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77-721: The PL/P programming language (an acronym of P rogramming L anguage for P rime (computers) ) is a mid-level programming language developed by Prime Computer to serve as their second primary system programming language after Fortran IV . PL/P was a subset of PL/I . Additions to the PRIMOS operating system for Prime 50 Series computers were written mostly in PL/P in later years. Certain PRIMOS modules written in Fortran IV during PRIMOS's early years were rewritten in PL/P. PL/P
154-426: A compiler . An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type ( imperative languages —which implement operations in a specified order) developed to perform well on the popular von Neumann architecture . While early programming languages were closely tied to
231-406: A heap and automatic garbage collection . For the next decades, Lisp dominated artificial intelligence applications. In 1978, another functional language, ML , introduced inferred types and polymorphic parameters . After ALGOL (ALGOrithmic Language) was released in 1958 and 1960, it became the standard in computing literature for describing algorithms . Although its commercial success
308-400: A logic called a type system . Other forms of static analyses like data flow analysis may also be part of static semantics. Programming languages such as Java and C# have definite assignment analysis , a form of data flow analysis, as part of their respective static semantics. Once data has been specified, the machine must be instructed to perform operations on the data. For example,
385-485: A Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing machine. A universal Turing machine can be used to simulate any Turing machine and by extension the purely computational aspects of any possible real-world computer. To show that something is Turing-complete, it is enough to demonstrate that it can be used to simulate some Turing-complete system. No physical system can have infinite memory, but if
462-424: A computing device can be simulated by a universal Turing machine . The Church–Turing thesis states that this is a law of mathematics – that a universal Turing machine can, in principle, perform any calculation that any other programmable computer can. This says nothing about the effort needed to write the program , or the time it may take for the machine to perform the calculation, or any abilities
539-411: A control unit. These two elements make this architecture Turing-complete. Even pure functional languages are Turing-complete. Turing completeness in declarative SQL is implemented through recursive common table expressions . Unsurprisingly, procedural extensions to SQL ( PLSQL , etc.) are also Turing-complete. This illustrates one reason why relatively powerful non-Turing-complete languages are rare:
616-447: A data type whose elements, in many languages, must consist of a single type of fixed length. Other languages define arrays as references to data stored elsewhere and support elements of varying types. Depending on the programming language, sequences of multiple characters, called strings , may be supported as arrays of characters or their own primitive type . Strings may be of fixed or variable length, which enables greater flexibility at
693-434: A language in which programs are guaranteed to complete and halt cannot compute the computable function produced by Cantor's diagonal argument on all computable functions in that language. A computer with access to an infinite tape of data may be more powerful than a Turing machine: for instance, the tape might contain the solution to the halting problem or some other Turing-undecidable problem. Such an infinite tape of data
770-422: A meaning to a grammatically correct sentence or the sentence may be false: The following C language fragment is syntactically correct, but performs operations that are not semantically defined (the operation *p >> 4 has no meaning for a value having a complex type and p->im is not defined because the value of p is the null pointer ): If the type declaration on the first line were omitted,
847-454: A performance cost. Programming language theory is the subfield of computer science that studies the design, implementation, analysis, characterization, and classification of programming languages. Programming languages differ from natural languages in that natural languages are used for interaction between people, while programming languages are designed to allow humans to communicate instructions to machines. The term computer language
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#1732786911972924-526: A universal computer, because the instructions that compute them do not allow for an infinite loop. In the early 20th century, David Hilbert led a program to axiomatize all of mathematics with precise axioms and precise logical rules of deduction that could be performed by a machine. Soon it became clear that a small set of deduction rules are enough to produce the consequences of any set of axioms. These rules were proved by Kurt Gödel in 1930 to be enough to produce every theorem. The actual notion of computation
1001-406: Is a set of allowable values and operations that can be performed on these values. Each programming language's type system defines which data types exist, the type of an expression , and how type equivalence and type compatibility function in the language. According to type theory , a language is fully typed if the specification of every operation defines types of data to which the operation
1078-421: Is a system of notation for writing computer programs . Programming languages are described in terms of their syntax (form) and semantics (meaning), usually defined by a formal language . Languages usually provide features such as a type system , variables , and mechanisms for error handling . An implementation of a programming language is required in order to execute programs, namely an interpreter or
