector keys, using equal? as the lookup predicate (so assoc, hash) (byte-vector program)
Each chart below has four data series:
probe/alist, average time taken to search for a key that is present in an alist
probe/alist/missing, average time taken to search for a key that is not present in an alist
probe/hasheq or probe/hash, average time taken to search for a key that is present in a hash table
probe/hasheq/missing or probe/hasheq/missing, average time taken to search for a key that is not present in a hash table
Here are average timings for fixnum keys:
Things to note:
Alists are here always faster than hasheq tables for 7 keys or
fewer, whether the key is present or not.
When the key is present in the lookup table, alists are on
average faster up to around 14 keys or so.
Length-64 byte vector keys
Here are average timings for length-64 random byte vector keys:
Things to note:
Alists are here always faster than hasheq tables for 4 keys or
fewer, whether the key is present or not.
When the key is present in the lookup table, alists are on
average faster up to around 16 keys or so.
Alists will be faster when you have very few keys - for eq?, around
seven or fewer, or for equal?, perhaps only as many as four,
depending on the size of each key.
If you expect with high probability that a given key will be present
in the table, the picture changes slightly: then, alists may be faster
on average up to around perhaps fifteen keys. Specifics of the
insertion order of your keys will naturally be very important in this
gRPC looks very interesting. From a quick
browse of the site, it looks like it differs from CORBA primarily in
It is first-order.
It eschews exceptions.
It supports streaming requests and/or responses.
(That’s setting aside differences between protobufs and GIOP.)
It’s the first point that I think is likely to be the big win. Much of
the complexity I saw with CORBA was to do with trying to pass object
(i.e. service endpoint) references back and forth in a transparent way.
Drop that misfeature, and everything from the IDL to the protocol to the
frameworks to the error handling to the implementations of services
themselves will be much simpler.
The way streaming is integrated is interesting too. There’s a clear
separation between (finite) data, including lists/arrays, in the
protobuf message-definition language, and (possibly non-finite) behavior
in the gRPC service-definition language. Streams, being coinductive, fit
naturally in the service-definition part.
From time to time, one stumbles across a website that has gone out of
its way to make it difficult to save images displayed on the page. A
common tactic is to disable right-click for the elements concerned.
From time to time, I make binary snapshot downloads of the RabbitMQ
plugins that I have developed. You will be able to find the most
recent downloads from this page. I sign the downloadable files with
It’s also easy to connect using your own DNS domain
For those of you who have DNS domains of your own, and would like a
email@example.com chat address, I heartily recommend
http://hosted.im/. All you do is add a couple of DNS records,
register at the site, and you have your own personal chat domain. You
can create accounts for yourself and your friends there, and have full
interoperability and federation with the global chat network.
Resist Balkanisation; support independent providers
The XMPP global chat network is the only open, federated chat
network still standing. As such, it deserves our support against the
hostile moves of large companies like Google, Apple, and Microsoft.
Supporting smaller chat account providers and/or running our own
servers is a great way to help keep the internet commons healthy.
There have been lots of demonstrations of monads in dynamically-typed
languages before; notably,
Oleg’s article on monads in Scheme. However, I haven’t
yet (Update:see below) seen one that smoothly
allows for return-type polymorphism.
This post introduces (1) coercions between monad representations and
(2) “undecided” quasi-monadic placeholder values. Taken together,
these give a Haskell-like feel for monads in a dynamically-typed
The techniques are illustrated using Racket, but aren’t specific to
How can we write monadic programs like this, where monad types are
implicit, just as they are in comparable Haskell programs?
The overall computation uses do-notation at IO type, while the
evens list uses do-notation at List type.
Simple monomorphic monads are easy. Here’s the List monad in Racket:
Let’s add some simple do-notation sugar:
Now we can write list comprehensions. For example, let’s select the
odd numbers from a list, and multiply each by two:
This is a fine definition, as far as it goes, but we’ve just run into
the first problem:
Monads behave differently at different types
Simply defining fail, return and bind as functions won’t work.
We need some kind of dynamic method dispatch. Haskell does this by
But there’s a deeper problem, too:
Monads don’t learn their types until it’s too late
How should we choose which dictionary to use? It’s easy with bind,
because the specific monad being bound is always given as bind’s
first argument. The bind implementation can be a method on the
This doesn’t work for return or fail. When they’re called, they
don’t know what kind of monad they should produce. That only becomes
clear later, when their results flow into a bind.
Haskell uses the type system. We have to do it at runtime, on a
To address these problems, we explicitly represent the dictionary we
The failer, returner and binder methods correspond to the monad
operations we met above, but coercer is new. It lets us dynamically
reinterpret a monad at a different monadic type. We’ll see its use
Now we can define our List monad class:
The not-coercable function is for use when it’s not possible to
reinterpret the type of a monad, which is the overwhelmingly common
case. It checks to make sure we’re already at the expected type, and
raises an exception if we’re not.
