My first blog ever, and for a Haskell oriented blog a Javascript flavored topic seemed to be a good start 🙂. I intend to spend time on my UHC adventures: internals, problems, solutions, open questions, etc etc. As I have been working on a Javascript backend for UHC it thus fits quite well here.
I started making a Javascript backend after ICFP 2010. A couple of people I spoke to at the ICFP (and already before) had expressed it would be a good idea to do so. There seem to be various attempts to do something functional with Javascript, either as a Haskell compiler backend (
YHC), or as a library (
Functional Javascript), or as a Haskell interpreter written in Javascript (
haskellinjavascript). Regretfully, none of these seem to be either alive or mature. Perhaps there is more.
For this entry, I’ll explain the interpreter for which code is generated, and how it interacts with Javascript. To make it into a full Haskell to Javascript compiler more than that is required, but I’ll go into the issues and todos in a followup blog entry.
Javascript interpreter
Functional programming in Haskell (obviously) is about functions, lazy applications of those functions, and forcing evaluation when we are interested in the actual computed value of applications. So those are the three ingredients modeled by objects in Javascript. A function Fun object is constructed given a Javascript function fun, and can be applied to arbitrary Javascript values:
function Fun( fun ) { ...
}
Fun.prototype = {
applyN : function ( args ) ...
needsNrArgs : function() ...
}
The main difference between strict and lazy functional languages is that the delay of a an actual computation must be represented explicitly, usually this is done by remembering the not yet applied function and its arguments (a closure, thunk). Here a Javascript apply object is used, in two variations, one for undersaturated function applications still lacking a known number of arguments (
AppLT), and one for the applications of which we do not know under-, over-, or exactly right saturation (
App):
AppLT.prototype = {
applyN : function ( args ) ...
needsNrArgs : function() ...
}
function AppLT( fun, args ) { ...
}
App.prototype = {
applyN : function ( args ) ...
}
function App( fun, args ) { ...
}
The last ingredient is a function
eval, necessary to force evaluation of an application:
function eval( x ) ...
So, let’s look at these in more detail, beginning with arbitrary, lazy, application. A design choice is to be able to arbitrarily mix Javascript values and interpreter values like evaluated and not yet evaluated applications. In order to distinguish these, the interpreter maintained values have a field
eOrV, short for “evaluator or value”, which either holds a Javascript function to
evaluate a not yet evaluated application, or the resulting
value of this computation:
function App( fun, args ) {
this.eOrV = function() {
var x = ( fun.applyN( args ) ) ;
this.eOrV = x ;
return x ;
}
}
The above constructor for an application takes a function and its arguments. The function
fun can be a
Fun,
AppLT, or another
App, the arguments
args are represented by a Javascript
Array holding arbitrary values. The
App construction piggybacks on Javascript closures by building a parameterless Javascript function to force evaluation. This function is put in the
eOrV field, which itself is overwritten when invoked: long live untyped interpreted languages
🙂! An
App thus represents closures; forcing an
App to evaluate (to WHNF) is done by the following (yet incorrect version of)
eval:
// Incorrect version of eval:
function eval( x ) {
if ( typeof x.eOrV == 'function' ) {
x = x.eOrV() ;
} else if ( x.eOrV ) {
x = x.eOrV ;
}
return x ;
}
This not yet correct version of
eval (two reasons why..) inspects the
eOrV field. If a function, it simply invokes it, if not, it returns the value. Internally,
applyN is used to actually (i.e. strictly) do the application. Each of the objects used by the interpreter knows how to deal with this. For an
App we first need to evaluate the
App closure (i.e. compute the delayed application), then apply it directly to the newly given arguments. However, we do not do the last part directly as this may lead us into too deep recursion, in particular tail recursion! Instead a new anonymous Javascript object is returned holding as its only field the function which will do this, thus allowing to return and free some of the Javascript stack:
App.prototype = {
applyN : function ( args ) {
var fun = eval(this) ;
return {
eOrV : function() {
return fun.applyN( args ) ;
} } ;
}
}
It now has become the responsibility of the caller of
applyN to continue with the evaluation, in our case the
eval function. The
eval function has to repeatedly test whether still progress can be made, the correct version is as follows:
function eval( x ) {
while ( x && x.eOrV ) {
if ( typeof x.eOrV == 'function' ) {
x = x.eOrV() ;
} else {
x = x.eOrV ;
}
}
return x ;
}
Additionally it also checks whether
x and
x.eOrV are defined before actually using them. Plain Javascript values pass unmodified through
eval, thus allowing interpreter and Javascript values to coexist.
