Principles of Programming Languages Chapter 15-16

Study Notes

Functional programming languages are based on mathematical functions, whereas imperative languages are based on the Von Neumann architecture.
Functional languages are argued to be more readable, reliable, and correct than imperative languages.
Common functional languages include Lisp, ML, Haskell, OCaml, and F#.
Functional languages do not have variables or state like imperative languages do.

A mathematical function is a mapping of a domain set to a range set.
A function definition specifies the domain and range sets, along with the mapping.
Mathematical functions are evaluated using recursion and conditional expressions, unlike imperative languages which use sequencing and iterative repetition.
Mathematical functions always map a particular element of the domain to the same element of the range.

A lambda expression specifies the parameter(s) and the mapping of a function.
Lambda expressions are applied to parameter(s) by placing the parameter(s) after the expression.
Example: (λ(x) x * x * x)(2) evaluates to 8.

A higher-order function takes functions as parameters or yields a function as its result, or both.
Function Composition is a common kind of higher-order function.
It takes two functions as parameters and yields a function whose value is the first actual parameter function applied to the result of the second.

The objective of functional programming language design is to mimic mathematical functions.
Repetition is specified with recursion rather than iteration.
The basic process of computation is fundamentally different in a functional programming language than in an imperative language.
Variables are not necessary in functional programming languages, unlike imperative languages.

Logic programming expresses programs in the form of symbolic logic and uses a logical inferencing process to produce results.
Logic programming languages are declarative languages that state the specifications of the desired results rather than detailed procedures.
Programs in logic programming languages are collections of facts and rules.
Prolog is a main example of a logic programming language, with applications in Relational Database Management Systems (RDBMSs), Expert Systems, and Natural-Language Processing.