PostconditionIn computer programming, a postcondition is a condition or predicate that must always be true just after the execution of some section of code or after an operation in a formal specification. Postconditions are sometimes tested using assertions within the code itself. Often, postconditions are simply included in the documentation of the affected section of code. For example: The result of a factorial is always an integer and greater than or equal to 1.
Design by contractDesign by contract (DbC), also known as contract programming, programming by contract and design-by-contract programming, is an approach for designing software. It prescribes that software designers should define formal, precise and verifiable interface specifications for software components, which extend the ordinary definition of abstract data types with preconditions, postconditions and invariants. These specifications are referred to as "contracts", in accordance with a conceptual metaphor with the conditions and obligations of business contracts.
Hoare logicHoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare, and subsequently refined by Hoare and other researchers. The original ideas were seeded by the work of Robert W. Floyd, who had published a similar system for flowcharts. The central feature of Hoare logic is the Hoare triple.
Scala (programming language)Scala (ˈskɑːlə ) is a strong statically typed high-level general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are aimed to address criticisms of Java. Scala source code can be compiled to Java bytecode and run on a Java virtual machine (JVM). Scala can also be compiled to JavaScript to run in a browser, or directly to a native executable.
Refinement (computing)Refinement is a generic term of computer science that encompasses various approaches for producing correct computer programs and simplifying existing programs to enable their formal verification. In formal methods, program refinement is the verifiable transformation of an abstract (high-level) formal specification into a concrete (low-level) executable program. Stepwise refinement allows this process to be done in stages. Logically, refinement normally involves implication, but there can be additional complications.
Liskov substitution principleThe Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced by Barbara Liskov in a 1987 conference keynote address titled Data abstraction and hierarchy. It is based on the concept of "substitutability" a principle in object-oriented programming stating that an object (such as a class) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program.
Formal verificationIn the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code.
Commutative ringIn mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings. A ring is a set equipped with two binary operations, i.e. operations combining any two elements of the ring to a third.
ArithmeticArithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.
Commutative algebraCommutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings; rings of algebraic integers, including the ordinary integers ; and p-adic integers. Commutative algebra is the main technical tool in the local study of schemes.
Commutative propertyIn mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, "3 − 5 ≠ 5 − 3"); such operations are not commutative, and so are referred to as noncommutative operations.
Elementary arithmeticElementary arithmetic is a branch of mathematics involving basic numerical operations, namely addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and being the foundation of all mathematics, elementary arithmetic is generally the first critical branch of mathematics to be taught in schools. Numerical digit Symbols called digits are used to represent the value of numbers in a numeral system. The most commonly used digits are the Arabic numerals (0 to 9).
Modular arithmeticIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.
PreconditionIn computer programming, a precondition is a condition or predicate that must always be true just prior to the execution of some section of code or before an operation in a formal specification. If a precondition is violated, the effect of the section of code becomes undefined and thus may or may not carry out its intended work. Security problems can arise due to incorrect preconditions. Often, preconditions are simply included in the documentation of the affected section of code.
Predicate transformer semanticsPredicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs". They define the semantics of an imperative programming paradigm by assigning to each statement in this language a corresponding predicate transformer: a total function between two predicates on the state space of the statement. In this sense, predicate transformer semantics are a kind of denotational semantics.
Open sourceOpen source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized software development model that encourages open collaboration. A main principle of open-source software development is peer production, with products such as source code, blueprints, and documentation freely available to the public.
Current sourceA current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term current sink is sometimes used for sources fed from a negative voltage supply. Figure 1 shows the schematic symbol for an ideal current source driving a resistive load. There are two types. An independent current source (or sink) delivers a constant current. A dependent current source delivers a current which is proportional to some other voltage or current in the circuit.
Source-to-source compilerA source-to-source translator, source-to-source compiler (S2S compiler), transcompiler, or transpiler is a type of translator that takes the source code of a program written in a programming language as its input and produces an equivalent source code in the same or a different programming language. A source-to-source translator converts between programming languages that operate at approximately the same level of abstraction, while a traditional compiler translates from a higher level programming language to a lower level programming language.
Source codeIn computing, source code, or simply code, is any collection of text, with or without comments, written using a human-readable programming language, usually as plain text. The source code of a program is specially designed to facilitate the work of computer programmers, who specify the actions to be performed by a computer mostly by writing source code. The source code is often transformed by an assembler or compiler into binary machine code that can be executed by the computer.
Cache (computing)In computing, a cache (kæʃ ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A cache hit occurs when the requested data can be found in a cache, while a cache miss occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs.
