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The comprehension is implemented as a macro that is expanded at compile time, you can see the expanded code using the expandMacro compiler option: var collectResult = newSeq ( Natural ( 0 )) for item in items ( @[- 9 , 1 , 42 , 0 , - 1 , 9 ] ): add ( collectResult , item + 1 ) collectResult
The natural number = is a generalised Dudeney number, [1] and for =, the numbers are known as Dudeney numbers. 0 {\displaystyle 0} and 1 {\displaystyle 1} are trivial Dudeney numbers for all b {\displaystyle b} and p {\displaystyle p} , all other trivial Dudeney numbers are nontrivial trivial Dudeney numbers .
The code above specifies a list of strings to be either empty, or a structure that contains a string and a list of strings. The self-reference in the definition permits the construction of lists of any (finite) number of strings. Another example of inductive definition is the natural numbers (or positive integers):
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers write once, run anywhere (), [16] meaning that compiled Java code can run on all platforms that support Java without the need to recompile. [17]
Parse tree of Python code with inset tokenization. The syntax of textual programming languages is usually defined using a combination of regular expressions (for lexical structure) and Backus–Naur form (a metalanguage for grammatical structure) to inductively specify syntactic categories (nonterminal) and terminal symbols. [7]
float and double, floating-point numbers with single and double precisions; boolean, a Boolean type with logical values true and false; returnAddress, a value referring to an executable memory address. This is not accessible from the Java programming language and is usually left out. [13] [14]
Take Pascal's triangle, which is a triangular array of numbers in which those at the ends of the rows are 1 and each of the other numbers is the sum of the nearest two numbers in the row just above it (the apex, 1, being at the top). The following is an APL one-liner function to visually depict Pascal's triangle:
The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0 ) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω .