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Programming Languages. Functional Programming Languages. This lesson describes the concept of a function and how programs can be viewed as functions. We then study a functional language – Lisp, and discuss some of its fundamental properties. Functions and Programming.
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Functional Programming Languages This lesson describes the concept of a function and how programs can be viewed as functions. We then study a functional language – Lisp, and discuss some of its fundamental properties.
Functions and Programming • Functional programming has a number of distinct advantages, which have traditionally made it popular for artificial intelligence, mathematical proof systems, and logic applications. • These include the uniform view of programs as functions, the treatment of functions as data, the limitation of side effects, and the use of automatic memory management. • A functional programming language has as a result great flexibility, conciseness of notation, and simple semantics.
The Drawback • Because of their dynamic nature, such languages historically were interpreted rather than compiled, • The major drawback has traditionally been the inefficiency of execution of functional languages. • with a resulting substantial loss in execution speed. • Even when compilers became available, the speedups obtained were inadequate. • But the semantic simplicity and orthogonality of design have made it a reasonable alternative for teaching computer science.
Programs as Functions • If we ignore the details of the computation, and focus on the result, then a program becomes simply a "black box" for obtaining output from input. • A program is a description of a specific computation. • From this point of view, a program is essentially equivalent to a mathematical function: • Definition: A function is a rule that associates to each x from some set X of values a unique y from another set Y of values: y = f(x)
Variables and Assignments • We can think of programs, procedures, and functions in a programming language as all being represented by the mathematical concept of a function. • In mathematics there is no concept of memory location, or values of variables, so that an assignment statement such as x = x + 1 makes no sense in functional programming. • In this sense, in functional programming, there are no variables, only constants, parameters, and values.
Loops • Most modern functional programming languages retain some notion of variable and assignment, and so are "impure”. • Pure functional programming is Turing complete in that any computation may be described using functions alone. • One consequence of the lack of variables and assignment in functional programming is that there also can be no loops. • A loop must have a control variable that is assigned as the loop executes, and this is not possible without variables and assignment.
Recursion • How do we write repeated operations in functional form? Recursion is the essential feature.
Example 2, Translation of first-order predicate calculus • Another consequence of the lack of variables and assignment is that there is no notion of the internal state of a function: • The value of any function depends only on the values of its parameters, and not on any previous computations, including calls to the function itself. • The property that a function’s value depends only on the values of its parameters is called referential transparency. • The value of any function also cannot depend on the order of evaluation of its parameters.
No State • The lack of variables and the referential transparency of functional programming make the semantics of functional programs particularly straightforward: there is no state. • Indeed, the lack of local state in functional programming makes it in a sense the opposite of object-oriented programming, where computation proceeds by changing the local state of objects.
Generality • We express this generality of functions in functional programming by saying that functions are first-class values. • Composition is itself a function that takes two functions as parameters and produces another function as its returned value. Such functions are sometimes called higher-order functions.
Function Definitions in Lisp • When the Lisp interpreter evaluates a list, it looks to see whether the first symbol on the list has a function definition attached to it; • or, put another way, whether the symbol points to a function definition. • If it does, the computer carries out the instructions in the definition. • A symbol that has a function definition is called a function.
Function Definitions in Lisp (2) • Lisp function definition has up to five parts: • (defun function-name (arguments...) "optional-documentation..." (interactive argument-passing-info); optional body... )
