smalltalk, apl, soy lisp, and higher order operands

APL, Smalltalk, Lisp. The holy trinity of programming languages. In this post I aim to better explain the Soy Lisp syntax which allows for all three to coexist.

Consider first the ability to drop parens when an expression is terminated via ".":

(func arg1 arg2)
//becomes
func arg1 arg2.

This creates an immediate problem w/ disambiguation when dealing with arguments, well thankfully we do not lose the ability to return to s-expressions when required e.g.:

func arg1 (func2 arg1 arg2).

What else can we glean from smalltalk? Perhaps the ability to cascade via ;, e.g.:

(((func arg1) arg2) arg3)
//becomes
func arg1; arg2; arg3.

In prior posts I have shown my preference for "square lambdas" e.g: [x | x y]. So I will not continue to rant about the benefits here. The last thing I will borrow from smalltalk is keyword constants (whilst keeping lisp keywords) e.g.:

(func :keyword1 var1 :keyword2 (lambda (x) (x :says 'peter))
//becomes
func keyword1: var1 keyword2: [x | x says: 'peter].

The above assumes func is a higher order function which knows how to dispatch keyword selector arguments, which is essentially how I would implement a smalltalk esque language on top of soy.

I think it is clear that functional programming in lisp can benefit from the smalltalk syntax whilst not losing the power of macro expansion and s-expressions.

This brings us to APL the other language I have toyed w/ writing interpreters for. The real crux of apl is working with higher order operators. e.g. reduce which takes on the left hand an operator which it then uses to reduce a set of numbers on the right. In traditional prefix notation this would end up like:

((/ +) 1 2 3 4)
//not bad but noisier than
+ / 1 2 3 4.
//which becomes
(+ / 1 2 3 4)

Which works just fine because + is a higher order operator which knows if its first argument is another operator it should return a function which does a + reduction.

(- (+ 5 5) 5)
//becomes
5 + 5 - 5.

In soy the latter works because numbers are "higher order operands" which can consume operators and return functions which consume more operators/operands as expected. Stay tuned for a web repl for those interested in playing with this. Bare in mind that both forms in all of these examples work with in the same environment as this is all syntactic sugar! Lisp wins again.

Alternative s-expression syntax for Soy Lisp

Soy is the name of my lisp dialect (previously called lisphp, and before that phlisp). This is quite a radical departure from standard lisp s-expression but not so far as to, say have infix notation or "sweet expressions". Rather this is a simple inverse of s-expression e.g.:

(if (predicate arg1 arg2)
    (thenFunc arg2)
    (elseFunc arg3))

Becomes:

if(predicate(arg1 arg2)
   thenFunc(arg2)
   elseFunc(arg3))

Your first question should be, "but wait! what about homoiconicity and the ability to have quasiquote macro definitions!?". I'm glad you asked, I have two proposals. 1) allow for a s-expression macro syntax, 2) allow for quasiquote to start with an atom:

defmacro(eat-apple person number-of-apples
         `person-eat(,person 'apple ,number-of-apples))

You may have noticed the other drawback with this syntax is that it makes having macros which handle sublists a tad more difficult. As any atom followed by (, applies the atom to the arguments inside of the parens. This can be resolved by using rest args for forms which anticipate the last expression to be treated as a lambda. Also Soy allows for [ | ] lambda forms and { } vector/dicts. So it is also possible that would resolve any ambiguities.

One of my major ambitions with this is to have a very simple syntax for exploring alternative object models, similar to my previous post about an alternative object model for javascript.

;simple keyword selector
some-object(set-first-name: 'peter and-last-name: 'jenkum)
;chaining 
some-object(some-keyword: arg1 selector: arg2) 
           (chained-selector: arg3 takes-closure: [ a | a(message: arg4)])
           (another-chained-selector: [_(anon-var)])

I really dig how close this comes to snythesizing what I love about smalltalk w/ lisp w/o really forsaking either.

One of the real "wins" with this is when you have function returning functions .. n you don't end up w/ a massive amount of nesting.

(def adder [x | [y | [z | + x  y z]]])
(((adder 6) 7) 8)

def(adder [x | [y | [z | +(x y z)]]])
adder(6)(7)(8)

I think the latter reads in a much more obvious "left to right" fashion.

