Object language
Encyclopedia
An object language is a language
which is the "object" of study in various fields including logic
, linguistics
, mathematics
and theoretical computer science
. The language being used to talk about an object language is called a metalanguage
. An object language may be a formal
or natural
language.
and linguistics
make use of metalanguages, which are languages for describing the nature of other languages. In mathematical logic, the object language is usually a formal language
. The language which a metalanguage is used to describe is the object language. It is called that because that language is the object under discussion using the metalanguage.
For instance, someone who says "In French, you say Bonjour to greet someone" uses English
as a metalanguage to describe the object language French
.
. Backus-Naur Form was one of the earliest used specification languages.
When compiler
s are written using systems like lex and yacc
, the rules the programmer writes look much like a formal specification, but it is considered an implementation
instead. Many programming language implementation
s are not strictly the same as their specifications, adding features or making implementation-dependent design decisions.
icons to create a Web page; all the steps to create the actual instructions which are run by computers are automatically performed, and not visible.)
One common practice for decades is to allow a programmer to use source language (whose use may still require extensive training), and have that language translated into object code which the computer can immediately use. The compiling of one into the other varies depending on what CPU is being given the instructions.
Object language in this context means something akin to "the object of what the programmer is trying to achieve". If the source language and object languages are viewed as formal (logical) languages, what the compiler does is interpret the source into the target language (this is different from the computer science use of interpreted language
meaning one which is not compiled). Object language should also not be confused with object-oriented language, which is a type of computer programming language
which changes the programmer's environment into convenient objects which can be used in something similar to a drag-and-drop fashion.
Object language in this context is synonymous with target language. The object language of a translation most often is a machine language, but can be some other kind of language, such as assembly language
.
Because the object language of compilation has usually been machine language, the term object file
has come to mean a file containing machine instructions, and sometimes the translated program itself is simply called an object.
, abstraction
or concept
, token
s of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in the formal language
s studied in mathematics
and logic
, the term "symbol" refers to the idea, and the marks are considered to be a token
instance of the symbol.
, abstraction
or concept
which is expressed using the symbol
s and formation rule
s (also called the formal grammar
) of a particular formal language. To say that a string
of symbols
is a wff with respect to a given formal grammar 
is equivalent to saying that 
belongs to the language generated by 
.
together with a deductive system
which consists of a set of inference rules and/or axiom
s. A formal system is used to derive
one expression from one or more other expressions previously expressed in the system. These expressions are called axiom
s, in the case of those previously supposed to be true, or theorem
s, in the case of those derived. A formal system may be formulated and studied for its intrinsic properties, or it may be intended as a description (i.e. a model
) of external phenomena.
or string of symbols which is derived
by using a formal system
. The string of symbols is a logical consequence of the axiom
s and rules
of the system.
s (called well-formed formula
s in the case of a formal language
) each of which is an axiom
or follows from the preceding sentences in the sequence by a rule of inference
. The last sentence in the sequence is a theorem
of a formal system
. The concept of natural deduction
is a generalization
of the concept of proof.
s in a formal language
.
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
which is the "object" of study in various fields including logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and theoretical computer science
Theoretical computer science
Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing....
. The language being used to talk about an object language is called a metalanguage
Metalanguage
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined. In logic and linguistics, a metalanguage is a language used to make statements about statements in another language...
. An object language may be a formal
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
or natural
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
language.
Formal languages
Mathematical logicMathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
make use of metalanguages, which are languages for describing the nature of other languages. In mathematical logic, the object language is usually a formal language
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
. The language which a metalanguage is used to describe is the object language. It is called that because that language is the object under discussion using the metalanguage.
For instance, someone who says "In French, you say Bonjour to greet someone" uses English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
as a metalanguage to describe the object language French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
.
Computer languages
There are two ways the term object language can be used in computing: a language which is the object of formal specification, and a language which is the object (goal) of a compiler or interpreter.Formal specification
Computer languages are object languages of the metalanguage in which their specification is written. In computer science this is referred to as the specification languageSpecification language
A specification language is a formal language used in computer science.Unlike most programming languages, which are directly executable formal languages used to implement a system, specification languages are used during systems analysis, requirements analysis and systems design.Specification...
. Backus-Naur Form was one of the earliest used specification languages.
When compiler
Compiler
A compiler is a computer program that transforms source code written in a programming language into another computer language...
s are written using systems like lex and yacc
Yacc
The computer program yacc is a parser generator developed by Stephen C. Johnson at AT&T for the Unix operating system. The name is an acronym for "Yet Another Compiler Compiler." It generates a parser based on an analytic grammar written in a notation similar to BNF.Yacc used to be available as...
, the rules the programmer writes look much like a formal specification, but it is considered an implementation
Implementation
Implementation is the realization of an application, or execution of a plan, idea, model, design, specification, standard, algorithm, or policy.-Computer Science:...
instead. Many programming language implementation
Programming language implementation
A programming language implementation is a system for executing programs written in a programming language.There are two general approaches to programming language implementation:...
s are not strictly the same as their specifications, adding features or making implementation-dependent design decisions.
