Preface:Constructive Type theory has been a topic of research interest to computer scientists,mathematicians, logicians and philosophers for a number of years. For computer scientists it providesa framework which brings together logic and programming languages in a most elegant and fertile way:program development and verification can proceed within a single system. Viewed in a different way,type theory is a functional programming language with some novel features, such as the totality ofall its functions, its expressive type system allowing functions whose result type depends upon thevalue of its input, and sophisticated modules and abstract types whose interfaces can contain logicalassertions as well as signature information. A third point of view emphasizes that programs (orfunctions) can be extracted from proofs in the logic.
From the cover:The study of type systems for programming languages now touches many areas of computer science, from language design and implementation to software engineering, network security, databases, and analysis of concurrent and distributed systems. This book offers accessible introductions to key ideas in the field, with contributions by experts on each topic. The topics covered include precise type analyses, which extend simple type systems to give them a better grip on the run time behavior of systems; type systems for low-level languages; applications of types to reasoning about computer programs; type theory as a framework for the design of sophisticated module systems; and advanced techniques in ML-style type inference. Advanced Topics in Types and Programming Languages builds on Benjamin Pierce's Types and Programming Languages (MIT Press, 2002); most of the chapters should be accessible to readers familiar with basic notations and techniques of operational semantics and type systems -- the material covered in the first half of the earlier book. Advanced Topics in Types and Programming Languages can be used in the classroom and as a resource for professionals. Most chapters include exercises, ranging in difficulty from quick comprehension checks to challenging extensions, many with solutions.
haskell programming from first principles pdf 75
In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner.
Functional programming is sometimes treated as synonymous with purely functional programming, a subset of functional programming which treats all functions as deterministic mathematical functions, or pure functions. When a pure function is called with some given arguments, it will always return the same result, and cannot be affected by any mutable state or other side effects. This is in contrast with impure procedures, common in imperative programming, which can have side effects (such as modifying the program's state or taking input from a user). Proponents of purely functional programming claim that by restricting side effects, programs can have fewer bugs, be easier to debug and test, and be more suited to formal verification.[1][2]
Functional programming has its roots in academia, evolving from the lambda calculus, a formal system of computation based only on functions. Functional programming has historically been less popular than imperative programming, but many functional languages are seeing use today in industry and education, including Common Lisp, Scheme,[3][4][5][6] Clojure, Wolfram Language,[7][8] Racket,[9] Erlang,[10][11][12] Elixir,[13] OCaml,[14][15] Haskell,[16][17] and F#.[18][19] Functional programming is also key to some languages that have found success in specific domains, like JavaScript in the Web,[20] R in statistics,[21][22] J, K and Q in financial analysis, and XQuery/XSLT for XML.[23][24] Domain-specific declarative languages like SQL and Lex/Yacc use some elements of functional programming, such as not allowing mutable values.[25] In addition, many other programming languages support programming in a functional style or have implemented features from functional programming, such as C++11, C#,[26] Kotlin,[27] Perl,[28] PHP,[29] Python,[30] Go,[31] Rust,[32] Raku,[33] Scala,[34] and Java (since Java 8).[35]
The lambda calculus, developed in the 1930s by Alonzo Church, is a formal system of computation built from function application. In 1937 Alan Turing proved that the lambda calculus and Turing machines are equivalent models of computation,[36] showing that the lambda calculus is Turing complete. Lambda calculus forms the basis of all functional programming languages. An equivalent theoretical formulation, combinatory logic, was developed by Moses Schönfinkel and Haskell Curry in the 1920s and 1930s.[37]
The first high-level functional programming language, LISP, was developed in the late 1950s for the IBM 700/7000 series of scientific computers by John McCarthy while at Massachusetts Institute of Technology (MIT).[39] LISP functions were defined using Church's lambda notation, extended with a label construct to allow recursive functions.[40] Lisp first introduced many paradigmatic features of functional programming, though early Lisps were multi-paradigm languages, and incorporated support for numerous programming styles as new paradigms evolved. Later dialects, such as Scheme and Clojure, and offshoots such as Dylan and Julia, sought to simplify and rationalise Lisp around a cleanly functional core, while Common Lisp was designed to preserve and update the paradigmatic features of the numerous older dialects it replaced.[41]
Information Processing Language (IPL), 1956, is sometimes cited as the first computer-based functional programming language.[42] It is an assembly-style language for manipulating lists of symbols. It does have a notion of generator, which amounts to a function that accepts a function as an argument, and, since it is an assembly-level language, code can be data, so IPL can be regarded as having higher-order functions. However, it relies heavily on the mutating list structure and similar imperative features.
In the mid 1960s, Peter Landin invented SECD machine,[43] the first abstract machine for a functional programming language,[44] described a correspondence between ALGOL 60 and the lambda calculus,[45][46] and proposed the ISWIM programming language.[47]
The 1973 language ML was created by Robin Milner at the University of Edinburgh, and David Turner developed the language SASL at the University of St Andrews. Also in Edinburgh in the 1970s, Burstall and Darlington developed the functional language NPL.[49] NPL was based on Kleene Recursion Equations and was first introduced in their work on program transformation.[50] Burstall, MacQueen and Sannella then incorporated the polymorphic type checking from ML to produce the language Hope.[51] ML eventually developed into several dialects, the most common of which are now OCaml and Standard ML.
In the 1970s, Guy L. Steele and Gerald Jay Sussman developed Scheme, as described in the Lambda Papers and the 1985 textbook Structure and Interpretation of Computer Programs. Scheme was the first dialect of lisp to use lexical scoping and to require tail-call optimization, features that encourage functional programming.
Higher-order functions are closely related to first-class functions in that higher-order functions and first-class functions both allow functions as arguments and results of other functions. The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class" is a computer science term for programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class entities like numbers can, including as arguments to other functions and as their return values).
Functional programming is very different from imperative programming. The most significant differences stem from the fact that functional programming avoids side effects, which are used in imperative programming to implement state and I/O. Pure functional programming completely prevents side-effects and provides referential transparency.
The pure functional programming language Haskell implements them using monads, derived from category theory.[79] Monads offer a way to abstract certain types of computational patterns, including (but not limited to) modeling of computations with mutable state (and other side effects such as I/O) in an imperative manner without losing purity. While existing monads may be easy to apply in a program, given appropriate templates and examples, many students find them difficult to understand conceptually, e.g., when asked to define new monads (which is sometimes needed for certain types of libraries).[80]
JavaScript, Lua,[89] Python and Go[90] had first class functions from their inception.[91] Python had support for "lambda", "map", "reduce", and "filter" in 1994, as well as closures in Python 2.2,[92] though Python 3 relegated "reduce" to the functools standard library module.[93] First-class functions have been introduced into other mainstream languages such as PHP 5.3, Visual Basic 9, C# 3.0, C++11, and Kotlin.[27][citation needed]
Similarly, the idea of immutable data from functional programming is often included in imperative programming languages,[97] for example the tuple in Python, which is an immutable array, and Object.freeze() in JavaScript.[98]
The real power of monads comes from the fact that computations are themselves just values that can be passed around as first-class citizens within the pure host language. This enables programmers to write new abstractions (domain-specific and custom-control structures) using the monadic primitives and nonproper morphisms. 2ff7e9595c
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