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For example, the implementation of set union in the OCaml standard library in theory is asymptotically faster than the equivalent function in the standard libraries of imperative languages (e.g., C++, Java) because the OCaml implementation can exploit the immutability of sets to reuse parts of input sets in the output (see persistent data ...
This article compares the syntax for defining and instantiating an algebraic data type (ADT), sometimes also referred to as a tagged union, in various programming languages. Examples of algebraic data types
In programming languages (especially functional programming languages) and type theory, an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied.
MakeSet creates 8 singletons. After some operations of Union, some sets are grouped together. The operation Union(x, y) replaces the set containing x and the set containing y with their union. Union first uses Find to determine the roots of the trees containing x and y. If the roots are the same, there is nothing more to do.
Since Caml is a functional programming language, it is easy to create and pass around functions in Caml programs. This ability has very many applications. Calculating the numerical derivative of a function is one example. The following Caml function d computes the numerical derivative of a given function f at a given point x:
A universe set is an absorbing element of binary union . The empty set ∅ {\displaystyle \varnothing } is an absorbing element of binary intersection ∩ {\displaystyle \cap } and binary Cartesian product × , {\displaystyle \times ,} and it is also a left absorbing element of set subtraction ∖ : {\displaystyle \,\setminus :}
Somewhat similar to a function, a data constructor is applied to arguments of an appropriate type, yielding an instance of the data type to which the type constructor belongs. For example, the data constructor Leaf is logically a function Int -> Tree, meaning that giving an integer as an argument to Leaf produces a value of the type Tree.
^c The value of n is provided by the SELECTED_REAL_KIND [8] intrinsic function. ^d ALGOL 68 G's runtime option --precision "number" can set precision for long long real s to the required "number" significant digits.