Tipo de datos booleanos

En informática , el tipo de datos booleano es un tipo de datos que tiene uno de dos valores posibles (generalmente denotados como verdadero y falso ) que pretende representar los dos valores de verdad de la lógica y el álgebra booleana . Lleva el nombre de George Boole , quien definió por primera vez un sistema algebraico de lógica a mediados del siglo XIX. El tipo de datos booleano se asocia principalmente con declaraciones condicionales , que permiten diferentes acciones al cambiar el flujo de control dependiendo de si una condición booleana especificada por el programadorse evalúa como verdadero o falso. Es un caso especial de un tipo de datos lógico más general (ver lógica probabilística ) - poi no siempre necesita ser booleano.

Generalidades

En los lenguajes de programación con un tipo de datos booleano incorporado, como Pascal y Java , los operadores de comparación como >y ≠generalmente se definen para devolver un valor booleano. Se pueden definir comandos condicionales e iterativos para probar expresiones con valores booleanos.

Los lenguajes sin tipos de datos booleanos explícitos, como C90 y Lisp , aún pueden representar valores de verdad mediante algún otro tipo de datos. Common Lisp usa una lista vacía para falso y cualquier otro valor para verdadero. El lenguaje de programación C utiliza un número entero tipo, donde las expresiones relacionales como i > jy expresiones lógicas conectadas por &&y ||se define para que tenga valor 1 si es verdadero y 0 si es falso, mientras que las partes de la prueba de if, while, for, etc., tratar cualquier valor distinto de cero como cierto. ^{[1] [2]} De hecho, una variable booleana puede considerarse (e implementarse) como una variable numérica con un dígito binario ( bit), which can store only two values. The implementation of Booleans in computers are most likely represented as a full word, rather than a bit; this is usually due to the ways computers transfer blocks of information.

Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR, NEQV, ^, !=), and negation (NOT, ~, !).

In some languages, like Ruby, Smalltalk, and Alice the true and false values belong to separate classes, i.e., True and False, respectively, so there is no one Boolean type.

In SQL, which uses a three-valued logic for explicit comparisons because of its special treatment of Nulls, the Boolean data type (introduced in SQL:1999) is also defined to include more than two truth values, so that SQL Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can also be restricted to just TRUE and FALSE though.

ALGOL and the built-in boolean type

One of the earliest programming languages to provide an explicit boolean data type is ALGOL 60 (1960) with values true and false and logical operators denoted by symbols '${\displaystyle \wedge }$' (and), '${\displaystyle \vee }$' (or), '${\displaystyle \supset }$' (implies), '${\displaystyle \equiv }$' (equivalence), and '${\displaystyle \neg }$' (not). Due to input device and character set limits on many computers of the time, however, most compilers used alternative representations for many of the operators, such as AND or 'AND'.

This approach with boolean as a built-in (either primitive or otherwise predefined) data type was adopted by many later programming languages, such as Simula 67 (1967), ALGOL 68 (1970),^[3] Pascal (1970), Ada (1980), Java (1995), and C# (2000), among others.

Fortran

The first version of FORTRAN (1957) and its successor FORTRAN II (1958) have no logical values or operations; even the conditional IF statement takes an arithmetic expression and branches to one of three locations according to its sign; see arithmetic IF. FORTRAN IV (1962), however, follows the ALGOL 60 example by providing a Boolean data type (LOGICAL), truth literals (.TRUE. and .FALSE.), Boolean-valued numeric comparison operators (.EQ., .GT., etc.), and logical operators (.NOT., .AND., .OR.). In FORMAT statements, a specific format descriptor ('L') is provided for the parsing or formatting of logical values.^[4]

Lisp and Scheme

The language Lisp (1958) never had a built-in Boolean data type. Instead, conditional constructs like cond assume that the logical value false is represented by the empty list (), which is defined to be the same as the special atom nil or NIL; whereas any other s-expression is interpreted as true. For convenience, most modern dialects of Lisp predefine the atom t to have value t, so that t can be used as a mnemonic notation for true.

This approach (any value can be used as a Boolean value) was retained in most Lisp dialects (Common Lisp, Scheme, Emacs Lisp), and similar models were adopted by many scripting languages, even ones having a distinct Boolean type or Boolean values; although which values are interpreted as false and which are true vary from language to language. In Scheme, for example, the false value is an atom distinct from the empty list, so the latter is interpreted as true.

Pascal, Ada, and Haskell

The language Pascal (1970) introduced the concept of programmer-defined enumerated types. A built-in Boolean data type was then provided as a predefined enumerated type with values FALSE and TRUE. By definition, all comparisons, logical operations, and conditional statements applied to and/or yielded Boolean values. Otherwise, the Boolean type had all the facilities which were available for enumerated types in general, such as ordering and use as indices. In contrast, converting between Booleans and integers (or any other types) still required explicit tests or function calls, as in ALGOL 60. This approach (Boolean is an enumerated type) was adopted by most later languages which had enumerated types, such as Modula, Ada, and Haskell.

C, C++, Objective-C, AWK

Initial implementations of the language C (1972) provided no Boolean type, and to this day Boolean values are commonly represented by integers (ints) in C programs. The comparison operators (>, ==, etc.) are defined to return a signed integer (int) result, either 0 (for false) or 1 (for true). Logical operators (&&, ||, !, etc.) and condition-testing statements (if, while) assume that zero is false and all other values are true.

After enumerated types (enums) were added to the American National Standards Institute version of C, ANSI C (1989), many C programmers got used to defining their own Boolean types as such, for readability reasons. However, enumerated types are equivalent to integers according to the language standards; so the effective identity between Booleans and integers is still valid for C programs.

Standard C (since C99) provides a boolean type, called _Bool. By including the header stdbool.h, one can use the more intuitive name bool and the constants true and false. The language guarantees that any two true values will compare equal (which was impossible to achieve before the introduction of the type). Boolean values still behave as integers, can be stored in integer variables, and used anywhere integers would be valid, including in indexing, arithmetic, parsing, and formatting. This approach (Boolean values are just integers) has been retained in all later versions of C. Note, that this does not mean that any integer value can be stored in a boolean variable.

C++ has a separate Boolean data type bool, but with automatic conversions from scalar and pointer values that are very similar to those of C. This approach was adopted also by many later languages, especially by some scripting languages such as AWK.

Objective-C also has a separate Boolean data type BOOL, with possible values being YES or NO, equivalents of true and false respectively.^[5] Also, in Objective-C compilers that support C99, C's _Bool type can be used, since Objective-C is a superset of C.

Java

In Java, the value of the boolean data type can only be either true or false.^[6]

Perl and Lua

Perl has no boolean data type. Instead, any value can behave as boolean in boolean context (condition of if or while statement, argument of && or ||, etc.). The number 0, the strings "0" and "", the empty list (), and the special value undef evaluate to false.^[7] All else evaluates to true.

Lua has a boolean data type, but non-boolean values can also behave as booleans. The non-value nil evaluates to false, whereas every other data type always evaluates to true, regardless of value.

Tcl

Tcl has no separate Boolean type. Like in C, the integers 0 (false) and 1 (true - in fact any nonzero integer) are used.^[8]

Examples of coding:

set v 1 if { $v } { puts "V is 1 or true" }

The above will show "V is 1 or true" since the expression evaluates to '1'

set v "" if { $v } ....

The above will render an error as variable 'v' cannot be evaluated as '0' or '1'

Python, Ruby, and JavaScript

Python, from version 2.3 forward, has a bool type which is a subclass of int, the standard integer type.^[9] It has two possible values: True and False, which are special versions of 1 and 0 respectively and behave as such in arithmetic contexts. Also, a numeric value of zero (integer or fractional), the null value (None), the empty string, and empty containers (i.e. lists, sets, etc.) are considered Boolean false; all other values are considered Boolean true by default.^[10] Classes can define how their instances are treated in a Boolean context through the special method __nonzero__ (Python 2) or __bool__ (Python 3). For containers, __len__ (the special method for determining the length of containers) is used if the explicit Boolean conversion method is not defined.

