# Revisiting Decimal (generic algorithms)

# Allen Wirfs-Brock (10 years ago)

Returning to Brendan's original question...

The problem I brought up at the Kona meeting was that the Decimal proposal did not consistently enable the writing of functions that implement generic numeric algorithms. By this I mean algorithms that can be applied to either Number or Decimal arguments and produce a result that is of the same type as its inputs for example:

function max3(a,b,c) {return Math.max(a,b,c)} // not generic in Kona proposal, max3(1m,2m,3m) ==> 3 (not 3m) // no generic Math functions so user must explicitly code either Math.max or Decimal.max

function fuzz(a) { return a + 0.1} //not generic in Kona draft, fuzz(1m) ===> 1.10000000000000008881784197001... (but see below) //Kona spec. uses binary floating point for all mixed mode operations

The second case is fixable with some work by making the Math functions all be generic.

Sam says the third case is a bug in the Kona spec. whose fix had already been agreed upon at the Redmond meeting. The fix, as I understand it, is that mixed mode arithmetic should be performed using decimal operations. However, that does not address my concern. With that fix in place, the results of fuzz(1m) would be something like 1.1000000000000000888178419700125232338905334472656250m (<-- note "m"). That is because the literal 0.1 would be lexed as a Number (ie, binary floating point) literal, stored as a binary approximation, and that binary approximation would be dynamically converted to the decimal floating point equivalent of the binary approximation by the add operations.

This problem cannot be fixed simply by tweaking the coercion rules. It probably requires that numeric literals be treated as generic values that are only interpreted situationally as either binary or decimal values in the context of a particular operations.

The design details of the integrations of multiple numeric data types (potentially not just Number and Decimal) and questions such as whether and how a dynamically typed language like ECMAScript should support such generic algorithms will have long lasting impact on the usability of the language. My perspective in Kona, when we talked about Decimal, was that these are Harmony scale issues that must be carefully thought through and that they should not be prematurely and irrevocably resolved as a consequence of an accelerated effort to include Decimal in ES3.1.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 11:16 AM, Allen Wirfs-Brock wrote:

Returning to Brendan's original question...

Thanks, this is a very informative reply.

[much good stuff deleted]

This problem cannot be fixed simply by tweaking the coercion rules.
It probably requires that numeric literals be treated as generic
values that are only interpreted situationally as either binary or
decimal values in the context of a particular operations.

That, or multimethods so we don't essentially carry around literals in
source form and pay high costs converting them according to context.
That was the ES4 solution at one point, until we started cutting.
Based on Dylan and Cecil precedents:

The design details of the integrations of multiple numeric data
types (potentially not just Number and Decimal) and questions such
as whether and how a dynamically typed language like ECMAScript
should support such generic algorithms will have long lasting impact
on the usability of the language. My perspective in Kona, when we
talked about Decimal, was that these are Harmony scale issues that
must be carefully thought through and that they should not be
prematurely and irrevocably resolved as a consequence of an
accelerated effort to include Decimal in ES3.1.

Well stated. Everyone agreed on this point, as well as on the spec not
being ready (and not in minor ways) -- both reasons led to decimal
being cut from 3.1. We should work on the long-term solution, since
bugs continue to be filed on unwanted rounding errors due to binary
double precision. And we should not make mixed-mode honey traps via
implicit conversions, including in JSON encoding.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 12:11 PM, Brendan Eich wrote:

This problem cannot be fixed simply by tweaking the coercion
rules. It probably requires that numeric literals be treated as
generic values that are only interpreted situationally as either
binary or decimal values in the context of a particular operations.

That, or multimethods so we don't essentially carry around literals
in source form and pay high costs converting them according to
context. That was the ES4 solution at one point, until we started
cutting. Based on Dylan and Cecil precedents:

# Allen Wirfs-Brock (10 years ago)

-----Original Message----- From: Brendan Eich [mailto:brendan at mozilla.com] Sent: Friday, January 16, 2009 12:12 PM

This problem cannot be fixed simply by tweaking the coercion rules. It probably requires that numeric literals be treated as generic values that are only interpreted situationally as either binary or decimal values in the context of a particular operations.

That, or multimethods so we don't essentially carry around literals in source form and pay high costs converting them according to context. That was the ES4 solution at one point, until we started cutting. Based on Dylan and Cecil precedents:

I think that carry dual encodings (both binary and decimal) for each numeric literal might be a reasonable approach as long as we only have two types. However choosing that over maintaining the source form sounds like an implementation rather than specification decision.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 2:25 PM, Allen Wirfs-Brock wrote:

I think that carry dual encodings (both binary and decimal) for
each numeric literal might be a reasonable approach as long as we
only have two types.