Object Code
At their basic level, computers act on what is given to them through a limited set of instructions which are understood by their CPUs. In the earliest computers, that meant programmers sometimes typed 1's and 0's to program. Since this requires considerable programmer training (and patience) to create instructions, later computer languages have gone to great lengths to simplify the programmer's task. (For example, now it's common for people with little training to drag-and-dropDrag-and-drop
In computer graphical user interfaces, drag-and-drop is the action of selecting a virtual object by "grabbing" it and dragging it to a different location or onto another virtual object...
icons to create a Web page; all the steps to create the actual instructions which are run by computers are automatically performed, and not visible.)
One common practice for decades is to allow a programmer to use source language (whose use may still require extensive training), and have that language translated into object code which the computer can immediately use. The compiling of one into the other varies depending on what CPU is being given the instructions.
Object language in this context means something akin to "the object of what the programmer is trying to achieve". If the source language and object languages are viewed as formal (logical) languages, what the compiler does is interpret the source into the target language (this is different from the computer science use of interpreted language
Interpreted language
Interpreted language is a programming language in which programs are 'indirectly' executed by an interpreter program. This can be contrasted with a compiled language which is converted into machine code and then 'directly' executed by the host CPU...
meaning one which is not compiled). Object language should also not be confused with object-oriented language, which is a type of computer programming language
Programming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
which changes the programmer's environment into convenient objects which can be used in something similar to a drag-and-drop fashion.
Object language in this context is synonymous with target language. The object language of a translation most often is a machine language, but can be some other kind of language, such as assembly language
Assembly language
An assembly language is a low-level programming language for computers, microprocessors, microcontrollers, and other programmable devices. It implements a symbolic representation of the machine codes and other constants needed to program a given CPU architecture...
.
Because the object language of compilation has usually been machine language, the term object file
Object file
An object file is a file containing relocatable format machine code that is usually not directly executable. Object files are produced by an assembler, compiler, or other language translator, and used as input to the linker....
has come to mean a file containing machine instructions, and sometimes the translated program itself is simply called an object.
Symbols
A symbol is an ideaIdea
In the most narrow sense, an idea is just whatever is before the mind when one thinks. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images...
, abstraction
Abstraction
Abstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
or concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
, token
Type-token distinction
In disciplines such as philosophy and knowledge representation, the type-token distinction is a distinction that separates an abstract concept from the objects which are particular instances of the concept...
s of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in the formal language
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
s studied in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, the term "symbol" refers to the idea, and the marks are considered to be a token
Type-token distinction
In disciplines such as philosophy and knowledge representation, the type-token distinction is a distinction that separates an abstract concept from the objects which are particular instances of the concept...
instance of the symbol.
Formulas
In the formal languages used in mathematical logic and computer science, a well-formed formula or simply formula is an ideaIdea
In the most narrow sense, an idea is just whatever is before the mind when one thinks. Very often, ideas are construed as representational images; i.e. images of some object. In other contexts, ideas are taken to be concepts, although abstract concepts do not necessarily appear as images...
, abstraction
Abstraction
Abstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
or concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
which is expressed using the symbol
Symbol (formal)
For other uses see Symbol In logic, symbols build literal utility to illustrate ideas. A symbol is an abstraction, tokens of which may be marks or a configuration of marks which form a particular pattern...
s and formation rule
Formation rule
In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. These rules only address the location and manipulation of the strings of the language. It does not describe anything...
s (also called the formal grammar
Formal grammar
A formal grammar is a set of formation rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax...
) of a particular formal language. To say that a string
String (computer science)
In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set or alphabet....
of symbols
is a wff with respect to a given formal grammar is equivalent to saying that belongs to the language generated by .Formal systems
A formal system is a formal languageFormal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
together with a deductive system
Deductive system
A deductive system consists of the axioms and rules of inference that can be used to derive the theorems of the system....
which consists of a set of inference rules and/or axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s. A formal system is used to derive
Formal proof
A formal proof or derivation is a finite sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system...
one expression from one or more other expressions previously expressed in the system. These expressions are called axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s, in the case of those previously supposed to be true, or theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s, in the case of those derived. A formal system may be formulated and studied for its intrinsic properties, or it may be intended as a description (i.e. a model
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...
) of external phenomena.
Theorems
A theorem is a symbolSymbol (formal)
For other uses see Symbol In logic, symbols build literal utility to illustrate ideas. A symbol is an abstraction, tokens of which may be marks or a configuration of marks which form a particular pattern...
or string of symbols which is derived
Formal proof
A formal proof or derivation is a finite sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system...
by using a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
. The string of symbols is a logical consequence of the axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s and rules
Rule of inference
In logic, a rule of inference, inference rule, or transformation rule is the act of drawing a conclusion based on the form of premises interpreted as a function which takes premises, analyses their syntax, and returns a conclusion...
of the system.
Formal proofs
A formal proof or derivation is a finite sequence of propositionProposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s (called well-formed formula
Well-formed formula
In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word which is part of a formal language...
s in the case of a formal language
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
) each of which is an axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
or follows from the preceding sentences in the sequence by a rule of inference
Rule of inference
In logic, a rule of inference, inference rule, or transformation rule is the act of drawing a conclusion based on the form of premises interpreted as a function which takes premises, analyses their syntax, and returns a conclusion...
. The last sentence in the sequence is a theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
of a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
. The concept of natural deduction
Natural deduction
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning...
is a generalization
Generalization
A generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it...
of the concept of proof.
Theories
A theory is a set of sentenceSentence (mathematical logic)
In mathematical logic, a sentence of a predicate logic is a boolean-valued well formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that may be true or false...
s in a formal language
Formal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
.