In Ruby, in contrast, only nil (Ruby's null value) and a special false object are false, all else (including the integer 0 and empty arrays) is true.

In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false^[11]are sometimes called falsy (of which the complement is truthy) to distinguish between strictly type-checked and coerced Booleans.^[12] As opposed to Python, empty containers (arrays , Maps, Sets) are considered truthy. Languages such as PHP also use this approach.

Next Generation Shell

Next Generation Shell, has Bool type. It has two possible values: true and false. Bool is not interchangeable with Int and have to be converted explicitly if needed. When a Boolean value of an expression is needed (for example in if statement), Bool method is called. Bool method for built-in types is defined such that it returns false for a numeric value of zero, the null value, the empty string, empty containers (i.e. lists, sets, etc.), external processes that exited with non-zero exit code; for other values Bool returns true. Types for which Bool method is defined can be used in Boolean context. When evaluating an expression in Boolean context, If no appropriate Bool method is defined, an exception is thrown.

SQL

Main article: Null (SQL) § Comparisons with NULL and the three-valued logic (3VL)

Booleans appear in SQL when a condition is needed, such as WHERE clause, in form of predicate which is produced by using operators such as comparison operators, IN operator, IS (NOT) NULL etc. However, apart from TRUE and FALSE, these operators can also yield a third state, called UNKNOWN, when comparison with NULL is made.

The treatment of boolean values differs between SQL systems.

For example, in Microsoft SQL Server, boolean value is not supported at all, neither as a standalone data type nor representable as an integer. It shows an error message "An expression of non-boolean type specified in a context where a condition is expected" if a column is directly used in the WHERE clause, e.g. SELECT a FROM t WHERE a, while statement such as SELECT column IS NOT NULL FROM t yields a syntax error. The BIT data type, which can only store integers 0 and 1 apart from NULL, is commonly used as a workaround to store Boolean values, but workarounds need to be used such as UPDATE t SET flag = IIF(col IS NOT NULL, 1, 0) WHERE flag = 0 to convert between the integer and boolean expression.

In PostgreSQL, there is a distinct BOOLEAN type as in the standard^[13] which allows predicates to be stored directly into a BOOLEAN column, and allows using a BOOLEAN column directly as a predicate in WHERE clause.

In MySQL, BOOLEAN is treated as an alias as TINYINT(1),^[14] TRUE is the same as integer 1 and FALSE is the same is integer 0.,^[15] and treats any non-zero integer as true when evaluating conditions.

The SQL92 standard introduced IS (NOT) TRUE, IS (NOT) FALSE, IS (NOT) UNKNOWN operators which evaluate a predicate, which predated the introduction of boolean type in SQL:1999

The SQL:1999 standard introduced a BOOLEAN data type as an optional feature (T031). When restricted by a NOT NULL constraint, a SQL BOOLEAN behaves like Booleans in other languages, which can store only TRUE and FALSE values. However, if it is nullable, which is the default like all other SQL data types, it can have the special null value also. Although the SQL standard defines three literals for the BOOLEAN type – TRUE, FALSE, and UNKNOWN – it also says that the NULL BOOLEAN and UNKNOWN "may be used interchangeably to mean exactly the same thing".^[16][17] This has caused some controversy because the identification subjects UNKNOWN to the equality comparison rules for NULL. More precisely UNKNOWN = UNKNOWN is not TRUE but UNKNOWN/NULL.^[18] As of 2012 few major SQL systems implement the T031 feature.^[19] Firebird and PostgreSQL are notable exceptions, although PostgreSQL implements no UNKNOWN literal; NULL can be used instead.^[20]

Microsoft Access, which uses the Microsoft Jet database engine,^[21] also doesn't have a boolean data type. Similar to MS SQL Server, it uses a BIT data type.^[22] In Access it is known as a Yes/No data type^[23] which can have two values; Yes (True) or No (False). The BIT data type in Access can also can be represented numerically; True is -1 and False is 0.^[24] This differs to MS SQL Server in two ways, even though both are Microsoft products:

1. Access represents TRUE as -1, while it is 1 in SQL Server
2. Access does not support the Null tri-state, supported by SQL Server

Tableau

Tableau Software has a BOOLEAN data type.^[25] The literal of a boolean value is True or False.^[26]

The Tableau boolean converts to a number using the INT() function. Wrapping a boolean field in INT() returns 1 (for True) or 0 (for False).^[27]

See also

• true and false (commands), for shell scripting
• Shannon's expansion
• stdbool.h, C99 definitions for boolean
• Boolean differential calculus

References

1. Kernighan, Brian W; Ritchie, Dennis M (1978). The C Programming Language (1st ed.). Englewood Cliffs, NJ: Prentice Hall. p. 41. ISBN 0-13-110163-3.
2. Plauger, PJ; Brodie, Jim (1992) [1989]. ANSI and ISO Standard C Programmer's reference. Microsoft Press. pp. 86–93. ISBN 1-55615-359-7.
3. "Report on the Algorithmic Language ALGOL 68, Section 10.2.2" (PDF). August 1968. Archived (PDF) from the original on 6 April 2008. Retrieved 30 April 2007.
4. Digital Equipment Corporation, DECSystem10 FORTRAN IV Programmers Reference Manual. Reprinted in Mathematical Languages Handbook. Online version Archived 2011-08-14 at the Wayback Machine accessed 2011-11-16.
5. "Guides and Sample Code". developer.apple.com. Archived from the original on 7 September 2011. Retrieved 1 May 2018.
6. "Java Booleans". W3Schools Online Web Tutorials. Retrieved 2021-02-17.
7. "perlsyn - Perl Syntax / Truth and Falsehood". Archived from the original on 26 August 2013. Retrieved 10 September 2013.
8. "PEP 285 -- Adding a bool type". 4 May 2011. Archived from the original on 28 March 2018. Retrieved 28 March 2018.
9. van Rossum, Guido (3 April 2002). "PEP 285 -- Adding a bool type". Archived from the original on 1 May 2013. Retrieved 15 May 2013.
10. "Expressions". Python v3.3.2 documentation. Archived from the original on 22 May 2013. Retrieved 15 May 2013.
11. "ECMAScript Language Specification" (PDF). p. 43. Archived from the original (PDF) on 2015-04-12. Retrieved 2011-03-12.
12. "The Elements of JavaScript Style". Douglas Crockford. Archived from the original on 17 March 2011. Retrieved 5 March 2011.
13. [1]
14. [2]
15. [3]
16. C. Date (2011). SQL and Relational Theory: How to Write Accurate SQL Code. O'Reilly Media, Inc. p. 83. ISBN 978-1-4493-1640-2.
17. ISO/IEC 9075-2:2011 §4.5
18. Martyn Prigmore (2007). Introduction to Databases With Web Applications. Pearson Education Canada. p. 197. ISBN 978-0-321-26359-9.
19. Troels Arvin, Survey of BOOLEAN data type implementation Archived 2005-03-09 at the Wayback Machine
20. "PostgreSQL: Documentation: 10: 8.6. Boolean Type". www.postgresql.org. Archived from the original on 9 March 2018. Retrieved 1 May 2018.
21. "Migrate an Access database to SQL Server". support.microsoft.com. Retrieved 2020-10-19.
22. o365devx. "SQL data types (Access desktop database reference)". docs.microsoft.com. Retrieved 2020-10-19.
23. "Introduction to data types and field properties". support.microsoft.com. Retrieved 2020-10-19.
24. "Boolean Data - MS-Access Tutorial". sourcedaddy.com. Retrieved 2020-10-19.
25. "Data Types". help.tableau.com. Retrieved 2020-10-19.
26. "Formatting Calculations in Tableau". help.tableau.com. Retrieved 2020-10-19.
27. "Boolean makes Tableau faster - true or false?". TAR Solutions. 2020-09-11. Retrieved 2020-10-19.