In
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, the Boolean (sometimes shortened to Bool) is a
data type
In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most progra ...
that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two
truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false'').
Computing
In some pro ...
s of
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...
and
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
. It is named after
George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with
conditional
Conditional (if then) may refer to:
*Causal conditional, if X then Y, where X is a cause of Y
*Conditional probability, the probability of an event A given that another event B has occurred
*Conditional proof, in logic: a proof that asserts a co ...
statements, which allow different actions by changing
control flow
In computer science, control flow (or flow of control) is the order in which individual statements, instructions or function calls of an imperative program are executed or evaluated. The emphasis on explicit control flow distinguishes an '' ...
depending on whether a programmer-specified Boolean ''condition'' evaluates to true or false. It is a special case of a more general ''logical data type—''logic does not always need to be Boolean (see
probabilistic logic).
Generalities
In
programming language
A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language.
The description of a programming ...
s with a built-in Boolean data type, such as
Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Frenc ...
and
Java
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mo ...
, the
comparison operators such as
>
and
≠
are usually defined to return a Boolean value.
Conditional
Conditional (if then) may refer to:
*Causal conditional, if X then Y, where X is a cause of Y
*Conditional probability, the probability of an event A given that another event B has occurred
*Conditional proof, in logic: a proof that asserts a co ...
and
iterative
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
commands may be defined to test Boolean-valued expressions.
Languages with no explicit Boolean data type, like
C90 and
Lisp, may still represent truth values by some other data type.
Common Lisp uses an empty
list for false, and any other value for true. The C programming language uses an
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
type, where relational expressions like
i > j
and logical expressions connected by
&&
and
, ,
are defined to have value 1 if true and 0 if false, whereas the test parts of
if
,
while
,
for
, etc., treat any non-zero value as true.
Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit (
bit), or as a bit string of length one, which can store only two values. The implementation of Booleans in computers are most likely represented as a full
word
A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...
, 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
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor ...
(
OR
,
,
,
+
),
equivalence (
EQV
,
=
,
),
exclusive or/non-equivalence (
XOR
,
NEQV
,
^
,
!=
,
¬
), and
negation (
NOT
,
~
,
!
,
¬
).
In some languages, like
Ruby
A ruby is a pinkish red to blood-red colored gemstone, a variety of the mineral corundum ( aluminium oxide). Ruby is one of the most popular traditional jewelry gems and is very durable. Other varieties of gem-quality corundum are called ...
,
Smalltalk, and
Alice
Alice may refer to:
* Alice (name), most often a feminine given name, but also used as a surname
Literature
* Alice (''Alice's Adventures in Wonderland''), a character in books by Lewis Carroll
* ''Alice'' series, children's and teen books by ...
the ''true'' and ''false'' values belong to separate
classes, e.g.,
True
and
False
, respectively, so there is no one Boolean ''type''.
In
SQL, which uses a
three-valued logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indetermina ...
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 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 '
' (and), '
' (or), '
' (implies), '
' (equivalence), and '
' (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
In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most progra ...
was adopted by many later programming languages, such as
Simula 67 (1967),
ALGOL 68 (1970),
Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Frenc ...
(1970),
Ada
Ada may refer to:
Places
Africa
* Ada Foah, a town in Ghana
* Ada (Ghana parliament constituency)
* Ada, Osun, a town in Nigeria
Asia
* Ada, Urmia, a village in West Azerbaijan Province, Iran
* Ada, Karaman, a village in Karaman Province, T ...
(1980),
Java
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mo ...
(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.
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 A scheme is a systematic plan for the implementation of a certain idea.
Scheme or schemer may refer to:
Arts and entertainment
* ''The Scheme'' (TV series), a BBC Scotland documentary series
* The Scheme (band), an English pop band
* ''The Schem ...
,
Emacs Lisp), and similar models were adopted by many
scripting language
A scripting language or script language is a programming language that is used to manipulate, customize, and automate the facilities of an existing system. Scripting languages are usually interpreted at runtime rather than compiled.
A scripting ...
s, 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''. Common Lisp, on the other hand, also provides the dedicated
boolean
type, derived as a specialization of the symbol.
Pascal, Ada, and Haskell
The language
Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Frenc ...
(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
Boolean
s 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
Ada may refer to:
Places
Africa
* Ada Foah, a town in Ghana
* Ada (Ghana parliament constituency)
* Ada, Osun, a town in Nigeria
Asia
* Ada, Urmia, a village in West Azerbaijan Province, Iran
* Ada, Karaman, a village in Karaman Province, T ...
, 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 (
int
s) 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 (
enum
s) were added to the
American National Standards Institute
The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The orga ...
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 language
A scripting language or script language is a programming language that is used to manipulate, customize, and automate the facilities of an existing system. Scripting languages are usually interpreted at runtime rather than compiled.
A scripting ...
s 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. 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
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mo ...
, the value of the boolean data type can only be either
true
or
false
.
Perl and Lua
Perl
Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offic ...
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. 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 value evaluates to true. This includes the empty string
""
and the number
0
, which are very often considered
false
in other languages.
PL/I
PL/I has no boolean data type. Instead, comparison operators generate BIT(1) values; '0'B represents false and '1'B represents true. The operands of, e.g.,
&
,
,
,
¬
, are converted to bit strings and the operations are performed on each bit. The ''element-expression'' of an
IF
statement is true if any bit is 1.