Excluding small integer literals, most numeric literals in my
experience are small enough that carrying 8 + 16 = 24 bytes loses, but
you're right that this is all implementation detail. Still, the spec
is informed by implementor feedback, to the point that it can't be
developed in a vacuum or it might be ignored.

However choosing that over maintaining the source form sounds
like an implementation rather than specification decision.

Speaking for Mozilla, we probably can't tolerate anything like
carrying around two representations, or source forms, for number
literals. I'd have to measure non-int literals to say for sure, but
gut check says no.

I'm not saying multimethods are the only way forward. I'm genuinely
interested in new thinking about numbers and decimal, because of that
most-frequently-dup'ed bug:

bugzilla.mozilla.org/show_bug.cgi?id=5856

But I do not see a solution for it yet, and your point that we need to
solve this just to get decimal+double into the language is right on.

# Sam Ruby (10 years ago)

On Fri, Jan 16, 2009 at 3:11 PM, Brendan Eich <brendan at mozilla.com> wrote:

On Jan 16, 2009, at 11:16 AM, Allen Wirfs-Brock wrote:

Returning to Brendan's original question...

Thanks, this is a very informative reply.

Indeed. This is the first time I understood (at a high level) the request. I'm not saying it wasn't explained before, or even that it wasn't explained well, but this is the first time I understood it (again at a high level, questions on details below).

[much good stuff deleted]

This problem cannot be fixed simply by tweaking the coercion rules. It probably requires that numeric literals be treated as generic values that are only interpreted situationally as either binary or decimal values in the context of a particular operations.

That, or multimethods so we don't essentially carry around literals in source form and pay high costs converting them according to context. That was the ES4 solution at one point, until we started cutting. Based on Dylan and Cecil precedents:

Like Allen says later, most small integers (i.e., the ones that fit exactly in a double precision binary value) can simply be retained as binary64. I suspect that covers the majority of constants in deployed javascript. Now let's consider the rest.

First, Allen's example:

function fuzz(a) { return a + 0.1}

Where fuzz(0.1)===0.2 and fuzz(0.1m)===0.2m

The only way I can see that working is if the constant is initially in a form that either is readily convertible to source, or stores both values. I don't understand how multimethods (on "+"?) affect this. If I'm missing something, please let me know (or simply provide a pointer to where I can educate myself).

Continuing on, let's tweak this a bit.

function fuzz(a) {var b=0.1; return a+b}

I would suggest that if the expectation would be that this function behaves the same as the previous one.

My interpretation is that this means that internally there are three data types, one that is double, one that is decimal, and one that somehow manages to be both. Internally in that this implementation detail ideally should not be visible to the application programmer. Again, I could be wrong (in the need for three data types, not on the opinion that this should not be visible), but pressing on...

function is_point_one(a) {var b=0.1; return b===a}

Is the expectation that this would return true for both 0.1 and 0.1m? This leads to a rather odd place where it would be possible for triple equals to not be transitive, i.e. a===b and b===c but not a!===c. That alone is enough to give me pause and question this approach.

Continuing trip down this looking glass, what should typeof(0.1) return? You might come to a different conclusion, and again I might be missing something obvious, but if these Schrödinger's catstants (sorry for the bad pun) can be assigned to variable, then I would assert that typeof(0.1) and typeof(0.1m) should both be 'number'.

Finally, this has bearing on the previous json discussion. If it is possible to defer the binding of a literal value to a particular variant of floating point (i.e., binary vs decimal), then there no longer is no need for a JSON parse to prematurely make this determination.

I suspect that these last two paragraphs will make Kris happy.

But I'll stop here. I may very well be out in the weeds at this point. But my initial take is that this approach produces a different (and somehow more fundamental) set of surprises that the approach than we had previously agreed on, and furthermore it isn't clear to me that this approach can be implemented in a way that has negligible performance impact for applications that never make use of decimal.

But I hope that one or both of you (or anybody else) can point out something that I'm missing.

• Sam Ruby
# David-Sarah Hopwood (10 years ago)

Allen Wirfs-Brock wrote: [...]

function fuzz(a) { return a + 0.1} //not generic in Kona draft, fuzz(1m) ===> 1.10000000000000008881784197001... (but see below) //Kona spec. uses binary floating point for all mixed mode operations

[...]

