Archive for the 'Functional Programming' Category

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PHP Functional Programming Part III: λ Lambda Calculus

lambdaCalcλ After learning how to program in Haskell, a pure functional programming language, in the edX course offered through TU DelftX I’m convinced more than ever that to do decent functional programming, you need to understand lambda calculus. I’m not saying that you need to master lambda calculus, but you need to understand it insofar as it applies to functional programming and differentiates imperative programming (what we do in sequential, procedural and OOP with PHP, Java, JavaScript, C++, and C#) and functional programming based on lambda calculus. In this post, I’d like to ease into lambda calculus and illustrate how it applies to functional programming in PHP.

It’s Not Like Other Programming Languages

A typical value a programmer may want to generate for a business site is the cost of an item plus shipping charges. By way of example, suppose that the shipping charges are all 11% of the cost of the item. You might write something like the following:

$priceNship = 14.95 + (14.95 * .11);

That’s not especially useful since you need to have a separate set of literals for each item to enter into the variable $priceNship.

You’re most likely to set up a method that handles such calculations with a variable generated through an argument. For example, you might have a class that looks like the following class and method:

class RetailStore
    private $priceNship;
    public function addShipping($x)
        $this->priceNship = $x + ($x * .11);
        return round($this->priceNship,2);
$worker = new RetailStore();
echo "Cost plus shipping: $" .  $worker->addShipping(14.95);

I used the $x identifier for the parameter for the addShipping() method instead of something more descriptive like $cost because you’ll often see an x-named variable in lambda calculus.

Casting in Lambda Calculus

When using lambda calculus, one of the key characteristics that I had problems getting used to in Haskell was what you might call stating a problem or abstracting a problem. The problem statement is an abstraction of the problem you want to solve using functional programming. Because lambda calculus strives for abstraction, we’ll start with a simple one:

λx.x + (.11 (x))

What does that mean? First of all λx denotes a lambda function. The x variable is bound to the λ function. (It’s known as a bound variable as opposed to free variables. This post deals with bound variables only.) Put into a PHP class and methods, and setting up a return routine, you have the following:

class RetailStoreFunc
    public function addShipping($x)
        // λx.x + (.11 (x))
        $priceNship = function ($x) {return $x + ($x * .11);};
        //Round off to 2 decimal points and return
        return round($priceNship($x),2);
$worker = new RetailStoreFunc();
echo "Cost plus shipping: $" . $worker->addShipping(14.95);

The λ function (lambda function) shows that the x value is added to the result of .11 times the value of x. In PHP, a λ function is the same as an anonymous or unnamed function. Now, looking at the PHP version of the λ function, you can see:

λx.x + (.11 (x)) = function ($x) {$x + (.11 *$x);};

If you compare the λ calculus with the PHP function, you can see that while the PHP function is a bit less abstract than the λ calculus expression, they are almost identical. Think of the λ calculus as nothing more than an abstraction of a solution.

If you can understand these introductory elements of λ calculus as applied to PHP, not only are you on the path to understanding λ calculus but also PHP functional programming. It’s not as difficult or large as other calculi; so, rest easy and continue.

Functions within Functions

Not only can λ functions return calculated values, they can return other λ functions. So, if you build one λ function, you can use it in another λ function. In this way you can build functional programs. Further, I have not found any contradiction between λ functions and functional programming and OOP in PHP. This next example shows another example of a λ functions in an OOP context, but unlike the first one this one 1) incorporate and returns one λ function in another, and 2) uses a private variable. You cannot assign a λ function to a variable that is not local (part of the method), but you can assign a non-local variable (e.g., private, public or protected) to store the results of a λ function—just not the λ function itself.

class RetailStoreReady
    private $final;
    public function addShipNtax($x)
        // λx.x + (.11 (x))
        $priceNship = function ($x) {return $x + (.11 * $x);};
        // λx.λx + (.07 (x)) (λx. $priceNship(x) + .07 (x))
        $totalWithTax = function ($x) use ($priceNship) {return $priceNship($x) + (.07 * $x);};
        //Using an embedded property ($final) for storing results
        return $this->final;
$worker = new RetailStoreReady();
echo "Cost plus shipping and tax: $" . $worker->addShipNtax(14.95);

In PHP, employ the use statement when one or more λ functions are within a λ function. To employ more than a single λ function within another λ function, you can separate the λ functions by a comma in the use statement as the following shows:

function ($x) use ($lambdaA, $lambdaB) {return $lambdaA($x) + $lambdaB($x);};

The ability of PHP to incorporate these functional programming elements indicates the commitment the PHP community has to functional programming.

