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a compiler for a subset of the language c that is written in rocq and formally verified 75 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 76 gadt s are available in the glasgow haskell compiler in ocaml 77 and in scala 78 and have been proposed as additions to other languages including java and c 79 referential transparency edit main article referential transparency 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 80 consider c assignment statement x x 10 this changes the value assigned to the variable x let us say that the initial value of x was 1 then two consecutive evaluations of the variable x yields 10 and 100 respectively clearly replacing x x 10 with either 10 or 100 gives a program a different meaning and so the expression is not referentially transparent in fact assignment statements are never referentially transparent now consider another function such as int plusone int x return x 1 is transparent as it does not implicitly change the input x and thus has no such side effects functional programs exclusively use this type of function and are therefore referentially transparent data structures edit main article purely functional data structure purely functional data structures are often represented in a different way to their imperative counterparts 81 for example the array with constant access and update times is a basic component of most imperative languages and many imperative data structures such as the hash table and binary heap are based on arrays 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 82 comparison to imperative programming edit 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 higher order functions are rarely used in older imperative programming a traditional imperative program might use a loop to traverse and modify a list a functional program on the other hand would probably use a higher order map function that takes a function and a list generating and returning a new list by applying the function to each list item imperative vs functional programming edit the following two examples written in java achieve the same effect they multiply all even numbers in an array by 10 and add them all storing the final sum in the variable result traditional imperative loop int numlist 1 2 3 4 5 6 7 8 9 10 int result 0 for int i numlist if i 2 0 result i 10 functional programming with higher order functions import java util arrays int numlist 1 2 3 4 5 6 7 8 9 10 int result arrays stream numlist filter n n 2 0 map n n 10 reduce 0 integer sum sometimes the abstractions offered by functional programming might lead to development of more robust code that avoids certain issues that might arise when building upon large amount of complex imperative code such as off by one errors see greenspun s tenth rule simulating state edit there are tasks for example maintaining a bank account balance that often seem most naturally implemented with state pure functional programming performs these tasks and i o tasks such as accepting user input and printing to the screen in a different way the pure functional programming language haskell implements them using monads derived from category theory 83 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 84 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 85 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 86 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 87 efficiency issues edit functional programming languages are typically less efficient in their use of cpu and memory than imperative languages such as c and pascal 88 this is related to the fact that some mutable data structures like arrays have a very straightforward implementation using present hardware 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 89 however such slowdowns are not universal 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 90 for programs that handle large matrices and multidimensional databases array functional languages such as j and k were designed with speed optimizations 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 91 even if the involved copying that may seem implicit when dealing with persistent immutable data structures might seem computationally costly some functional programming languages like clojure solve this issue by implementing mechanisms for safe memory sharing between formally immutable data 92 rust distinguishes itself by its approach to data immutability which involves immutable references 93 and a concept called lifetimes 94 immutable data with separation of identity and state and shared nothing schemes can also potentially be more well suited for concurrent and parallel programming by the virtue of reducing or eliminating the risk of certain concurrency hazards since concurrent operations are usually atomic and this allows eliminating the need for locks this is how for example java util concurrent classes are implemented where some of them are immutable variants of the corresponding classes that are not suitable for concurrent use 95 functional programming languages often have a concurrency model that instead of shared state and synchronization leverages message passing mechanisms such as the actor model where each actor is a container for state behavior child actors and a message queue 96 97 this approach is common in erlang elixir or akka 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 1993 69 discusses theoretical issues related to memory leaks from lazy evaluation and o sullivan et al 2008 98 give some practical advice for analyzing and fixing them 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 99 abstraction cost edit some functional programming languages might