On Phutility

Phutility is a collection of tools which I utilize in many of my other projects. For example the Node class is utilized by both covenants (sql builder) and also phmop (meta object protocol). Today though I am going to be discussing some of the work that I have been doing in Func to lay the framework for "higher order object oriented programming" with phmop. To give you an idea of what I am driving at, consider:

defineClass('Person', 
    slot('someMethod', function($self) {
        $args = func_get_args();
        $self = array_shift($args);
        $options = appos($args);
        if($self->{$options[ifField]} == $options[isValue]) {
            $self->call($options[callMethod], $options[withValues]);
        }
    })->accessor('someMethod'));

$person = new Person;
$person->someMethod(
    ifField, 'age',
    isValue, 30, 
    callMethod, 'someMethod2', 
    withValues, array(300));

There are a few things we can cleanup. Firstly lets create a function "method" which wraps up simple functions which utilize an accessor which is the same as their internal name. Then lets utilize a higher order function "Func\options" which returns a function which has the last param defined as an options hash to clean things up:

defineClass('Person', 
    method('someMethod', Func\options(function($self, $options) {
        if($self->{$options[ifField]} == $options[isValue]) {
            $self->call($options[callMethod], $options[withValues]);}})));

But we can go further by creation an optionsMethod which wraps up the need for the explicit Func\options call. Also we can have it pass a param which gives us back a std class for options rather than an array.

defineClass('Person', 
    optionsMethod('someMethod', function($self, $options) {
        if($self->{$options->ifField} == $options->isValue) {
            $self->call($options->callMethod, $options->withValues);}}));

For the sake of completeness let me show off another way this could be defined more explicitly taking advantage of Func\keyword which evaluates a closure and then returns a function which responds to an appositive style call:

$keywordFunc = Func\keyword(function($age, $name, $color) {
    return array('age' => $age, 'name' => $name, 'color' => $color);
});

print_r($keywordFunc(
    age, 30, 
    color, 'blue', 
    name, 'peter'));

array(
    'age' => 30,
    'name' => 'peter',
    'color' => 'blue');

As you can see this allows us to pass the params in any order we please (which to be fair our Func\options implementation does as well but packaged into an $options var). So now we will skip to step 3 of what a keywordMethod would look like in use:

defineClass('Person', 
    keywordMethod('someMethod', 
        function($self, $ifField, $isValue, $callMethod, $withValues) {
            if($self->$ifField == $isValue) {
                $self->call($callMethod, $withValues);}}));

$person = new Person;
$person->someMethod(
    ifField, 'age',
    isValue, 30, 
    callMethod, 'someMethod2', 
    withValues, array(300));

I think this makes clear why both a meta object protocol and higher order functions are so awesome when they can play together. Rather than having only inheritence, interfaces, or even mixins, as the tool for making things more elegant we can easily add new features to our language with simple function composition.

Considering a MetaObject Protocol for PHP

The purpose of a "MetaObject Protocol" is to allow for defining the very nature of how an object system functions. This means the ability to add traits/mixins, aspects, multiple inheritance, "Generics" etc. w/o requiring compilation or low level tinkering. One major advantage is that this means not having to wait for a revision of your language to express certain design patterns.

As usual php is so close, yet so far away. However ab/utiliz/ing the magic methods you can actually get pretty close to something resembling the CLOS system. To accomplish this it requires a few building blocks which I have abstracted into my Phutility library. Primarily the MetaArg and Node which provide the building blocks for composing declarative domain specific languages.

The majority of the magic occurs via macro expansion in CLOS. We are going to make up for that via declaring an abstract syntax tree (AST) which we will expand and weave into our method dispatch mechanism.

Enough talk, let's code. First our goal is be able to declare classes and methods.

defineClass('Shape',
    slot('width'),
    slot('height'),
    method('getHeight', function($self) {
        return $self->height;
    }), 
    method('getArea', function($self) {
        return $self->width * $self->height;
    })
);

$shape = new Shape(
    width, 20, 
    height, 50
);

echo $shape->getHeight();
echo $shape->getArea();

defineGeneric('beforeGetArea', 
    before(getArea),
    arity(Shape), 
    function($self) {
        echo "Called before get area!\n";
    }
);

echo $shape->getArea(); //outputs "Called before get area!" and then area

Looks like a class and acts like a class. But most definitely not a raw class. How does this work? Principally we keep the meta information about each class in a Registry. Each class defined results in a simple declaration of "class X extends \phmop\StandardClass{}" which allows the usual "new Class" syntax. It writes this to a cache directory and does a require_once on it so as to avoid eval.

The base Obj class looks something like:

class StandardClass {
    public $slots = array();

    public function __call($slot, $args) {
        return Registry::dispatchMethod($this, $slot, $args);
    }

    public function &__get($slot) {
        return Registry::getSlot($this, $slot);
    }

    public function __set($slot, $value) {
        Registry::setSlot($this, $slot, $value);
    }

    public function __construct() {
        foreach(Appos(func_get_args()) as $key => $val) { 
            $this->$key = $val;
        }
    }
}

So pretty clearly the real magic is taking place in the way that defineClass, defineGeneric, and friends interoperate with the Registry.