Do You Really Need λ Calculus to learn Functional Programming in PHP?

If you read Simon Holywell’s book Functional Programming in PHP, you will find mention of λ calculus, but only a mention. Indirectly, there are some examples, and I found that some basic understanding of λ calculus is very helpful. But λ calculus is not a requirement for functional programming in PHP or any other language. However, if you do understand something about λ calculus, it is extremely helpful to better grasp functional programming in virtually any programming language. In future posts on functional programming, I will be introducing more elements of λ calculus that pertain to better understanding and using functional programming in PHP.


PHP Functional Programming Part II: OOP & Immutable Objects


In his book on Functional Programming in PHP Simon Holywell laments the lack of immutable structures in PHP, and while he suggests some hacks to insure immutability, we can make-do with some different hacks I’ll suggest. (Most of the hacks are mind-hacks–a way of thinking about data.) The idea of having a programming language where all objects are immutable (unchanging) sounds pretty awful. Not only that, it sounds impractical. Take, for example, a Boolean. It has two states; true and false. In functional programming, that means the Boolean variable is mutable, and so it’s out. However, you can have two objects that we can call, Alpha and `Alpha. Alpha is true and `Alpha is false. (The tick mark [`] is the key below the ‘esc’ key on your keyboard.) So instead of changing the state of Alpha from true to false, you change the object from Alpha to `Alpha.

Why would anyone want to do that? It has to do with the concept of referential transparency. In a concrete sense it means that if an object (reference) were replaced by its value, it would not affect the program. Consider the following:

   $alpha= function() use ($val) {return $val * $val;};

can be replaced by;


Nothing in the program will change if either $alpha variable is used. For a simple example of referential transparency, that’s no great shakes. Besides we lose the value of changing states. However, functional programming eschews the concept of changing states. To quote one functional programmer,

Do not try to change the state; that’s impossible. Instead only try to realize the truth: There is no state.

Again, this looks nuts both conceptually and in the real world. Take, for instance, a thermometer that changes from freezing (32F / 0C) to not freezing (say 50F / 10C). The temperature has changed states! How can anyone say it has not? Or a child changes states into an adult, or a caterpillar changes states to a butterfly?

According to the functional programming model, a freezing temperature is a different object than a non-freezing one; an adult is a different object than a child, and (clearly) a butterfly is a different object than a caterpillar. So, if I say that the thermometer has changed from 32° to 33°, it is not state that has changed, it is a different object. Objects can be as granular as you like, and if you think of atoms arranged to display a ruler, you can move from one atom (object) to the next atom (object) with no state involved at all.

The State Design Pattern: Wasn’t it Immutable All Along?

The State design pattern would seem to be the polar opposite of functional programming. However, if we examine it closely, we can re-conceptualize it as object swapping. Take a simple two-state example: a light going on and off. There’s a light-on object and a light-off object. The design is the same, but we think about it in different ways. Also, the individual state methods can include nothing but lambda functions or closures. Consider Figure 1. An “on” light JPG and an “off” light JPG can be considered two separate states or two immutable objects.

Figure 1: Two States or Two Immutable Objects

Figure 1: Two States or Two Immutable Objects

To make the State pattern more “immutable-like” the interface has two constants with the URLs for the two different images. To get started, Play the light switch State application and Download the files:

The application uses a simple State design pattern. All requests go through the Context, which keeps track of the current state. However, this implementation fudged a bit because each time the UI calls the Client, it creates a new Context object; so no state is saved, and I had to add a statement to use the called method to set the correct state for switching the light on and off. (Note to self: Get busy on the RESTful API!) Also, I added two constants to the interface (IState) to impose an immutable property in the state implementations. Figure 2 shows the class diagram of the implementation:

Figure 2: State design pattern implementation

Figure 2: State design pattern implementation

The pattern diagram in Figure 2 provides an overview of the classes and key methods in those classes. The LightSwitch class is just an HTML document wrapped in a PHP class, an it is where a request originates in this model. The other roles you can see in the following outline:

  • Client: Get the request from the UI (LightSwitch) and using a Context instance and method, the request is sent to the Context.
  • Context: Always the most important participant in a State design pattern, it determines the current state and passes the request to it via the appropriate method based on the request.
  • IState: The State interface specifies the required methods and may include constants.
  • Concrete States: The On / Off states (IState implementations) return the requested state-as-an-object.