This problem cannot be fixed simply by tweaking the coercion rules. It probably requires that numeric literals be treated as generic values that are only interpreted situationally as either binary or decimal values in the context of a particular operations.

I am not aware of any precedent for this approach in other languages, and I'm very skeptical about whether it can be made to work in ECMAScript. Consider

function id(x) { return x; }

What is the result and type of id(0.1) in this approach, and why?

# David-Sarah Hopwood (10 years ago)

David-Sarah Hopwood wrote:

Allen Wirfs-Brock wrote: [...]

function fuzz(a) { return a + 0.1} //not generic in Kona draft, fuzz(1m) ===> 1.10000000000000008881784197001... (but see below) //Kona spec. uses binary floating point for all mixed mode operations

[...]

This problem cannot be fixed simply by tweaking the coercion rules. It probably requires that numeric literals be treated as generic values that are only interpreted situationally as either binary or decimal values in the context of a particular operations.

I am not aware of any precedent for this approach in other languages, and I'm very skeptical about whether it can be made to work in ECMAScript. Consider

function id(x) { return x; }

What is the result and type of id(0.1) in this approach, and why?

• if binary 0.1, then we would have

1m + 0.1 !== 1m + id(0.1)

which breaks referential transparency (in the absence of side-effects)

• if decimal 0.1m, then we break compatibility with ES3.

• if the value remains generic, then such values must be supported at run-time as a third numeric type besides number and decimal, which seems unsupportably complex to me.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 4:30 PM, Sam Ruby wrote:

Indeed. This is the first time I understood (at a high level) the request. I'm not saying it wasn't explained before, or even that it wasn't explained well, but this is the first time I understood it (again at a high level, questions on details below).

It's good to get this understood widely -- it probably did not come
through in the notes from Kona (useful as they were). Sorry on my part
for that, kudos again to Allen.

Like Allen says later, most small integers (i.e., the ones that fit exactly in a double precision binary value) can simply be retained as binary64.

Or machine ints -- ALU >> FPU still.

I suspect that covers the majority of constants in deployed javascript. Now let's consider the rest.

First, Allen's example:

function fuzz(a) { return a + 0.1}

Where fuzz(0.1)===0.2 and fuzz(0.1m)===0.2m

The only way I can see that working is if the constant is initially in a form that either is readily convertible to source, or stores both values. I don't understand how multimethods (on "+"?) affect this. If I'm missing something, please let me know (or simply provide a pointer to where I can educate myself).

I did, see followup links to reading-lists, from which I'll pick a

Continuing on, let's tweak this a bit.

function fuzz(a) {var b=0.1; return a+b}

I would suggest that if the expectation would be that this function behaves the same as the previous one.

My interpretation is that this means that internally there are three data types, one that is double, one that is decimal, and one that somehow manages to be both. Internally in that this implementation detail ideally should not be visible to the application programmer. Again, I could be wrong (in the need for three data types, not on the opinion that this should not be visible), but pressing on...

No, Allen allowed for that, but of course this generic type has to
propagate at runtime through variable and function abstraction.

function is_point_one(a) {var b=0.1; return b===a}

Is the expectation that this would return true for both 0.1 and 0.1m?

I don't see how this could work.

This leads to a rather odd place where it would be possible for triple equals to not be transitive, i.e. a===b and b===c but not a!===c.

Er, a!==c ;-).

That alone is enough to give me pause and question this approach.

Me too.

Continuing trip down this looking glass, what should typeof(0.1) return? You might come to a different conclusion, and again I might be missing something obvious, but if these Schrödinger's catstants (sorry for the bad pun) can be assigned to variable, then I would assert that typeof(0.1) and typeof(0.1m) should both be 'number'.

It should be clear that I won't go this far. My reply to Allen was
gently suggesting that his suggestion would not fly on implementation
efficiency grounds, but I think you've poked bigger holes. I'm still
interested in multimethods, including for operators.

Finally, this has bearing on the previous json discussion. If it is possible to defer the binding of a literal value to a particular variant of floating point (i.e., binary vs decimal), then there no longer is no need for a JSON parse to prematurely make this determination.

I suspect that these last two paragraphs will make Kris happy.

The previous paragraphs should induce unhappiness that trumps that
illusory joy, though.

But I'll stop here. I may very well be out in the weeds at this point. But my initial take is that this approach produces a different (and somehow more fundamental) set of surprises that the approach than we had previously agreed on, and furthermore it isn't clear to me that this approach can be implemented in a way that has negligible performance impact for applications that never make use of decimal.