We need some way of learning which dictionary to use for a given monad
instance. It’s here that Racket’s generics come in:
This declares a new generic interface, gen:monad, with a single
method, monad->monad-class. It supplies implementations of
gen:monad for the builtin types null? and pair?, in each case
returning the List monad-class when asked.
Now we can implement bind and coerce, not just for a single monad, but for all
They use monad->monad-class to find the relevant dictionary, extract
the right method from the dictionary, and delegate to it.
Note that bind dispatches on its first argument, while coerce
dispatches on its second argument: monad instances get to decide how
they are bound and how (or if!) they are to be interpreted at other
Next, we introduce neutral quasi-monad instances for when return
and fail don’t know which monad type to use. Because we might bind
such a quasi-monad before it collapses into a particular type, we need
to define a quasi-monad to represent binds in superposition, too.
The Return method dictionary looks very similar to the
implementation of the
with the addition of a return-struct box around the carried value:
There are two interesting things to note here:
The bind implementation is a direct statement of one of the monad
return x >>= f ≡ f x
The coerce implementation rebuilds the
monad using the return implementation from the target monad.
The Return coerce implementation gives us the equivalent of
return-type polymorphism, letting us avoid sprinkling monad type
annotations throughout our code.
The coerce method for an undetermined failure calls the new
monad-class’s failer method to produce the correct representation
for the final monad.
Likewise, coerce for a suspended-bindre-binds its parameters, after first coercing
them into the now-known monad.
You might have noticed a call to coerce in the bind implementation
for List above:
This is necessary because f might simply (return 1), which is one
of these neutral quasi-monad instances that needs to be told what kind
of thing it should be before it can be used. On the other hand, f
might have returned (list 1), in which case List’s coercer method
will notice that no conversion needs to be done.
The IO Monad
Racket is an eager, imperative language, and so doesn’t need an IO
monad the way Haskell does. But we can define one anyway, to see what
it would be like.
It’s also useful as a template for implementing unusual control
structures for monadic embedded domain-specific languages.
Values in the IO type denote sequences of delayed actions. We’ll
represent these using two structure types, one for return and one
Lifting Racket’s primitive input/output procedures into our IO type is
Finally, we need a way to actually execute a built-up chain of
Revisiting the Challenge Problem
We now have all the pieces we need to run the challenge program given
The challenge comes from the end of Oleg’s article on
monadic programming in Scheme. His example uses many different types
of monad together, using the monomorphic technique he developed:
With our polymorphic monads, we are able to use the generic
do-notation macro defined above, and write instead
which compares favourably to the Haskell
A somewhat fleshed-out implementation of these ideas is available
making monad-classes directly callable and allowing (coerce List
foo) to be written as (List foo).
It uses the
to let monad instances flexibly adapt themselves to each other in
coercions. For example, lists, streams and sets can all be
It uses Racket’s built-in exception type to represent pending
failures instead of the simple structure sketched above. This way,
failures may carry stack traces and an informative error message.
It includes a simple State monad, with sget and sput
I based this work on some
experiments I ran back in 2006
in writing a monadic library for Scheme. Racket offers much better
support for object-oriented/generic programming (among many other
things!) than vanilla Scheme does, which makes for smoother
integration between my monad library and the rest of the language.
Ben Wolfson pointed me to his
monad library for clojure in a
about this post. It seems to be using a very similar approach, with
“neutral” carriers for monadic values that stay neutral until a later
point in the program. The main difference seems to be that with my
approach, no “run” step is needed for some monads, since monadic
values carry their bind implementation with them. Ben’s library
supplies the bind implementation at “run” time instead.
Update, 20150127: Paul Khuong pointed me to
his Scheme monad implementation
this twitter conversation.
It doesn’t have dynamic-dispatch for automatically determining the
appropriate bind implementation, but I suspect it could be added;
perhaps in his join operator, which makes an interesting contrast to
the technique explored in this post. The really nice thing about the
delimited continuation approach to monads is that the return is
implicit. You never mention return explicitly in monadic code.
That makes a big difference, because return-type polymorphism is only
needed to handle explicit returns! By placing the return right
next to the appropriate run operation, the delimited continuation
technique neatly sidesteps the problem.
Haskell’s return is generic: it injects a value into any monad at
all. Which specific monad is used depends on the context. This is
impossible to directly implement in general without static analysis.
Lacking such static analyses in dynamically-typed languages, achieving
the equivalent of Haskell’s return is challenging, even though
implementing particular monomorphic variations is straightforward.
The trick is to make return produce a kind of superposition which
doesn’t collapse to a specific monad type until it touches a monad
that already knows what type it is.
In this post, I’ve shown how this kind of monad “coercion” works well
to give the kind of return-type polymorphism we need to make monads
feel in Racket similar to the way they do in Haskell.
No implementations are given for their failer and
returner methods, since they are only quasi-monad classes, and
it’s not possible for user code to ever be in the Fail or Bind
“Giving a professional illustrator a goal for a poster usually
results in what was desired. If one tries this with an artist, one
will get what the artist needed to create that day. Sometimes we
make, to have, sometimes to know and express.” — Alan Kay