ML (programming language)

Paradigm multi-paradigm: imperative, functional
Designed by Robin Milner & others at the University of Edinburgh
First appeared 1973 (1973)
Typing discipline static, strong, inferred, safe
Standard ML, Caml
Influenced by
Clojure, Coq, Cyclone, C++, Elm, F#, Haskell, Idris, Miranda, Nemerle, Opa, Erlang, Rust, Scala

ML is a general-purpose 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. It has roots in the Lisp language, and has been characterized as "LISP with types". Historically, ML stands for MetaLanguage: it was conceived to develop proof tactics in the LCF theorem prover (whose language, pplambda, a combination of the first-order 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 system, whose type inference algorithm can automatically assign 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 well-typed ML program does not cause runtime type errors.[2]


Features of ML include a call-by-value evaluation strategy, first-class 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.

ML can be referred to as an impure functional language, because although it encourages functional programming, it does allow side-effects (like languages such as Lisp, but unlike a purely functional language such as Haskell). Like most programming languages, ML uses eager evaluation, meaning that all subexpressions are always evaluated, though 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, ATS, and Elm.[3]

ML's strengths are mostly applied in language design and manipulation (compilers, analyzers, theorem provers), but it is a general-purpose language also used in bioinformatics, financial systems, and applications including a genealogical database, a peer-to-peer client/server program, etc.


The following examples use the syntax of Standard ML. The other most widely used ML dialect, OCaml, differs in various insubstantial ways.


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), that is, fac accepts an integer as an argument and returns an integer result. 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)
    if (n < 0) then raise Fail "negative argument"
    else fac n

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 tail-recursive 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)
    if (n < 0) then raise Fail "negative argument"
    else fac (n, 1)

List reverse

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 easy-to-read, style:

fun reverse xs = let
  fun rev [] acc = acc
    | rev (hd::tl) acc = rev tl (hd::acc)
  rev xs []

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


  1. Gordon, Michael J. C. (1996). "From LCF to HOL: a short history". Retrieved 2007-10-11.
  2. Robin Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17(3):348 – 375, 1978.
  3. Tate, Bruce A.; Daoud, Fred; Dees, Ian; Moffitt, Jack (2014). "3. Elm". Seven More Languages in Seven Weeks (Book version: P1.0-November 2014 ed.). The Pragmatic Programmers, LLC. pp. 97, 101. ISBN 978-1-941222-15-7. On page 101, Elm creator Evan Czaplicki says: 'I tend to say “Elm is an ML-family language” to get at the shared heritage of all these languages.' ["these languages" is referring to Haskell, OCaml, SML, and F#]


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