But I hope that one or both of you (or anybody else) can point out something that I'm missing.

Not me, and I see David-Sarah has observed that dual representation
cannot be confined to literals.

But I'd still like to encourage thinking outside of the narrow ES3-ish
box in which Decimal has been cast. If not multimethods, some other
novel (to ES, not to well-researched language design) is needed.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 5:30 PM, David-Sarah Hopwood wrote:

David-Sarah Hopwood wrote:

function id(x) { return x; }

What is the result and type of id(0.1) in this approach, and why?

• if binary 0.1, then we would have

1m + 0.1 !== 1m + id(0.1)

which breaks referential transparency (in the absence of side- effects)

• if decimal 0.1m, then we break compatibility with ES3.

• if the value remains generic, then such values must be supported at run-time as a third numeric type besides number and decimal, which seems unsupportably complex to me.

Agreed on all points.

Have you looked at multimethods in Cecil?

Good discussion, let's keep it going.

# Sam Ruby (10 years ago)

On Fri, Jan 16, 2009 at 8:30 PM, Brendan Eich <brendan at mozilla.com> wrote:

Like Allen says later, most small integers (i.e., the ones that fit exactly in a double precision binary value) can simply be retained as binary64.

Or machine ints -- ALU >> FPU still.

Agreed. Those values that could fit in int32 before could continue to do so.

I suspect that covers the majority of constants in deployed javascript. Now let's consider the rest.

First, Allen's example:

function fuzz(a) { return a + 0.1}

Where fuzz(0.1)===0.2 and fuzz(0.1m)===0.2m

The only way I can see that working is if the constant is initially in a form that either is readily convertible to source, or stores both values. I don't understand how multimethods (on "+"?) affect this. If I'm missing something, please let me know (or simply provide a pointer to where I can educate myself).

I must be dense. My previous understanding of multimethods was that it depends on the assumption that the type of each argument can be determined. That article doesn't change that for me.

Continuing on, let's tweak this a bit.

function fuzz(a) {var b=0.1; return a+b}

I would suggest that if the expectation would be that this function behaves the same as the previous one.

So, here's the problem. At the point of the ';' in the above, what is the result of typeof(b)?

The problem gets worse rapidly. The above may seem to be appealing at first, but it degenerates rapidly. Consider:

function fuzz(a) {var b=0.05; var c=0.05; var d=b+c; return a+d}

Should this return the same results as the previous fuzz functions? What is the value of typeof(d)?

My interpretation is that this means that internally there are three data types, one that is double, one that is decimal, and one that somehow manages to be both. Internally in that this implementation detail ideally should not be visible to the application programmer. Again, I could be wrong (in the need for three data types, not on the opinion that this should not be visible), but pressing on...

No, Allen allowed for that, but of course this generic type has to propagate at runtime through variable and function abstraction.

I don't follow.

function is_point_one(a) {var b=0.1; return b===a}

Is the expectation that this would return true for both 0.1 and 0.1m?

I don't see how this could work.

Before proceeding, let me simplify that:

function is_point_one(a) {return a===0.1}

The point of "fuzz" was that 0.1 as a literal would be interpreted as a binary64 or as a decimal128 based on what it was combined with. Why would this example be any different?

This leads to a rather odd place where it would be possible for triple equals to not be transitive, i.e. a===b and b===c but not a!===c.

Er, a!==c ;-).

That alone is enough to give me pause and question this approach.

Me too.

Continuing trip down this looking glass, what should typeof(0.1) return? You might come to a different conclusion, and again I might be missing something obvious, but if these Schrödinger's catstants (sorry for the bad pun) can be assigned to variable, then I would assert that typeof(0.1) and typeof(0.1m) should both be 'number'.

It should be clear that I won't go this far. My reply to Allen was gently suggesting that his suggestion would not fly on implementation efficiency grounds, but I think you've poked bigger holes. I'm still interested in multimethods, including for operators.

I don't see how this reasonably can be done half way.

And while multimethods are appealing for other reasons, I don't think they relate to what Allen is suggesting.

• Sam Ruby
# Brendan Eich (10 years ago)

On Jan 16, 2009, at 5:54 PM, Sam Ruby wrote:

I must be dense. My previous understanding of multimethods was that it depends on the assumption that the type of each argument can be determined. That article doesn't change that for me.

Good! :-P

Not static typing, mind you; but typing nonetheless.

