Basic Lisp Techniques (Common Lisp and Knowledge-based Engineering Book 1)
An interesting case is that of Scala  — it is frequently written in a functional style, but the presence of side effects and mutable state place it in a grey area between imperative and functional languages. Lambda calculus provides a theoretical framework for describing functions and their evaluation.
It is a mathematical abstraction rather than a programming language—but it forms the basis of almost all current functional programming languages. An equivalent theoretical formulation, combinatory logic , is commonly perceived as more abstract than lambda calculus and preceded it in invention. Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the foundations of mathematics. 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.
Information Processing Language IPL is sometimes cited as the first computer-based functional programming language. 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 mutating list structure and similar imperative features. In the early s, Iverson and Roger Hui created J. In the mids, Arthur Whitney , who had previously worked with Iverson, created K , which is used commercially in financial industries along with its descendant Q.
A Functional Style and its Algebra of Programs". Meanwhile, the development of Scheme , a simple lexically scoped and impurely functional dialect of Lisp, as described in the influential Lambda Papers and the classic textbook Structure and Interpretation of Computer Programs , brought awareness of the power of functional programming to the wider programming-languages community.
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This led to new approaches to interactive theorem proving and has influenced the development of subsequent functional programming languages. With Miranda being proprietary, Haskell began with a consensus in to form an open standard for functional programming research; implementation releases have been ongoing since More recently it has found use in niches such as parametric CAD courtesy of the OpenSCAD language built on the CSG geometry framework, although it's inability to reassign values has led to much confusion among users who are often unfamiliar with Functional programming as a concept.
Functional programming continues to be used in commercial settings. A number of concepts and paradigms are specific to functional programming, and generally foreign to imperative programming including object-oriented programming. However, programming languages often cater to several programming paradigms, so programmers using "mostly imperative" languages may have utilized some of these concepts.
Higher-order functions are functions that can either take other functions as arguments or return them as results. 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 functions enable partial application or currying , a technique that applies a function to its arguments one at a time, with each application returning a new function that accepts the next argument.
This lets a programmer succinctly express, for example, the successor function as the addition operator partially applied to the natural number one. This means that pure functions have several useful properties, many of which can be used to optimize the code:. While most compilers for imperative programming languages detect pure functions and perform common-subexpression elimination for pure function calls, they cannot always do this for pre-compiled libraries, which generally do not expose this information, thus preventing optimizations that involve those external functions. Some compilers, such as gcc , add extra keywords for a programmer to explicitly mark external functions as pure, to enable such optimizations.
Fortran 95 also lets functions be designated pure. Iteration looping in functional languages is usually accomplished via recursion.
Recursive functions invoke themselves, letting an operation be repeated until it reaches the base case. Although some recursion requires maintaining a stack, tail recursion can be recognized and optimized by a compiler into the same code used to implement iteration in imperative languages. The Scheme language standard requires implementations to recognize and optimize tail recursion. Tail recursion optimization can be implemented by transforming the program into continuation passing style during compiling, among other approaches.
Common patterns of recursion can be abstracted away using higher-order functions, with catamorphisms and anamorphisms or "folds" and "unfolds" being the most obvious examples. Such recursion schemes play a role analogous to built-in control structures such as loops in imperative languages.
Lisp (programming language)
Most general purpose functional programming languages allow unrestricted recursion and are Turing complete , which makes the halting problem undecidable , can cause unsoundness of equational reasoning , and generally requires the introduction of inconsistency into the logic expressed by the language's type system. Some special purpose languages such as Coq allow only well-founded recursion and are strongly normalizing nonterminating computations can be expressed only with infinite streams of values called codata.
As a consequence, these languages fail to be Turing complete and expressing certain functions in them is impossible, but they can still express a wide class of interesting computations while avoiding the problems introduced by unrestricted recursion. Functional programming limited to well-founded recursion with a few other constraints is called total functional programming. Functional languages can be categorized by whether they use strict eager or non-strict lazy evaluation, concepts that refer to how function arguments are processed when an expression is being evaluated.
The technical difference is in the denotational semantics of expressions containing failing or divergent computations. Under strict evaluation, the evaluation of any term containing a failing subterm fails. For example, the expression:. Under lazy evaluation, the length function returns the value 4 i. In brief, strict evaluation always fully evaluates function arguments before invoking the function.
Lazy evaluation does not evaluate function arguments unless their values are required to evaluate the function call itself. The usual implementation strategy for lazy evaluation in functional languages is graph reduction. Hughes argues for lazy evaluation as a mechanism for improving program modularity through separation of concerns , by easing independent implementation of producers and consumers of data streams. Especially since the development of Hindley—Milner type inference in the s, functional programming languages have tended to use typed lambda calculus , rejecting all invalid programs at compilation time and risking false positive errors , as opposed to the untyped lambda calculus , that accepts all valid programs at compilation time and risks false negative errors , used in Lisp and its variants such as Scheme , though they reject all invalid programs at runtime, when the information is enough to not reject valid programs.
The use of algebraic datatypes makes manipulation of complex data structures convenient; the presence of strong compile-time type checking makes programs more reliable in absence of other reliability techniques like test-driven development , while type inference frees the programmer from the need to manually declare types to the compiler in most cases.
Some research-oriented functional languages such as Coq , Agda , Cayenne , and Epigram are based on intuitionistic type theory , which lets types depend on terms. Such types are called dependent types. These type systems do not have decidable type inference and are difficult to understand and program with. Through the Curry—Howard isomorphism , then, well-typed programs in these languages become a means of writing formal mathematical proofs from which a compiler can generate certified code.