When
applyN is invoked on an
App it actually does not much more than delegate the real work to
Fun and
AppLT, which both deal with application by consuming the right amount of arguments to achieve a saturated function call. A
Fun knows how many arguments it requires, this can be extracted from Javascript function objects:
function Fun( fun ) {
this.needs = fun.length ;
this.fun = fun ;
}
When
applyN is invoked on a
Fun with too few arguments, an
AppLT is constructed, thus remembering the partial unsaturated application. When given exactly enough it just calls the function, and when given more arguments than required, it slices off the right amount of arguments for calling the function, and then continues in the same way as
App did by returning a Javascript continuation object for the remainder of the application.
Fun.prototype = {
applyN : function ( args ) {
if ( args.length < this.needs ) {
return new AppLT( this, args ) ;
} else if ( args.length == this.needs ) {
var x = this.fun.apply( null, args ) ;
return x ;
} else {
var fun = eval( this.fun.apply( null, args.slice( 0, this.needs ) ) ) ;
var remargs = args.slice( this.needs ) ;
return {
eOrV : function() {
return fun.applyN( remargs ) ;
} } ;
}
} ,
needsNrArgs : function() {
return this.needs ;
} ,
}
Finally, undersaturated applications are encoded with
AppLT objects. Its implementation resembles
App and
Fun, so the code is just here for completeness:
AppLT.prototype = {
applyN : function ( args ) {
var needs = this.needsNrArgs() ;
if ( args.length < needs ) {
return new AppLT( this, args ) ;
} else if ( args.length == needs ) {
return this.fun.applyN( this.args.concat( args ) ) ;
} else {
var fun = eval( this.applyN( args.slice( 0, needs ) ) ) ;
return {
eOrV : function() {
return fun.applyN( args.slice( needs ) ) ;
} } ;
}
} ,
needsNrArgs : function() {
return this.fun.needsNrArgs() - this.args.length ;
} ,
}
function AppLT( fun, args ) {
this.fun = fun ;
this.args = args ;
}
This is it! We can now do some real Haskell programming, although it is still manual labor.
Using the interpreter
As an example, a version of the primes sieve is used:
-- Haskell version
module Sieve where
notMultiple x y = not ((y `div` x) * x == y)
sieve (h:t) = h : sieve (filter (notMultiple h) t)
main :: IO ()
main = putStrLn (show (last (take 500 (sieve [2..]))))
Without a
Prelude all functions have to be manually encoded, for example with the aid of helper function
fun multiplication is defined as follows:
function fun(f) { return new Fun(f) ; }
var mul = fun( function(a,b) {
return eval(a) * eval(b) ;
} ) ;
Multiplication is a primitive and requires its operands to be evaluated.
For manipulating lazy lists a couple of additional helper functions come in handy:
function app1(f,a ) { return new App(f,[a ]) ; }
function app2(f,a,b) { return new App(f,[a,b]) ; }
function eval1(f,a ) { return eval( f.applyN([a ]) ) ; }
function eval2(f,a,b) { return eval( f.applyN([a,b]) ) ; }
app1 (and variants) construct lazy application nodes,
eval1 (and variants) apply arguments and enforce evaluation.
Lists are encoded as arrays, with a tag in front:
function cons(x,y) { return [0,x,y] ; }
var nil = [1] ;
function head(l) { return l[1] ; }
function tail(l) { return l[2] ; }
function isNil(x) { return x[0] == 1 ; }
The above functions already assume that their arguments are already evaluated. With these functions
filter can now be implemented:
var filter = fun( function(a,b) {
var list = eval(b) ;
var test = eval1( a, head(list) ) ;
if ( test ) {
return cons( head(list), app2( filter, a, tail(list) ) ) ;
} else {
return app2( filter, a, tail(list) ) ;
}
} ) ;
The equivalent of the infinite lazy list
[a..] is the function
from:
var from = fun( function(a) {
return cons( a, app1( from, app2( add, a, 1 ) ) ) ;
} ) ;
Other function definitions are ‘just like that’, i.e. predictably follow the same ideas. We then end with the equivalent of
sieve and its application:
var sieve = fun( function(a) {
var list = eval(a) ;
return cons( head(list)
, app1( sieve
, app2( filter
, app1( notMultiple2, head(list) )
, tail(list)
) ) ) ;
} ) ;
var mainSieve = app2( take, 500, app1( sieve, app1( from, 2 ) ) ) ;
Finally, we just show the last element:
function show( x ) {
var x = eval(x) ;
document.write( eval(x) ) ;
}
show( app1( last, mainSieve ) ) ;
So, is this is all there is to functional programming in Javascript? Regretfully not, as a Haskell compiler needs to deal with foreign function interfaces in general, libraries, deployment, IO interfacing, etc etc. But that is for the next blog entry…
In the meantime the source code for this entry can be found on
git@github.com:atzedijkstra/javascript-runtime-for-UHC.git
@UHC 