My interpretation is that this means that internally there are three data types, one that is double, one that is decimal, and one that somehow manages to be both. Internally in that this implementation detail ideally should not be visible to the application programmer. Again, I could be wrong (in the need for three data types, not on
the opinion that this should not be visible), but pressing on...

No, Allen allowed for that, but of course this generic type has to
propagate at runtime through variable and function abstraction.

I don't follow.

My reading of Allen's message was that the generic type was for
literals only, and would collapse (as in a superposed wave function)
into decimal or double on first operational use. but use can be
delayed through variable or parameter assignment. So the generic or
both-double-and-decimal type must be used more widely than just for
literal terms at runtime.

function is_point_one(a) {var b=0.1; return b===a}

Is the expectation that this would return true for both 0.1 and 0.1m?

I don't see how this could work.

Before proceeding, let me simplify that:

function is_point_one(a) {return a===0.1}

The point of "fuzz" was that 0.1 as a literal would be interpreted as a binary64 or as a decimal128 based on what it was combined with. Why would this example be any different?

It wouldn't, but that breaks one of three important properties
(referential transparency, compatibility, or implementation
efficiency) as DSH has pointed out.

It should be clear that I won't go this far. My reply to Allen was
gently suggesting that his suggestion would not fly on implementation
efficiency grounds, but I think you've poked bigger holes. I'm still
interested in multimethods, including for operators.

I don't see how this reasonably can be done half way.

Right.

And while multimethods are appealing for other reasons, I don't think they relate to what Allen is suggesting.

They do not -- they are the only sane alternative that I know of.

# David-Sarah Hopwood (10 years ago)

Brendan Eich wrote:

On Jan 16, 2009, at 5:30 PM, David-Sarah Hopwood wrote:

David-Sarah Hopwood wrote:

function id(x) { return x; }

What is the result and type of id(0.1) in this approach, and why?

• if binary 0.1, then we would have

1m + 0.1 !== 1m + id(0.1)

which breaks referential transparency (in the absence of side-effects)

• if decimal 0.1m, then we break compatibility with ES3.

• if the value remains generic, then such values must be supported at run-time as a third numeric type besides number and decimal, which seems unsupportably complex to me.

Agreed on all points.

A final nail in the coffin for the last (three-type) option above:

In ES3, the expression Number(0.1 + 0.1 + 0.1) would give Number(0.1) + Number(0.1) + Number(0.1) == 0.3000000000000000444089209850062616169452667236328125

In the three-type option, it would give Number(0.3) == 0.299999999999999988897769753748434595763683319091796875

(Decimal expansions are computed using SpiderMonkey's implementation of toFixed. The point is simply that they are different.)

So the three-type option does not maintain compatibility, at least if we are concerned with exact values.

It could be argued that most ES3.x programs are probably not relying on the exact errors introduced by double-precision IEEE 754, but that seems risky to me. By that argument, ignoring performance, you could unconditionally implement all numbers as decimals, and I don't think many people here would accept that as being compatible.

Compatibility could, in principle, be maintained by adding a third kind of literal for generic values, with a different suffix. However, I think it is likely that unless generic values used the suffix-free numeric literal form, they would remain too rarely used to make any difference to the issue that Allen is concerned about.

Have you looked at multimethods in Cecil?

I've previously studied Cecil's multimethods and type system in detail (it's very nicely designed IMHO), but I'm not sure that it is what we need here. Multimethods address the problem of how to concisely define type-dependent functions, but the implementations of those functions still have to be given explicitly for each type combination on which the behaviour differs (ignoring inheritance and subtyping, which I don't think are relevant here).

To address the problem raised by Allen, you would probably want to implicitly define implementations that used different types for constants, depending on the argument types to a given function (and it is not clear how that would work for mixed-type arguments).

In any case, I think we first need to decide what the semantics would be after any desugaring of multimethods.

# Mark S. Miller (10 years ago)

On Fri, Jan 16, 2009 at 5:34 PM, Brendan Eich <brendan at mozilla.com> wrote:

Have you looked at multimethods in Cecil?

On your recommendation, I have. I really wanted to like it. I really tried to like it. In the end I was repelled in horror at its complexity.

Good discussion, let's keep it going.

Indeed. After I made a simple proposal < esdiscuss/2009-January/008535>,

On Fri, Jan 9, 2009 at 7:56 AM, Michael Daumling <mdaeumli at adobe.com> wrote:

The discussion about operator overloading quickly went away from the JavaScript'ish approach that ExtendScript and your proposal used towards generic functions. At some time, the discussion stranded in areas too exotic for me. There is a rationale here: discussion:operators

The objections listed there are

I think this feature is too weak to be included. Here are some reasons why I

think that:

• Uncontrollable subtleties in dispatch: Adding eg a == operator to one class and then comparing an instance x of that class to a value y of another type means that the result can easily differ depending on whether the programmer writes x == y or y == x. (If y has an operator == too then its operator will be preferred in the latter case.) The most the author of the == operator can do about this is to add types to the operator's signature so that strict mode catches the bug or the program fails predictably at run-time.

I'd argue that this is a feature, not a bug. Whether an operator is

commutative depends on the meaning of that operator on that data type. "x * y" should mean the same as "y * x" if they are scalar numbers but not if they are matrices.

• No inheritance: in almost all cases we would wish that if instances of A and B are comparable with a certain semantics then instances of their respective subclasses C and D are too.

That objection doesn't apply to my proposal. (I'm not sure it does to

• No compositionality: As the operators are tied to classes, a program that wishes to use two separately authored classes A and B cannot define their relations in terms of operators, the classes must be altered because they do not know about each other.

Again, I'd argue that this is a feature, not a bug. Likewise, if I see the

expression "x.foo(y)" and the meaning of the foo operation does not treat its operands opaquely, if neither x nor y know about each other's interface, then I'd expect the operation to fail. If some party outside of x and y could define a generic foo that could make this operation succeed anyway, I'd consider that a bug.

Including operators as currently proposed would probably give us a headache if we wish to introduce a more powerful feature (probably based on some sort of ad-hoc overloading) in the future.

Functional folks often refer to oo polymorphism (or "late binding") as "ad-hoc polymorphism", to distinguish it from their parametric polymorphism. If this is what is meant, then my proposal and Adobe's both provide ad-hoc polymorphism. If, as I suspect, something else is meant, I await hearing what it might be.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 7:38 PM, David-Sarah Hopwood wrote:

It could be argued that most ES3.x programs are probably not relying on the exact errors introduced by double-precision IEEE 754, but that seems risky to me.

Emphatically agreed. People file dups of bug 5856 but they also
knowingly and unknowingly depend on IEEE 754 behavior in detail.

By that argument, ignoring performance, you could unconditionally implement all numbers as decimals, and I don't think many people here would accept that as being compatible.

This was the path favored by Mike Cowlishaw and (sometimes, IIRC) by
Doug Crockford. It was rejected by at least me (for Mozilla) and
Maciej (for Apple).

To address the problem raised by Allen, you would probably want to implicitly define implementations that used different types for constants, depending on the argument types to a given function (and it is not clear how that would work for mixed-type arguments).

Another idea for constants that seems strictly more usable than any
suffix requirement or complicated constant-parameter-based dispatch:
"use decimal". The idea is to change the meaning of literals andn
operators. Again the problem of built-ins, or really of interfacing
with the rest of the world not scoped by the lexical pragma, remains.

In any case, I think we first need to decide what the semantics would be after any desugaring of multimethods.

The goal is "DWIM", which is why we've circled around these implicit
or low-cost-if-explicit approaches.

• changing the number type to decimal by fiat;
• adding a "use decimal" pragma;
• trying to keep literals generic.

The high-cost explicit alternative is to tell 'em "use the m suffix!"
That probably will not work out well in the real world. It's a syntax
tax hike: it will require all user agents to be upgraded (unlike "use
decimal"), and yet people will still forget to use the suffix.

I'm still interested in better "use decimal" design ideas.

# Brendan Eich (10 years ago)

On Jan 16, 2009, at 9:05 PM, Mark S. Miller wrote:

On Fri, Jan 16, 2009 at 5:34 PM, Brendan Eich <brendan at mozilla.com>
wrote: Have you looked at multimethods in Cecil?

On your recommendation, I have. I really wanted to like it. I really
tried to like it. In the end I was repelled in horror at its
complexity.

You and David-Sarah should discuss your differenct reactions -- I'd
genuinely appreciate the insights.

Good discussion, let's keep it going.

Indeed. After I made a simple proposal <esdiscuss/2009-January/008535

,

BTW, as I said to you at the TC39 meeting, I think the language is
better off with what you propose in the Harmony timeframe than with
nothing in the way of extensible operator support. Also, as Waldemar's
notes reflect, after discussion we concluded that this is insufficient
for decimal.