not optimize abstractions such as higher order functions like map or filter as efficiently as the underlying imperative operations consider as an example the following two ways to check if 5 is an even number in clojure even 5 equals mod 5 2 0 when benchmarked using the criterium tool on a ryzen 7900x gnu linux pc in a leiningen repl 2 11 2 running on java vm version 22 and clojure version 1 11 1 the first implementation which is implemented as defn even returns true if n is even throws an exception if n is not an integer added 1 0 static true n if integer n zero bit and clojure lang rt uncheckedlongcast n 1 throw illegalargumentexception str argument must be an integer n has the mean execution time of 4 76 ms while the second one in which equals is a direct invocation of the underlying java method has a mean execution time of 2 8 μs roughly 1700 times faster part of that can be attributed to the type checking and exception handling involved in the implementation of even for instance the lo library for go which implements various higher order functions common in functional programming languages using generics in a benchmark provided by the library s author calling map is 4 slower than an equivalent for loop and has the same allocation profile 100 which can be attributed to various compiler optimizations such as inlining 101 one distinguishing feature of rust are zero cost abstractions this means that using them imposes no additional runtime overhead this is achieved thanks to the compiler using loop unrolling where each iteration of a loop be it imperative or using iterators is converted into a standalone assembly instruction without the overhead of the loop controlling code if an iterative operation writes to an array the resulting array s elements will be stored in specific cpu registers allowing for constant time access at runtime 102 functional programming in non functional languages edit it is possible to use a functional style of programming in languages that are not traditionally considered functional languages 103 for example both d 104 and fortran 95 62 explicitly support pure functions javascript lua 105 python and go 106 had first class functions from their inception 107 python had support for lambda map reduce and filter in 1994 as well as closures in python 2 2 108 though python 3 relegated reduce to the functools standard library module 109 first class functions have been introduced into other mainstream languages such as perl 5 0 in 1994 php 5 3 visual basic 9 c 3 0 c 11 and kotlin 29 in perl lambda map reduce filter and closures are fully supported and frequently used the book higher order perl released in 2005 was written to provide an expansive guide on using perl for functional programming in php anonymous classes 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 java anonymous classes can sometimes be used to simulate closures 110 however anonymous classes are not always proper replacements to closures because they have more limited capabilities 111 java 8 supports lambda expressions as a replacement for some anonymous classes 112 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 for example the strategy pattern simply dictates use of a higher order function and the visitor pattern roughly corresponds to a catamorphism or fold similarly the idea of immutable data from functional programming is often included in imperative programming languages 113 for example the tuple in python which is an immutable array and object freeze in javascript 114 comparison to logic programming edit logic programming can be viewed as a generalisation of functional programming in which functions are a special case of relations 115 for example the function mother x y every x has only one mother y can be represented by the relation mother x y whereas functions have a strict input output pattern of arguments relations can be queried with any pattern of inputs and outputs consider the following logic program mother charles elizabeth mother harry diana the program can be queried like a functional program to generate mothers from children mother harry x x diana mother charles x x elizabeth but it can also be queried backwards to generate children mother x elizabeth x charles mother x diana x harry it can even be used to generate all instances of the mother relation mother x y x charles y elizabeth x harry y diana compared with relational syntax functional syntax is a more compact notation for nested functions for example the definition of maternal grandmother in functional syntax can be written in the nested form maternal_grandmother x mother mother x the same definition in relational notation needs to be written in the unnested form maternal_grandmother x y mother x z mother z y here means if and means and however the difference between the two representations is simply syntactic in ciao prolog relations can be nested like functions in functional programming 116 grandparent x parent parent x parent x mother x parent x father x mother charles elizabeth father charles phillip mother harry diana father harry charles grandparent x y x harry y elizabeth x harry y phillip ciao transforms the function like notation into relational form and executes the resulting logic program using the standard prolog execution strategy applications edit text editors edit emacs a highly extensible text editor family uses its own lisp dialect for writing plugins the original author of the most popular emacs implementation gnu emacs and emacs lisp richard stallman considers lisp one of his favorite programming languages 117 spreadsheets edit spreadsheets can be considered a form of pure zeroth order...
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