I am going to end things here for now as I need to make a few posts about some of the inner workings of phutility to really get into the thick of things.

Revision to php TCO trampoline

github.com/shaunxcode/php-trampoline

Sometimes I wake up at 6am with the frightful knowledge that there is an edge case to something I wrote somewhere which is incorrect. The only thing worse than knowing someone on the internet is wrong (http://xkcd.com/386/) is knowing you were wrong on the internet.

I realized in a dream that my trampoline would not work with higher order functions as it currently stands because the while loop is based on is_callable, obviously if your function is meant to return a function you would not want it to be executed immediately (particularly because it probably expects arguments etc.). All of a sudden the whole throwing an exception approach made sense - however thanks to php5.3s __invoke method I can handle this cleanly by wrapping each tail call in an instance of TrampolineBounce and then check "$return instanceof TrampolineBounce".

I figured if I am going to need a Trampoline class I may as well leverage __callStatic to allow for easier invocation of trampolined functions. With out further ado:

namespace Trampoline;

class Bounce {
        private $func;
        public function __construct($func) {
                $this->func = $func;
        }

        function __invoke() {
                return call_user_func_array($this->func, array());
        }
}

class Trampoline {
        public static function Bounce($func) {
                return new Bounce($func);
        }

        public static function __callStatic($func, $args) {
                $return = call_user_func_array($func, $args);
                while($return instanceof Bounce) {
                        $return = $return();
                }

                return $return;
        }
}

function even($n) {
        return $n == 0 ? true : Trampoline::Bounce(function() use($n) { return odd($n - 1);});
}

function odd($n) {
        return $n == 0 ? false : Trampoline::Bounce(function() use($n) { return even($n - 1);});
}


echo Trampoline::even(1500) ? 'Yep' : 'Nope';

tail call optimization in php 5.3

*note this has been revised: (http://commonphp.blogspot.com/2010/12/revision-to-php-tco-trampoline.html) *

So I have been holding off on releasing my php lisp for the past couple of months for a few reasons. The first was I wanted to get quasiquotes/macros working correctly and the other was I wanted to get TCO working correctly. I checked quasiquotation and macro expansion off a few weeks ago and have been wrestling with TCO since. There are many work arounds such as only using higher order functions like map etc. which "underneath" use php foreach/while etc. but this always felt like a hack. Today I will show how I am accomplishing TCO. It is actually "pretty" enough that I would even use this technique in "normal" php if the need arose i.e. when implementing an algorithm where mutual recursion is the cleanest way of dealing with a given problem.

I had heard "tail" of a magical device called a "trampoline" but had yet to see one implemented in php. First lets set the scene for why such a thing is necessary.

Regular mutually recursive functions:

function even($n) { 
    return $n == 0 ? true : odd($n - 1);
}

function odd($n) { 
    return $n == 0 ? false: even($n - 1);
}

echo even(15000000) ? 'Yep' : 'Nope'; 

Result?
Fatal error: Allowed memory size of 335544320 bytes exhausted (tried to allocate 261900 bytes)

As you can imagine this would blow the stack pretty quickly. The solution is to return closures which close over the next function to be executed by the trampoline:

function trampoline($func, $args) { 
    $return = call_user_func_array($func, $args);
    while(is_callable($return)) {
        $return = $return();
    }
    return $return;
}

Ready for trampoline version of functions, notice the closures being returned:

function even($n) { 
    return $n == 0 ? true : function() use($n) { return odd($n - 1); };
}

function odd($n) { 
    return $n == 0 ? false : function() use($n) { return even($n - 1); };
}

echo trampoline('even', array(15000000)) ? 'Yep' : 'Nope';

No more blowing the stack!

For another example here's a tail call version of factorial:

function fact($n) {
    $product = function($min, $max) use($n, &$product) { 
    return $min == $n ? 
        $max : 
        function() use(&$product, $min, $max) {
            return $product(bcadd($min, 1), bcmul($min, $max));
        };
    };
    return $product(1, $n);
}

echo trampoline('fact', array(5050));