On Fri, Jan 9, 2009 at 7:56 AM, Michael Daumling
JavaScript'ish approach that ExtendScript and your proposal used
towards generic functions. At some time, the discussion stranded in
areas too exotic for me. There is a rationale here: discussion:operators

The objections listed there are

I think this feature is too weak to be included. Here are some
reasons why I think that:

Uncontrollable subtleties in dispatch: Adding eg a == operator to
one class and then comparing an instance x of that class to a value
y of another type means that the result can easily differ depending
on whether the programmer writes x == y or y == x. (If y has an
operator == too then its operator will be preferred in the latter
to add types to the operator's signature so that strict mode catches
the bug or the program fails predictably at run-time. I'd argue that this is a feature, not a bug. Whether an operator is
commutative depends on the meaning of that operator on that data
type. "x * y" should mean the same as "y * x" if they are scalar
numbers but not if they are matrices.

Yes, but for many commutative operators there's no benefit and only
cost to double-dispatch.

No inheritance: in almost all cases we would wish that if instances
of A and B are comparable with a certain semantics then instances of
their respective subclasses C and D are too. That objection doesn't apply to my proposal. (I'm not sure it does

Depends on how you define "subclasses", but let's say this does not
apply for prototype-based delegation. Ok -- fair enough.

No compositionality: As the operators are tied to classes, a program
that wishes to use two separately authored classes A and B cannot
define their relations in terms of operators, the classes must be
altered because they do not know about each other. Again, I'd argue that this is a feature, not a bug. Likewise, if I
see the expression "x.foo(y)" and the meaning of the foo operation
does not treat its operands opaquely, if neither x nor y know about
each other's interface, then I'd expect the operation to fail. If
some party outside of x and y could define a generic foo that could
make this operation succeed anyway, I'd consider that a bug.

That's what I knew you'd say, but Chambers made the case well enough:

The generalization of receiver-based dispatch to multiple dispatch
provides a number of advantages. For example, multimethods support
safe covariant overriding in the face of subtype polymorphism,
providing a natural solution to the binary method problem [Bruce et
al. 1995; Castagna 1995]. More generally, multimethods are useful
whenever multiple class hierarchies must cooperate to implement a
method’s functionality. For example, the code for handling an event in
an event-based system depends on both which event occurs and which
component is handling the event.

MultiJava: Design Rationale, Compiler Implementation, and Applications Curtis Clifton, Todd Millstein, Gary T. Leavens, and Craig Chambers

www.cs.washington.edu/research/projects/cecil/pubs/mj-toplas.html

Over and over, in Mozilla code and especially on the web, we've seen
"code mashups" where one does not always have the money, or even the
ability, to monkey-patch class A or class B to understand each other.
Wrapping can be done to make a class C with operators, at some cost.
Why this is always a feature and never a bug is not clear, and
Chambers, et al. have researched a fix to it, viewing it as a bug to
motivate their research.

Including operators as currently proposed would probably give us a
headache if we wish to introduce a more powerful feature (probably

Functional folks often refer to oo polymorphism (or "late binding")
as "ad-hoc polymorphism", to distinguish it from their parametric
polymorphism. If this is what is meant, then my proposal and Adobe's
both provide ad-hoc polymorphism. If, as I suspect, something else
is meant, I await hearing what it might be.

According to en.wikipedia.org/wiki/Polymorphism_(computer_science) (hey, it's referenced):

There are two fundamentally different kinds of polymorphism,
originally informally described by Christopher Strachey in 1967. If
the range of actual types that can be used is finite and the
combinations must be specified individually prior to use, it is called
Ad-hoc polymorphism. If all code is written without mention of any
specific type and thus can be used transparently with any number of
new types, it is called parametric polymorphism. John C. Reynolds (and
later Jean-Yves Girard) formally developed this notion of polymorphism
as an extension to the lambda calculus (called the polymorphic lambda
calculus, or System F).

So multimethods use parametric polymorphism.

operators via double-dispatch now, then adding multiple dispatch in
some form later and being prevented by compatibility considerations
from changing operators. Best to ask him directly, though -- I'll do
that.

# Brendan Eich (10 years ago)

On Jan 18, 2009, at 4:48 PM, Brendan Eich wrote:

In any case, I think we first need to decide what the semantics would be after any desugaring of multimethods.

The goal is "DWIM", which is why we've circled around these implicit
or low-cost-if-explicit approaches.

Of course DWIM is ill-defined, but bug 5856 and dups suggest much of
the problem comes from the language supporting numeric literals
written in base 10 with certain precision or significance, but then
mistreating them via conversion to binary and inevitable operation
using only binary operators.