1155-505: Is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by
1232-415: Is allowed, the fewer type errors can be detected. Early programming languages often supported only built-in, numeric types such as the integer (signed and unsigned) and floating point (to support operations on real numbers that are not integers). Most programming languages support multiple sizes of floats (often called float and double ) and integers depending on the size and precision required by
1309-419: Is applicable. In contrast, an untyped language, such as most assembly languages , allows any operation to be performed on any data, generally sequences of bits of various lengths. In practice, while few languages are fully typed, most offer a degree of typing. Because different types (such as integers and floats ) represent values differently, unexpected results will occur if one type is used when another
1386-452: Is called a Turing oracle . Even a Turing oracle with random data is not computable ( with probability 1 ), since there are only countably many computations but uncountably many oracles. So a computer with a random Turing oracle can compute things that a Turing machine cannot. All known laws of physics have consequences that are computable by a series of approximations on a digital computer. A hypothesis called digital physics states that this
1463-469: Is expected. Type checking will flag this error, usually at compile time (runtime type checking is more costly). With strong typing , type errors can always be detected unless variables are explicitly cast to a different type. Weak typing occurs when languages allow implicit casting—for example, to enable operations between variables of different types without the programmer making an explicit type conversion. The more cases in which this type coercion
1540-418: Is impossible to determine whether this characteristic will hold. This impossibility poses problems when analyzing real-world computer programs. For example, one cannot write a tool that entirely protects programmers from writing infinite loops or protects users from supplying input that would cause infinite loops. One can instead limit a program to executing only for a fixed period of time ( timeout ) or limit
1617-441: Is no accident because the universe itself is computable on a universal Turing machine. This would imply that no computer more powerful than a universal Turing machine can be built physically. The computational systems (algebras, calculi) that are discussed as Turing-complete systems are those intended for studying theoretical computer science . They are intended to be as simple as possible, so that it would be easier to understand
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#17327869119721694-403: Is often used to specify the execution semantics of languages commonly used in practice. A significant amount of academic research goes into formal semantics of programming languages , which allows execution semantics to be specified in a formal manner. Results from this field of research have seen limited application to programming language design and implementation outside academia. A data type
1771-444: Is sometimes used interchangeably with "programming language". However, usage of these terms varies among authors. In one usage, programming languages are described as a subset of computer languages. Similarly, the term "computer language" may be used in contrast to the term "programming language" to describe languages used in computing but not considered programming languages – for example, markup languages . Some authors restrict
1848-474: Is stored. The simplest user-defined type is an ordinal type whose values can be mapped onto the set of positive integers. Since the mid-1980s, most programming languages also support abstract data types , in which the representation of the data and operations are hidden from the user , who can only access an interface . The benefits of data abstraction can include increased reliability, reduced complexity, less potential for name collision , and allowing
1925-429: Is the halting problem : create an algorithm that takes as input a program in some Turing-complete language and some data to be fed to that program, and determines whether the program, operating on the input, will eventually stop or will continue forever. It is trivial to create an algorithm that can do this for some inputs, but impossible to do this in general. For any characteristic of the program's eventual output, it
2002-442: Is the potential for errors to go undetected. Complete type inference has traditionally been associated with functional languages such as Haskell and ML . With dynamic typing, the type is not attached to the variable but only the value encoded in it. A single variable can be reused for a value of a different type. Although this provides more flexibility to the programmer, it is at the cost of lower reliability and less ability for
2079-416: Is the set of regular languages , which are generated by regular expressions and which are recognized by finite automata . A more powerful but still not Turing-complete extension of finite automata is the category of pushdown automata and context-free grammars , which are commonly used to generate parse trees in an initial stage of program compiling . Further examples include some of the early versions of
2156-402: Is used (in languages that require such declarations) or that the labels on the arms of a case statement are distinct. Many important restrictions of this type, like checking that identifiers are used in the appropriate context (e.g. not adding an integer to a function name), or that subroutine calls have the appropriate number and type of arguments, can be enforced by defining them as rules in