Result?
48424893876442346868149955534231630311152316586879831768663469768542209496025625521335165836597244986775871359731653944863304801472363186993340977071916545094098397335673370033050095301846673812319519184368943848940208083286841710046697935471447379350531958006231636490517114754236601801475241025829782559539886360417931118962453657701734674670226076209971728976092053885317753609072349073735823517244188123450674446015646408575152721563438720528695200000950089076496921144117143216432888312645825602479454709341393797835166357888263581672355452853869124012486552503932416596193377435247315025743200744002301394585228500268455104719958806656594340592125681513366273489623936710098205543483870278942617415439360839831622538877203695372405175195820803498878614463408507559071691975942963055323977023975579962356660525443011519924497192606177308403911494610046020125224506026847906849303464211582255596044461695809931170735992902861015153948973924760246045409447614027579732580231716105662183345892311470363765765619375852044952237375592745997667408717094345683918382540158972633294341661753292428842087402347931146455707829443369742629955406096433554614672210416043568566713315721328986242009438119615170550083892805000693555351590233960368408610557369747063249171375287938142229602269575258888078115537273321885243640816116313033760859934727694805934472650247398590268106132632051710011975357435411073973400518009267243861234604382480972044372345571394804592046625365990943593155118312928026092849203020843936635478814979107242813498013904401479307173527813374488927846868388843629960975688405420793866362748625568963809336537735196635482323869611480442317616213118017936592673957745954854119905353862738630397953491904711075413351939493239103430359228666385849114266162025489907918597974910444817388693635468572983832473160429177887474388606642754513228627277514269543214565586593047881932646980529181738704933529003783674019143726269073240250043051103116046759758599556492457493255007087656022414606222859948126380313826837273496022239059049197478197470692778763575742323649675518937743998020384086092356484327490394949151360442183700474945898304321062066355143800014715430781407860862440970162255814321544952627961522489938257459652704978558232366966762259286202122152536234765500508950380085381022529769410646695981455932497274422145956223070614311782386939393660505071468075609946312266961804079078124972138751570252042991908322662337184841517195535818561858155408260788044667462475133702274158651640293943156955741104099223849587202623924618562507307459878359309762592535803298228381823574279830281362305301068394370171580376856819398786773168976316243886413852653396055497826310062540076987247412010421678922894559582379982459315131410353844686814801084428315428961052501286596189198414322404856396902069457672137306587727429077418184644185029820725981473585275798688633870939149445242039540994144936753560145261967645980942905198036844963065770953567278843744815101688364553167567561127581285151504170857163788476814410430818485342212602471021116122232536945437600193563274350613219002205135771961855617387540043201574995936521078443417355808962389471634447182986942493573328833479027327904592963332830948909056606878114712587614797355021919494836468834407159424831076501904939674180550971070685974826026825572462514492992573071756584471446779582538562871889253777491503761958039422843336111308820256625552392100765429247159402181090198939792727134760027285582388085697688779314720476653237742989447851866203189262136310101262960823946227816914290542573075004229606139191853412465867836753036378462157616915664130017838805074756547841197620513628237540972492294319305705734478032962949128924196666202655682340324787692515590130551301935088659828410687356942341790891345277677382788831208787364801395111486357308798265828146035781558094135067110230536901270297547242166950881473214274739101845553727897045531119954725288893493225046788944932736466460550726919323972814208640861318915500012832311138673106892856437774916302054198800992266101283582978474791023088963610289841529824634218025633260218581419143652195694797922926870213605428040752771533690783079334348985159752481190866305108822791928707079718613729022578623134006395058165941963834815415900225540158365512962747234118295298072392721688699472738462833608355509413369430747483292086244416854740060940250464784905488189338770945263660330117646978971876652613557429461658723058825915031208985735140615497693407650641375234834094995218262573623896322220855235269130698919365626682758374382064483940359436309642974808514506879129036989811006578121058886468214783989745311306991381502598738427646690529026148074559926029141700545754931041231062108024348298640252182862477489626497023992723452959298403206063199087668949604632790351230972033067574210447769545912131839504735995523543564698434762288745349217285435045940022877153117114056361355516568793184887831573689961226955484323093901470710251285589637162339096014594590326637778408537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So in other words PHLISP should be officially released by christmas eve.

quasiquote for primitive lisp

I was searching for a basic quasiquote implementation in lisp which mentioned a paper by Alan Bawden. Anyway it was difficult to find via google so I figured I would type it up here for posterity. The original paper can be found: here.

(define (qq-expand x)
  (cond ((tag-comma? x)
         (tag-data x))
        ((tag-comma-atsign? x)
         (error "Illegal"))
        ((tag-backquote? x)
         (qq-expand (qq-expand (tag-data x))))
        ((pair? x)
         `(append ,(qq-expand-list (car x))
                  ,(qq-expand (cdr x))))
        (else '', x)))

(define (qq-expand-list x)
  (cond ((tag-comma? x)
         `(list ,(tag-data x)))
        ((tag-comma-atsign? x)
         (tag-data x))
        ((tag-backquote? x)
         (qq-expand-list (qq-expand (tag-data x))))
        ((pair? x)
         `(list (append ,(qq-expand-list (car x))
                        ,(qq-expand (cdr x)))))
        (else ''(,x))))