With that overview in mind, you can better understand all of the singular roles of the participants. (Continue to see listings and explanations.)
Continue reading ‘PHP Functional Programming Part II: OOP & Immutable Objects’


PHP Functional Programming Part I: An Introduction

functionThe Functional Alternative

For some time now, I’ve been interested in functional programming. I had heard that it was an alternative to imperative programming (OOP languages, including PHP, are considered imperative languages) and if you sniff around you can find snarky comments by functional programmers about OOP. For the most part, though, the concern and need for functional programming has centered around multi-threaded and multi-core programming. If you can imagine two different threads using two different cores in your computer working in parallel to process a single giant list or array, you can understand how useful it is to divide the array in half and have different threads process each half. Since about 2005, all computers (except Raspberry-Pi types) are multi-core. Even my old iPhone 4S has a dual core A5 processor. With multi-threaded and parallel programming, though, you have to rejoin the multiple threads once each is finished to get a final result. Here’s where you have to be careful because you want to be sure that the values you’re handling have not changed in one thread and not the other or differently in both threads. You want to use immutable values to avoid surprises when the threads’ results are re-joined.

Where to Start?

A good starting point is Functional Programming in PHP by Simon Holywell. It’s about as simple as a book on functional programming can be, and you’ll find lots of examples. If you’re looking for material on lambda (λ) calculus and functional programming in PHP, you’ll only get a chapter that is ¾ of a single page, but Holywell goes on to say in the ever-so-brief chapter (chapter-ette?) on PHP lambdas,

…but just about every piece of functional code ever written makes use of lambda functions, and they are an important building block to add to your tool kit and should be mastered ….

Not to overstate a point, but Holywell is absolutely right, and so the reader is left wondering, why so brief a discussion of lambdas–a chapter that’s only three-quarters of a page? Well, the rest of the book has lots of lambda functions in use, and I imagine that the author figured the reader would be able to work it out on his/her own. (Maybe this point might be re-thought in the next edition of the book and the chapter be expanded.) In the meantime a useful online source can be found at Lambdas in PHP on the phpbuilder site.

If you really want to go nuts on functional programming, you can learn Haskell. On October 14, 2014 (in a couple weeks!) edX (the Harvard/MIT initiated free online course program) is offering Introduction to Functional Programming through The Netherland’s premiere technical university, Delft University of Technology. In the past I’ve learned that whenever I learn another programming language, I can always bring something back to PHP. Besides, the course introduction notes that PHP is one of the languages that has incorporated functional programming structures into its lexicon. You can take the course for free or get a certification for about $50. It’s 6 weeks long and will take between 6-8 hours a week of study.

For a quick and dirty differentiation between imperative programming and declarative (functional) programming, Microsoft has a nice little anonymous table that summarizes the difference. Being Microsoft, they put in a plug for their products and point out that C# can handle both functional and imperative programming. Since PHP 5.3, PHP too handles both types of programming; so we’re not dealing with an either or situation when it comes to OOP and functional programming in languages like PHP and C#.

So What Are Lambdas?

Lambda functions are anonymous functions, introduced in PHP 5.3.0. Essentially, a lambda function is one that stores an immutable value in a variable. For example,the following class has incorporated a lambda function to calculate the square of a value as part of the method doLambda().

< ?php
class Lambda1
   function doLambda()
        $lambda_func = function($stuff) { return $stuff * $stuff; };
        echo "The square value is: " . $lambda_func(8) . "<p />";
$worker=new Lambda1();
//Results - The square value is: 64

To call a lambda function an anonymous function is true, but to assume that all anonymous functions are lambda expressions criminally oversimplifies the lambda calculus behind lambda expressions. To help move on in understanding of PHP lambda expressions stated as anonymous functions, take a look at Figure 1.

Figure 1: Elements of a lambda expression

Figure 1: Elements of a lambda expression

The parts of a lambda function are pretty straightforward, and you have to remember to add the semi-colon (;) after the lambda body in addition to the one at the end of expressions within the lambda body. Otherwise, it looks pretty much like a named function without the name.

Essential is the requirement to include the return statement in the lambda expression. In fact, it’s probably a better programming practice to use a return statement with all methods; a practice I’ve often overlooked myself. (See No Side Effects below.)
Continue reading ‘PHP Functional Programming Part I: An Introduction’