2233-481: Is usually defined using a combination of regular expressions (for lexical structure) and Backus–Naur form (for grammatical structure). Below is a simple grammar, based on Lisp : This grammar specifies the following: The following are examples of well-formed token sequences in this grammar: 12345 , () and (a b c232 (1)) . Not all syntactically correct programs are semantically correct. Many syntactically correct programs are nonetheless ill-formed, per
2310-557: The CPU that performs instructions on data is separate, and data must be piped back and forth to the CPU. The central elements in these languages are variables, assignment , and iteration , which is more efficient than recursion on these machines. Many programming languages have been designed from scratch, altered to meet new needs, and combined with other languages. Many have eventually fallen into disuse. The birth of programming languages in
2387-410: The hardware , over time they have developed more abstraction to hide implementation details for greater simplicity. Thousands of programming languages—often classified as imperative, functional , logic , or object-oriented —have been developed for a wide variety of uses. Many aspects of programming language design involve tradeoffs—for example, exception handling simplifies error handling, but at
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2464-416: The 1830s until the 1940s, mechanical calculating machines such as adders and multipliers were built and improved, but they could not perform a conditional branch and therefore were not Turing-complete. In the late 19th century, Leopold Kronecker formulated notions of computability, defining primitive recursive functions . These functions can be calculated by rote computation, but they are not enough to make
2541-455: The 1950s was stimulated by the desire to make a universal programming language suitable for all machines and uses, avoiding the need to write code for different computers. By the early 1960s, the idea of a universal language was rejected due to the differing requirements of the variety of purposes for which code was written. Desirable qualities of programming languages include readability, writability, and reliability. These features can reduce
2618-413: The abstraction of a universal computer is defined as a device with a Turing-complete instruction set, infinite memory, and infinite available time. In computability theory , several closely related terms are used to describe the computational power of a computational system (such as an abstract machine or programming language ): Turing completeness is significant in that every real-world design for
2695-487: The code is reached; this is called finalization. There is a tradeoff between increased ability to handle exceptions and reduced performance. For example, even though array index errors are common C does not check them for performance reasons. Although programmers can write code to catch user-defined exceptions, this can clutter a program. Standard libraries in some languages, such as C, use their return values to indicate an exception. Some languages and their compilers have
2772-402: The cost of increased storage space and more complexity. Other data types that may be supported include lists , associative (unordered) arrays accessed via keys, records in which data is mapped to names in an ordered structure, and tuples —similar to records but without names for data fields. Pointers store memory addresses, typically referencing locations on the heap where other data
2849-408: The cost of readability. Natural-language programming has been proposed as a way to eliminate the need for a specialized language for programming. However, this goal remains distant and its benefits are open to debate. Edsger W. Dijkstra took the position that the use of a formal language is essential to prevent the introduction of meaningless constructs. Alan Perlis was similarly dismissive of
2926-432: The cost of training programmers in a language, the amount of time needed to write and maintain programs in the language, the cost of compiling the code, and increase runtime performance. Programming language design often involves tradeoffs. For example, features to improve reliability typically come at the cost of performance. Increased expressivity due to a large number of operators makes writing code easier but comes at
3003-433: The details of the hardware, instead being designed to express algorithms that could be understood more easily by humans. For example, arithmetic expressions could now be written in symbolic notation and later translated into machine code that the hardware could execute. In 1957, Fortran (FORmula TRANslation) was invented. Often considered the first compiled high-level programming language, Fortran has remained in use into
3080-461: The first programming languages. The earliest computers were programmed in first-generation programming languages (1GLs), machine language (simple instructions that could be directly executed by the processor). This code was very difficult to debug and was not portable between different computer systems. In order to improve the ease of programming, assembly languages (or second-generation programming languages —2GLs) were invented, diverging from
3157-444: The idea. Turing completeness In computability theory , a system of data-manipulation rules (such as a model of computation , a computer's instruction set , a programming language , or a cellular automaton ) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing ). This means that this system
