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Paradigm  multiparadigm: imperative, functional  

Designed by  Robin Milner & others at the University of Edinburgh  
First appeared  1973  
static, strong, inferred, safe  

ML is a generalpurpose functional programming language developed by Robin Milner and others in the early 1970s at the University of Edinburgh,^{[1]} whose syntax is inspired by ISWIM. Historically, ML stands for metalanguage: it was conceived to develop proof tactics in the LCF theorem prover (whose language, pplambda, a combination of the firstorder predicate calculus and the simply typed polymorphic lambda calculus, had ML as its metalanguage). It is known for its use of the Hindley–Milner type inference algorithm, which can automatically infer the types of most expressions without requiring explicit type annotations. Additionally, the use of this algorithm ensures type safety—there is a formal proof that a welltyped ML program does not cause runtime type errors.^{[2]}
Contents
Overview[edit]
ML is often referred to as an impure functional language, because it allows sideeffects, unlike purely functional programming languages such as Haskell.
Features of ML include a callbyvalue evaluation strategy, firstclass functions, automatic memory management through garbage collection, parametric polymorphism, static typing, type inference, algebraic data types, pattern matching, and exception handling. ML uses static scoping rules.^{[citation needed]}
Unlike Haskell, ML uses eager evaluation, which means that all subexpressions are always evaluated. However, lazy evaluation can be achieved through the use of closures. Thus one can create and use infinite streams as in Haskell, but their expression is indirect.
Today there are several languages in the ML family; the two major dialects are Standard ML (SML) and Caml, but others exist, including F# — a language that Microsoft supports for their .NET platform. Ideas from ML have influenced numerous other languages, like Haskell, Cyclone, Nemerle, and ATS.^{[citation needed]}
ML's strengths are mostly applied in language design and manipulation (compilers, analyzers, theorem provers), but it is a generalpurpose language also used in bioinformatics, financial systems, and applications including a genealogical database, a peertopeer client/server program, etc.^{[citation needed]}
Examples[edit]
The following examples use the syntax of Standard ML. The other most widely used ML dialect, OCaml, differs in various insubstantial ways.
Factorial[edit]
The factorial function expressed as pure ML:
fun fac (0 : int) : int = 1
 fac (n : int) : int = n * fac (n  1)
This describes the factorial as a recursive function, with a single terminating base case. It is similar to the descriptions of factorials found in mathematics textbooks. Much of ML code is similar to mathematics in facility and syntax.
Part of the definition shown is optional, and describes the types of this function. The notation E : t can be read as expression E has type t. For instance, the argument n is assigned type integer (int), and fac (n : int), the result of applying fac to the integer n, also has type integer. The function fac as a whole then has type function from integer to integer (int > int). Thanks to type inference, the type annotations can be omitted and will be derived by the compiler. Rewritten without the type annotations, the example looks like:
fun fac 0 = 1
 fac n = n * fac (n  1)
The function also relies on pattern matching, an important part of ML programming. Note that parameters of a function are not necessarily in parentheses but separated by spaces. When the function's argument is 0 (zero) it will return the integer 1 (one). For all other cases the second line is tried. This is the recursion, and executes the function again until the base case is reached.
This implementation of the factorial function is not guaranteed to terminate, since a negative argument causes an infinite descending chain of recursive calls. A more robust implementation would check for a nonnegative argument before recursing, as follows:
fun fact n = let
fun fac 0 = 1
 fac n = n * fac (n  1)
in
if (n < 0) then raise Fail "negative argument"
else fac n
end
The problematic case (when n is negative) demonstrates a use of ML's exception system.
The function can be improved further by writing its inner loop in a tailrecursive style, such that the call stack need not grow in proportion to the number of function calls. This is achieved by adding an extra, "accumulator", parameter to the inner function. At last, we arrive at
fun factorial n = let
fun fac (0, acc) = acc
 fac (n, acc) = fac (n  1, n * acc)
in
if (n < 0) then raise Fail "negative argument"
else fac (n, 1)
end
List reverse[edit]
The following function "reverses" the elements in a list. More precisely, it returns a new list whose elements are in reverse order compared to the given list.
fun reverse [] = []
 reverse (x::xs) = (reverse xs) @ [x]
This implementation of reverse, while correct and clear, is inefficient, requiring quadratic time for execution. The function can be rewritten to execute in linear time in the following more efficient, though less easytoread, style:
fun reverse xs = let
fun rev [] acc = acc
 rev (hd::tl) acc = rev tl (hd::acc)
in
rev xs []
end
Notably, this function is an example of parametric polymorphism. That is, it can consume lists whose elements have any type, and return lists of the same type.
See also[edit]
 Dependent ML, an extension of ML with dependent typing that led to the development of ATS
 Lazy ML, an experimental lazily evaluated ML dialect from the early 1980s that paved the way for compilation of callbyneed languages such as Haskell and Clean
 Rpal, an educational language related to ML
Standard ML's implementations[edit]

 Alice ML, an extension of Standard ML with support for parallel programming using futures
 MLton, a powerful wholeprogram optimizing compiler strictly conforming to the Definition
 Moscow ML, an implementation originally based on Caml Light
 SML/NJ, an implementation with extensions for concurrent programming developed at Princeton University and Bell Laboratories
Books[edit]
 The Definition of Standard ML, Robin Milner, Mads Tofte, Robert Harper, MIT Press 1990; (Revised edition adds author David MacQueen), MIT Press 1997. ISBN 0262631814
 Commentary on Standard ML, Robin Milner, Mads Tofte, MIT Press 1997. ISBN 0262631377
 ML for the Working Programmer, Lawrence Paulson, Cambridge University Press 1991, 1996, ISBN 0521570506
 Harper, Robert (2005). Programming in Standard ML (PDF). Carnegie Mellon University.
 Elements of ML Programming, Jeffrey D. Ullman, PrenticeHall 1994, 1998. ISBN 0137903871
References[edit]
 ^ Gordon, Michael J. C. (1996). "From LCF to HOL: a short history". Retrieved 20071011.
 ^ Robin Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17(3):348 – 375, 1978.
External links[edit]
 Standard ML of New Jersey, another popular implementation
 F#, an ML implementation using the Microsoft .NET framework
 MLton, a wholeprogram optimizing Standard ML compiler
 Mythryl, "SML with a Posix face"
 sML, Successor ML
 CakeML, a readevalprint loop version of ML with formally verified runtime and translation to assembler
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