# Introduction to Programming Languages/Programming Language Paradigms
### Programming Language Paradigms

Programming languages can be roughly classified in two categories: imperative and declarative. This classification, however, is not strict. It only means that some programming languages foster more naturally a particular way to develop programs. Imperative programming puts emphasis on how to do something while declarative programming expresses what is the solution to a given problem. Declarative Languages can be further divided into Functional and Logic languages. Functional Languages treat the computation as the evaluation of mathematical functions whereas Logic Languages treat the computation as axioms and derivation rules.

#### Imperative Languages

Imperative languages follow the model of computation described in the Turing Machine; hence, they maintain the fundamental notion of a state. In that formalism, the state of a program is given by the configuration of the memory tape, and the pointer in table of rules. In a modern computer, the state is given by the values stored in the memory and in the registers. In particular, a special register, the program counter, defines the next instruction to be executed. Instructions are a very important concept in imperative programming. An imperative program issues to the machines orders that define the next actions to be taken. These actions change the state of the machine. In other words, imperative programs are similar to a recipe in which the necessary steps to do something are defined and ordered. Instructions are combined together to make up commands. There are three main categories of commands: assignments, branches and sequences.
* An assignment changes the state of the machine, by updating its memory with a new value. Usually an assignment is represented by a left-hand side, which denotes a memory location, and a right-hand side, which indicates the value that will be stored there.
* A branch changes the state of the program by updating the program counter. Examples of branches include commands such as if, while, for, switch, etc.
* Sequences are used to chain commands together, hence building more expressive programs. Some languages require a special symbol to indicate the termination of commands. In C, for instance, we must finish them with a semicolon. Other languages, such as Pascal, require a special symbol in between commands that form a sequence. In Pascal this special symbol is again the semicolon.
The program below, written in C, illustrates these concepts. This function describes how to get the factorial of an integer number. The first thing that we must do to accomplish this objective is to assign the number 1 into the memory cell called f. Next, while the memory cell called n holds a value that is greater than 1, we must update f with the value of that cell multiplied by the current value of n, and we must decrease by one the value stored at n. At the end of these iterations we have the factorial of the input n stored in f.
Imperative languages are the dominant programming paradigm in the industry. There are many hypothesis that explain this dominance, and for a good discussion, we can recommend Philip Wadler's excellent paper. Examples of imperative languages include C, Pascal, Basic, Assembler.
There are other multi-paradigm languages that also support partially or even fully the imperative paradigm like C++, JavaScript but as multi-paradigm languages they are not good examples as real utilization of the languages would not fit the description.

#### Declarative Languages

A program in a declarative language declares one truth. In other words, such a program describes a proof that some truth holds. These programs are much more about "what" is the solution of a problem, than "how" to get that solution. These programs are made up of expressions, not commands. An expression is any valid sentence in the programming language that returns a value. These languages have a very important characteristics: referential transparency. This property implies that any expression can be replaced by its value. For instance, a function call that computes the factorial of 5 can be replaced by its result, 120. Declarative languages are further divided into two very important categories: functional languages and logic languages.
Functional programming is based on a formalism called the lambda calculus. Like the Turing Machine, the lambda calculus is also used to define which problems can be solved by computers. A program in the functional paradigm is similar to the notation that we use in mathematics. Functions have no state, and every data is immutable. A program is the composition of many functions. These languages have made popular some techniques such as higher order functions and parametric polymorphism. The program below, written in Standard ML, is the factorial function. Notice this version of factorial is quite different from our last program, which was written in C. This time we are not explaining what to do to get the factorial. We are simply stating what is the factorial of a given number n. It is usual, in the declarative world, to use the thing to explain itself. The factorial of a number n is the chain of multiplications n * (n-1) * (n-2) * ... * 3 * 2 * 1. We do not know beforehand how large is n. Thus, to provide a general description of the factorial of n, we say that this quantity is n multiplied by the factorial of n-1. Inductively we know how to compute that last factorial. Given that we also know how to multiply two integer numbers, we have the final quantity.
There are many functional languages in use today. Noticeable examples include, in addition to Standard ML, languages such as Ocaml, Lisp, Haskell and F Sharp. Functional languages are not heavily used in the software industry. Nevertheless, there have been some very mature projects written in such languages. For example, the Facebook social network's chat service was written in the functional language Erlang.
Logic programming is the second subcategory in the declarative programming paradigm. Logic programs describe problems as axioms and derivation rules. They rely on a powerful algorithm called unification to prove properties about the axioms, given the inference rules. Logic languages are built on top of a formalism called Horn Clauses. There exist only a few members in the family of logic programming languages. The most well-known among these members is Prolog. The key property of referential transparency, found in functional programming, is also present in logic programming. Programs in this paradigm do not describe how to reach the solution of a problem. Rather, they explain what is this solution. The program below, written in Prolog, computes the factorial function. Just like the SML program, this version of the factorial function also describes what is the factorial of a number, instead of which computations must be performed to obtain it.
Prolog and related languages are even less used in the industry than the functional languages. Nevertheless, logic programming remains very important in the academia. For example, Prolog and Lisp are the languages of choice for artificial intelligence enthusiasts.

#### Programming Paradigm as a Programmer's choice

There are some languages in which developing imperative programs is more natural. Similarly, there are programming languages in which developing declarative programs, be it functional or logic, is more natural.
The paradigm decision may depend on a myriad of factors. From the complexity of the problem being addressed (Object Oriented Programming evolved in part from the need to simplify and model complex problems) to issues like programmer and code interchangeability, consistency and patternization, in a consistent effort to make programming an engineered and industrial activity.
However, in the last stages of decision, the programming philosophy can be said to be more a decision of the programmer, than an imposition of the programming language itself. For instance, the function below, written in C, finds factorials in a very declarative way:
On the other hand, it is also possible to craft an imperative implementation of the factorial function in a declarative language. For instance, below we have an imperative implementation written in SML. In this example, the construction ref denotes a reference to a memory location. The bang ! reads the value stored at that location, and the command while has the same semantics as in imperative languages.
Incidentally, we observe that many features of functional languages end up finding a role in the design of imperative languages. For instance, Java and C++ today rely on parametric polymorphism, in the form of generics or templates, to provide developers with ways to build software that is more reusable. Parametric polymorphism is a feature typically found in statically typed functional languages. Another example of this kind of migration is type inference, today present in different degrees in languages such as C# and Scala. Type inference is another feature commonly found in statically typed functional languages. This last programming language, Scala, is a good example of how different programming paradigms meet together in the design of modern programming languages. The function below, written in Scala, and taken from this language's tutorial, is an imperative implementation of the well-known quicksort algorithm:
And below we have this very algorithm implemented in a more declarative way in the same language. It is easy to see that the declarative approach is much more concise. Once we get used to this paradigm, one could argue that the declarative version is also more clear too. However, the imperative version is more efficient, because it does the sorting in place; that is, it does not allocate extra space to perform the sorting.
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