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3234-402: The invention of the microprocessor , computers in the 1970s became dramatically cheaper. New computers also allowed more user interaction, which was supported by newer programming languages. Lisp , implemented in 1958, was the first functional programming language. Unlike Fortran, it supported recursion and conditional expressions , and it also introduced dynamic memory management on
3311-429: The language's rules; and may (depending on the language specification and the soundness of the implementation) result in an error on translation or execution. In some cases, such programs may exhibit undefined behavior . Even when a program is well-defined within a language, it may still have a meaning that is not intended by the person who wrote it. Using natural language as an example, it may not be possible to assign
3388-417: The languages intended for execution. He also argues that textual and even graphical input formats that affect the behavior of a computer are programming languages, despite the fact they are commonly not Turing-complete, and remarks that ignorance of programming language concepts is the reason for many flaws in input formats. The first programmable computers were invented at the end of the 1940s, and with them,
3465-414: The limitation of finite memory is ignored, most programming languages are otherwise Turing-complete. In colloquial usage, the terms "Turing-complete" and "Turing-equivalent" are used to mean that any real-world general-purpose computer or computer language can approximately simulate the computational aspects of any other real-world general-purpose computer or computer language. In real life, this leads to
3542-811: The limits of computation. Here are a few: Most programming languages (their abstract models, maybe with some particular constructs that assume finite memory omitted), conventional and unconventional, are Turing-complete. This includes: Some rewrite systems are Turing-complete. Turing completeness is an abstract statement of ability, rather than a prescription of specific language features used to implement that ability. The features used to achieve Turing completeness can be quite different; Fortran systems would use loop constructs or possibly even goto statements to achieve repetition; Haskell and Prolog, lacking looping almost entirely, would use recursion . Most programming languages are describing computations on von Neumann architectures , which have memory (RAM and register) and
3619-511: The machine language to make programs easier to understand for humans, although they did not increase portability. Initially, hardware resources were scarce and expensive, while human resources were cheaper. Therefore, cumbersome languages that were time-consuming to use, but were closer to the hardware for higher efficiency were favored. The introduction of high-level programming languages ( third-generation programming languages —3GLs)—revolutionized programming. These languages abstracted away
3696-405: The machine may possess that have nothing to do with computation. Charles Babbage 's analytical engine (1830s) would have been the first Turing-complete machine if it had been built at the time it was designed. Babbage appreciated that the machine was capable of great feats of calculation, including primitive logical reasoning, but he did not appreciate that no other machine could do better. From
3773-400: The meaning of languages, as opposed to their form ( syntax ). Static semantics defines restrictions on the structure of valid texts that are hard or impossible to express in standard syntactic formalisms. For compiled languages, static semantics essentially include those semantic rules that can be checked at compile time. Examples include checking that every identifier is declared before it
3850-803: The more powerful the language is initially, the more complex are the tasks to which it is applied and the sooner its lack of completeness becomes perceived as a drawback, encouraging its extension until it is Turing-complete. The untyped lambda calculus is Turing-complete, but many typed lambda calculi, including System F , are not. The value of typed systems is based in their ability to represent most typical computer programs while detecting more errors. Rule 110 and Conway's Game of Life , both cellular automata , are Turing-complete. Some software and video games are Turing-complete by accident, i.e. not by design. Software: Games: Social media: Computational languages: Biology: Many computational languages exist that are not Turing-complete. One such example
3927-639: The new programming languages uses static typing while a few numbers of new languages use dynamic typing like Ring and Julia . Some of the new programming languages are classified as visual programming languages like Scratch , LabVIEW and PWCT . Also, some of these languages mix between textual and visual programming usage like Ballerina . Also, this trend lead to developing projects that help in developing new VPLs like Blockly by Google . Many game engines like Unreal and Unity added support for visual scripting too. Every programming language includes fundamental elements for describing data and
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#17327869119724004-764: The notion of computation is essentially unique. In 1941 Konrad Zuse completed the Z3 computer. Zuse was not familiar with Turing's work on computability at the time. In particular, the Z3 lacked dedicated facilities for a conditional jump, thereby precluding it from being Turing complete. However, in 1998, it was shown by Rojas that the Z3 is capable of simulating conditional jumps, and therefore Turing complete in theory. To do this, its tape program would have to be long enough to execute every possible path through both sides of every branch. The first computer capable of conditional branching in practice, and therefore Turing complete in practice,