Rexx
Rexx has no boolean data type. Instead, comparison operators generate 0 or 1; 0 represents false and 1 represents true. The operands of, e.g.,
&
,
,
,
¬
, must be 0 or 1.
Tcl
Tcl has no separate Boolean type. Like in C, the integers 0 (false) and 1 (true—in fact any nonzero integer) are used.
Examples of coding:
The above will show since the expression evaluates to 1.
The above will render an error, as variable 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. 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 (lists,
sets, etc.) are considered Boolean false; all other values are considered Boolean true by default. 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
A ruby is a pinkish red to blood-red colored gemstone, a variety of the mineral corundum ( aluminium oxide). Ruby is one of the most popular traditional jewelry gems and is very durable. Other varieties of gem-quality corundum are called ...
, 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
JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of websites use JavaScript on the client side for webpage behavior, of ...
, the empty string (
""
),
null
,
undefined
,
NaN
, +0,
−0
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are identical. However, in computing, some number representations allow for the existence of two zeros, often denoted b ...
and
false
are sometimes called ''falsy'' (of which the
complement is ''truthy'') to distinguish between strictly
type-checked and
coerced Booleans. As opposed to Python, empty containers (arrays , Maps, Sets) are considered truthy. Languages such as
PHP also use this approach.
SQL
Booleans appear in SQL when a
condition is needed, such as
clause, in form of predicate which is produced by using operators such as comparison operators, operator, etc. However, apart from and , these operators can also yield a third state, called , when comparison with
is made.
The SQL92 standard introduced and operators which evaluate a predicate, which predated the introduction of boolean type in
SQL:1999.
The SQL:1999 standard introduced a data type as an optional feature (T031). When restricted by a constraint, a SQL behaves like Booleans in other languages, which can store only and 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 type – and it also says that the and "may be used interchangeably to mean exactly the same thing".
This has caused some controversy because the identification subjects to the equality comparison rules for NULL. More precisely is not but .
As of 2012 few major SQL systems implement the T031 feature. Firebird and
PostgreSQL
PostgreSQL (, ), also known as Postgres, is a free and open-source relational database management system (RDBMS) emphasizing extensibility and SQL compliance. It was originally named POSTGRES, referring to its origins as a successor to the ...
are notable exceptions, although PostgreSQL implements no literal; can be used instead.
The treatment of boolean values differs between SQL systems.
For example, in
Microsoft SQL Server
Microsoft SQL Server is a relational database management system developed by Microsoft. As a database server, it is a software product with the primary function of storing and retrieving data as requested by other software applications—which ...
, boolean value is not supported at all, neither as a standalone data type nor representable as an integer. It shows the 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 clause, e.g. , while a statement such as yields a syntax error. The data type, which can only store integers 0 and 1 apart from , is commonly used as a workaround to store Boolean values, but workarounds need to be used such as to convert between the integer and boolean expression.
Microsoft Access
Microsoft Access is a database management system (DBMS) from Microsoft that combines the relational Access Database Engine (ACE) with a graphical user interface and software-development tools (not to be confused with the old Microsoft Access ...
, which uses the
Access Database Engine (ACE/JET), also does not have a boolean data type. Similar to MS SQL Server, it uses a data type. In Access it is known as a Yes/No data type 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. This differs to MS SQL Server in two ways, even though both are Microsoft products:
# Access represents as −1, while it is 1 in SQL Server
# Access does not support the Null tri-state, supported by SQL Server
PostgreSQL
PostgreSQL (, ), also known as Postgres, is a free and open-source relational database management system (RDBMS) emphasizing extensibility and SQL compliance. It was originally named POSTGRES, referring to its origins as a successor to the ...
has a distinct type as in the standard, which allows predicates to be stored directly into a column, and allows using a column directly as a predicate in a clause.
In
MySQL
MySQL () is an open-source relational database management system (RDBMS). Its name is a combination of "My", the name of co-founder Michael Widenius's daughter My, and "SQL", the acronym for Structured Query Language. A relational database ...
, is treated as an alias of ; is the same as integer 1 and is the same is integer 0. Any non-zero integer is true in conditions.
Tableau
Tableau Software
Tableau Software ( ) is an American interactive data visualization software company focused on business intelligence. It was founded in 2003 in Mountain View, California, and is currently headquartered in Seattle, Washington. In 2019 the c ...
has a BOOLEAN data type. The literal of a boolean value is
True
or
False
.
The Tableau
INT()
function converts a boolean to a number, returning 1 for True and 0 for False.
Forth
Forth (programming language) has no boolean type, it uses regular integers: value 0 (all bits low) represents false, and -1 (all bits high) represents true. This allows the language to define only one set of logical operators, instead of one for mathematical calculations and one for conditions.
See also
*
True and false (commands)
In Unix-like operating systems, true and false are commands whose only function is to always return with a predetermined exit status. Programmers and scripts often use the exit status of a command to assess success (exit status zero) or failur ...
for
shell scripting
*
Shannon's expansion
*
Boolean differential calculus
*
Three-valued logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indetermina ...
References
{{DEFAULTSORT:Boolean Data Type
Boolean algebra
Data types
Primitive types
Articles with example ALGOL 68 code