1. changing the number type to decimal by fiat;
2. adding a "use decimal" pragma;
3. trying to keep literals generic.

The high-cost explicit alternative is to tell 'em "use the m
suffix!" That probably will not work out well in the real world.
It's a syntax tax hike: it will require all user agents to be
upgraded (unlike "use decimal"), and yet people will still forget to
use the suffix.

I'm still interested in better "use decimal" design ideas.

Allen made another proposal, which Waldemar mentioned in his notes
from the TC39 meeting:

1. All literals lex as decimal, string to number likewise converts to
decimal; but contagion is to binary, Math.sin/PI/etc. remain binary.
JSON would parse to decimal in this proposal.

This variation may require opt-in as Waldemar pointed out: people
write 1e400 to mean Infinity.

This variation preserves wrappers, so a Decimal converter function
(when invoked) and constructor (via new, and to hold a .prototype home
for methods). The committee plunks for more of this primitive/wrapper
business, since we have wrappers and primitives for numbers and other
types, and backward compatibility requires keeping them. Operators
work mostly as implemented already by Sam (results here, with some out- of-date results; notably typeof 1.1m should be "decimal" not "object"
-- and not "number").

Sam and I are going to work on adapting Sam's SpiderMonkey
implementation, along with our existing ES3.1-based JSON codec and
trace-JITting code, to try this out. More details as we get into the
work.

Since the bug is about usability, we have to prototype and test on
real users, ideally a significant number of users. We crave comments
and ideas from es-discuss too, of course.

# Brendan Eich (10 years ago)

On Jan 30, 2009, at 6:28 PM, Brendan Eich wrote:

According to en.wikipedia.org/wiki/Polymorphism_(computer_science) (hey, it's referenced):

There are two fundamentally different kinds of polymorphism,
originally informally described by Christopher Strachey in 1967. If
the range of actual types that can be used is finite and the
combinations must be specified individually prior to use, it is
called Ad-hoc polymorphism. If all code is written without mention
of any specific type and thus can be used transparently with any
number of new types, it is called parametric polymorphism. John C.
Reynolds (and later Jean-Yves Girard) formally developed this notion
of polymorphism as an extension to the lambda calculus (called the
polymorphic lambda calculus, or System F).

So multimethods use parametric polymorphism.

Correction: multimethods are ad-hoc too, since you have write a
particular type combination. For dyadic operators, the multiple- argument dispatch differs from single (left, receiver) dispatch, but
the type combinations are still finite and specified.

Not sure this matters. The real argument is about single vs. multiple
dispatch.

operators via double-dispatch now, then adding multiple dispatch in
some form later and being prevented by compatibility considerations
from changing operators. Best to ask him directly, though -- I'll do
that.

Lars meant exactly that -- in any conversation tending toward a future
version of the language where multimethods or something that addresses
the "bugs" (or features from the other point of view) of single- dispatch operators might come along, standardizing single dispatch and
requiring double(-single)-dispatch from left to right, with
"reverse_add" and so on, would be future-hostile.

# Sam Ruby (10 years ago)

Brendan Eich wrote:

This variation preserves wrappers, so a Decimal converter function (when invoked) and constructor (via new, and to hold a .prototype home for methods). The committee plunks for more of this primitive/wrapper business, since we have wrappers and primitives for numbers and other types, and backward compatibility requires keeping them. Operators work mostly as implemented already by Sam (results here intertwingly.net/blog/2008/08/27/ES-Decimal-Updates, with some out-of-date results; notably typeof 1.1m should be "decimal" not "object" -- and not "number").

More up to date results can be found here:

intertwingly.net/stories/2008/09/20/estest.html

Which was discussed here:

esdiscuss/2008-December/008316

Sam and I are going to work on adapting Sam's SpiderMonkey implementation, along with our existing ES3.1-based JSON codec and trace-JITting code, to try this out. More details as we get into the work.

Since the bug is about usability, we have to prototype and test on real users, ideally a significant number of users. We crave comments and ideas from es-discuss too, of course.

I'd like to highlight one thing: Mike and I agreed to "no visible cohorts" with the full knowledge that it would be a significant usability issue. We did so in order to get decimal in 3.1. In the context of Harmony, I feel that is is important that we fully factor in usability concerns. Prototyping and testing on real users, ideally with a significant number of users, is an excellent way to proceed.

/be

• Sam Ruby