4081-455: The operations or transformations applied to them, such as adding two numbers or selecting an item from a collection. These elements are governed by syntactic and semantic rules that define their structure and meaning, respectively. A programming language's surface form is known as its syntax . Most programming languages are purely textual; they use sequences of text including words, numbers, and punctuation, much like written natural languages. On
4158-436: The option of turning on and off error handling capability, either temporarily or permanently. One of the most important influences on programming language design has been computer architecture . Imperative languages , the most commonly used type, were designed to perform well on von Neumann architecture , the most common computer architecture. In von Neumann architecture, the memory stores both data and instructions, while
4235-436: The order of execution of key instructions via the use of semaphores , controlling access to shared data via monitor , or enabling message passing between threads. Many programming languages include exception handlers, a section of code triggered by runtime errors that can deal with them in two main ways: Some programming languages support dedicating a block of code to run regardless of whether an exception occurs before
4312-483: The other hand, some programming languages are graphical , using visual relationships between symbols to specify a program. The syntax of a language describes the possible combinations of symbols that form a syntactically correct program. The meaning given to a combination of symbols is handled by semantics (either formal or hard-coded in a reference implementation ). Since most languages are textual, this article discusses textual syntax. The programming language syntax
4389-442: The parsing phase. Languages that have constructs that allow the programmer to alter the behavior of the parser make syntax analysis an undecidable problem , and generally blur the distinction between parsing and execution. In contrast to Lisp's macro system and Perl's BEGIN blocks, which may contain general computations, C macros are merely string replacements and do not require code execution. The term semantics refers to
4466-516: The pixel shader languages embedded in Direct3D and OpenGL extensions. In total functional programming languages, such as Charity and Epigram , all functions are total and must terminate. Charity uses a type system and control constructs based on category theory , whereas Epigram uses dependent types . The LOOP language is designed so that it computes only the functions that are primitive recursive . All of these compute proper subsets of
4543-434: The power of flow-control instructions (for example, providing only loops that iterate over the items of an existing array). However, another theorem shows that there are problems solvable by Turing-complete languages that cannot be solved by any language with only finite looping abilities (i.e., languages that guarantee that every program will eventually finish to a halt). So any such language is not Turing-complete. For example,
4620-413: The practical concepts of computing virtualization and emulation . Real computers constructed so far can be functionally analyzed like a single-tape Turing machine (which uses a "tape" for memory); thus the associated mathematics can apply by abstracting their operation far enough. However, real computers have limited physical resources, so they are only linear bounded automaton complete. In contrast,
4697-585: The program would trigger an error on the undefined variable p during compilation. However, the program would still be syntactically correct since type declarations provide only semantic information. The grammar needed to specify a programming language can be classified by its position in the Chomsky hierarchy . The syntax of most programming languages can be specified using a Type-2 grammar, i.e., they are context-free grammars . Some languages, including Perl and Lisp, contain constructs that allow execution during
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#17327869119724774-489: The programmer specifies a desired result and allows the interpreter to decide how to achieve it. During the 1980s, the invention of the personal computer transformed the roles for which programming languages were used. New languages introduced in the 1980s included C++, a superset of C that can compile C programs but also supports classes and inheritance . Ada and other new languages introduced support for concurrency . The Japanese government invested heavily into
4851-417: The programmer. Storing an integer in a type that is too small to represent it leads to integer overflow . The most common way of representing negative numbers with signed types is twos complement , although ones complement is also used. Other common types include Boolean —which is either true or false—and character —traditionally one byte , sufficient to represent all ASCII characters. Arrays are
4928-420: The programming language to check for errors. Some languages allow variables of a union type to which any type of value can be assigned, in an exception to their usual static typing rules. In computing, multiple instructions can be executed simultaneously. Many programming languages support instruction-level and subprogram-level concurrency. By the twenty-first century, additional processing power on computers
5005-404: The semantics may define the strategy by which expressions are evaluated to values, or the manner in which control structures conditionally execute statements . The dynamic semantics (also known as execution semantics ) of a language defines how and when the various constructs of a language should produce a program behavior. There are many ways of defining execution semantics. Natural language