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While these languages are mainly of interest in academic research including in formalized mathematics , they have begun to be used in engineering as well. Compcert is a compiler for a subset of the C programming language that is written in Coq and formally verified. A limited form of dependent types called generalized algebraic data types GADT's can be implemented in a way that provides some of the benefits of dependently typed programming while avoiding most of its inconvenience. Functional programs do not have assignment statements, that is, the value of a variable in a functional program never changes once defined.
This eliminates any chances of side effects because any variable can be replaced with its actual value at any point of execution. So, functional programs are referentially transparent. Let us say that the initial value of x was 1 , then two consecutive evaluations of the variable x yields 10 and respectively. In fact, assignment statements are never referentially transparent. Functional programs exclusively use this type of function and are therefore referentially transparent. It is possible to use a functional style of programming in languages that are not traditionally considered functional languages.
In C , anonymous classes are not necessary, because closures and lambdas are fully supported. Libraries and language extensions for immutable data structures are being developed to aid programming in the functional style in C. Many object-oriented design patterns are expressible in functional programming terms: Similarly, the idea of immutable data from functional programming is often included in imperative programming languages,  for example the tuple in Python, which is an immutable array.
Purely functional data structures are often represented in a different way than their imperative counterparts.
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Arrays can be replaced by maps or random access lists, which admit purely functional implementation, but have logarithmic access and update times. Purely functional data structures have persistence , a property of keeping previous versions of the data structure unmodified. In Clojure, persistent data structures are used as functional alternatives to their imperative counterparts.
Persistent vectors, for example, use trees for partial updating. Calling the insert method will result in some but not all nodes being created. Functional programming is very different from imperative programming. Pure functional programming completely prevents side-effects and provides referential transparency.
Higher-order functions are rarely used in older imperative programming. A traditional imperative program might use a loop to traverse and modify a list. There are tasks for example, maintaining a bank account balance that often seem most naturally implemented with state. The pure functional programming language Haskell implements them using monads , derived from category theory. 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. Functional languages also simulate states by passing around immutable states.
This can be done by making a function accept the state as one of its parameters, and return a new state together with the result, leaving the old state unchanged. Impure functional languages usually include a more direct method of managing mutable state. Clojure , for example, uses managed references that can be updated by applying pure functions to the current state. This kind of approach enables mutability while still promoting the use of pure functions as the preferred way to express computations.
Alternative methods such as Hoare logic and uniqueness have been developed to track side effects in programs. Some modern research languages use effect systems to make the presence of side effects explicit. Functional programming languages are typically less efficient in their use of CPU and memory than imperative languages such as C and Pascal.
Flat arrays may be accessed very efficiently with deeply pipelined CPUs, prefetched efficiently through caches with no complex pointer chasing , or handled with SIMD instructions. It is also not easy to create their equally efficient general-purpose immutable counterparts. For purely functional languages, the worst-case slowdown is logarithmic in the number of memory cells used, because mutable memory can be represented by a purely functional data structure with logarithmic access time such as a balanced tree.
For programs that perform intensive numerical computations, functional languages such as OCaml and Clean are only slightly slower than C according to The Computer Language Benchmarks Game. Immutability of data can in many cases lead to execution efficiency by allowing the compiler to make assumptions that are unsafe in an imperative language, thus increasing opportunities for inline expansion. Lazy evaluation may also speed up the program, even asymptotically, whereas it may slow it down at most by a constant factor however, it may introduce memory leaks if used improperly.
Launchbury  discusses theoretical issues related to memory leaks from lazy evaluation, and O'Sullivan et al. However, the most general implementations of lazy evaluation making extensive use of dereferenced code and data perform poorly on modern processors with deep pipelines and multi-level caches where a cache miss may cost hundreds of cycles [ citation needed ]. Imperative programs have the environment and a sequence of steps manipulating the environment.
Functional programs have an expression that is successively substituted until it reaches normal form. An example illustrates this with different solutions to the same programming goal calculating Fibonacci numbers. Printing first 10 Fibonacci numbers, functional expression style .
Printing a list with first 10 Fibonacci numbers, functional expression style . Printing the 11th Fibonacci number, functional expression style .
Printing the 11th Fibonacci number, functional expression style,  tail recursive. I've heard before from computer scientists and from researchers in the area of AI that that Lisp is a good language for research and development in artificial intelligence. Does this still apply, with the proliferation of neural networks and deep learning? What was their reasoning for this? What languages are current deep-learning systems currently built in? First, I guess that you mean Common Lisp which is a standard language specification, see its HyperSpec.
Then, Common Lisp is great for symbolic AI. Common Lisp is great for symbolic artificial intelligence because:.
Notice that neither neural network nor deep learning is in the symbolic artificial intelligence field. See also this question. Notice that the programming language might not be very important. In the Artificial General Intelligence research topic, some people work on the idea of a AI system which would generate all its own code so are designing it with a bootstrapping approach. Then, the code which is generated by such a system can even be generated in low level programming languages like C. There are number of reasons why the language wasn't able to maintain it's name.
It hides the low level details though. If you are only looking for results and not how you get there, then Matlab will be good. But if you want to learn even low level detailed stuff, then I will suggest you go through LISP at-least once. Language might not be that important if you have the understanding of various AI algorithms and techniques. I will suggest you to read "Artificial Intelligence: A Modern Approach by Stuard J. Russell and Peter Norvig". I am currently reading this book, and it's a very good book. AI is a wide field that goes far beyond machine learning, deep learning, neural networks, etc.
In some of these fields, the programming language does not matter at all except for speed issues , so LISP would certainly not be a topic there. I am only aware of one single planner that is written in LISP.