5082-686: The so-called fifth-generation languages that added support for concurrency to logic programming constructs, but these languages were outperformed by other concurrency-supporting languages. Due to the rapid growth of the Internet and the World Wide Web in the 1990s, new programming languages were introduced to support Web pages and networking . Java , based on C++ and designed for increased portability across systems and security, enjoyed large-scale success because these features are essential for many Internet applications. Another development
5159-525: The term "programming language" to Turing complete languages. Most practical programming languages are Turing complete, and as such are equivalent in what programs they can compute. Another usage regards programming languages as theoretical constructs for programming abstract machines and computer languages as the subset thereof that runs on physical computers, which have finite hardware resources. John C. Reynolds emphasizes that formal specification languages are just as much programming languages as are
5236-401: The twenty-first century. Around 1960, the first mainframes —general purpose computers—were developed, although they could only be operated by professionals and the cost was extreme. The data and instructions were input by punch cards , meaning that no input could be added while the program was running. The languages developed at this time therefore are designed for minimal interaction. After
5313-424: The twenty-first century. C allows access to lower-level machine operations more than other contemporary languages. Its power and efficiency, generated in part with flexible pointer operations, comes at the cost of making it more difficult to write correct code. Prolog , designed in 1972, was the first logic programming language, communicating with a computer using formal logic notation. With logic programming,
5390-475: The underlying data structure to be changed without the client needing to alter its code. In static typing , all expressions have their types determined before a program executes, typically at compile-time. Most widely used, statically typed programming languages require the types of variables to be specified explicitly. In some languages, types are implicit; one form of this is when the compiler can infer types based on context. The downside of implicit typing
5467-476: Was service-oriented programming , designed to exploit distributed systems whose components are connected by a network. Services are similar to objects in object-oriented programming, but run on a separate process. C# and F# cross-pollinated ideas between imperative and functional programming. After 2010, several new languages— Rust , Go , Swift , Zig and Carbon —competed for the performance-critical software for which C had historically been used. Most of
5544-407: Was increasingly coming from the use of additional processors, which requires programmers to design software that makes use of multiple processors simultaneously to achieve improved performance. Interpreted languages such as Python and Ruby do not support the concurrent use of multiple processors. Other programming languages do support managing data shared between different threads by controlling
5621-603: Was isolated soon after, starting with Gödel's incompleteness theorem . This theorem showed that axiom systems were limited when reasoning about the computation that deduces their theorems. Church and Turing independently demonstrated that Hilbert's Entscheidungsproblem (decision problem) was unsolvable, thus identifying the computational core of the incompleteness theorem. This work, along with Gödel's work on general recursive functions , established that there are sets of simple instructions, which, when put together, are able to produce any computation. The work of Gödel showed that
5698-550: Was limited, most popular imperative languages—including C , Pascal , Ada , C++ , Java , and C# —are directly or indirectly descended from ALGOL 60. Among its innovations adopted by later programming languages included greater portability and the first use of context-free , BNF grammar. Simula , the first language to support object-oriented programming (including subtypes , dynamic dispatch , and inheritance ), also descends from ALGOL and achieved commercial success. C, another ALGOL descendant, has sustained popularity into
5775-430: Was that of dynamically typed scripting languages — Python , JavaScript , PHP , and Ruby —designed to quickly produce small programs that coordinate existing applications . Due to their integration with HTML , they have also been used for building web pages hosted on servers . During the 2000s, there was a slowdown in the development of new programming languages that achieved widespread popularity. One innovation
5852-528: Was the ENIAC in 1946. Zuse's Z4 computer was operational in 1945, but it did not support conditional branching until 1950. Computability theory uses models of computation to analyze problems and determine whether they are computable and under what circumstances. The first result of computability theory is that there exist problems for which it is impossible to predict what a (Turing-complete) system will do over an arbitrarily long time. The classic example
5929-503: Was the most widespread compiled programming language used for commercial PRIMOS applications , outpacing the use of the Prime C compiler, the CPL (PRIMOS) scripting language, and the Fortran IV compiler in commercial applications. This programming-language -related article is a stub . You can help Misplaced Pages by expanding it . Programming language A programming language
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