Software is a collection of instructions and data that tell the computer how to work. This is in contrast to physical hardware, from which the system is built and actually performs the work. In computer science and software engineering, computer software is all information processed by computer systems, including programs and data. Computer software includes computer programs, libraries and related non-executable data, such as online documentation or digital media. Computer hardware and software require each other and neither can be realistically used on its own.
Database normalization is the process of structuring a relational database in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by Edgar F. Codd as part of his relational model.
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that each return a value, rather than a sequence of imperative statements which change the state of the program.
ML is a general-purpose functional programming language. ML is statically-scoped. It is known for its use of the polymorphic Hindley–Milner type system, which automatically assigns the types of most expressions without requiring explicit type annotations, and ensures type safety – there is a formal proof that a well-typed ML program does not cause runtime type errors. ML provides pattern matching for function arguments, garbage collection, imperative programming, call-by-value and currying. It is used heavily in programming language research and is one of the few languages to be completely specified and verified using formal semantics. Its types and pattern matching make it well-suited and commonly used to operate on other formal languages, such as in compiler writing, automated theorem proving, and formal verification.
A prototype is an early sample, model, or release of a product built to test a concept or process. It is a term used in a variety of contexts, including semantics, design, electronics, and software programming. A prototype is generally used to evaluate a new design to enhance precision by system analysts and users. Prototyping serves to provide specifications for a real, working system rather than a theoretical one. In some design workflow models, creating a prototype is the step between the formalization and the evaluation of an idea.
In computer science, specifically software engineering and hardware engineering, formal methods are a particular kind of mathematically rigorous techniques for the specification, development and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical proofs.
In theoretical computer science, correctness of an algorithm is asserted when it is said that the algorithm is correct with respect to a specification. Functional correctness refers to the input-output behavior of the algorithm.
A typed lambda calculus is a typed formalism that uses the lambda-symbol to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered. From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.
Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.
Coq is an interactive theorem prover first released in 1989. It allows for the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification. Coq works within the theory of the calculus of inductive constructions, a derivative of the calculus of constructions. Coq is not an automated theorem prover but includes automatic theorem proving tactics (procedures) and various decision procedures.
Proof of concept (POC), also known as proof of principle, is a realization of a certain method or idea in order to demonstrate its feasibility, or a demonstration in principle with the aim of verifying that some concept or theory has practical potential. A proof of concept is usually small and may or may not be complete.
Software prototyping is the activity of creating prototypes of software applications, i.e., incomplete versions of the software program being developed. It is an activity that can occur in software development and is comparable to prototyping as known from other fields, such as mechanical engineering or manufacturing.
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
In mathematical logic and theoretical computer science, a rewrite system has the (strong) normalization property or is terminating if every term is strongly normalizing; that is, if every sequence of rewrites eventually terminates with an irreducible term, also called a normal form. A rewrite system may also have the weak normalization property, meaning that for every term, there exists at least one particular sequence of rewrites that eventually yields a normal form, i.e., an irreducible term.
Agda is a dependently typed functional programming language originally developed by Ulf Norell at Chalmers University of Technology with implementation described in his PhD thesis. The original Agda system was developed at Chalmers by Catarina Coquand in 1999. The current version, originally known as Agda 2, is a full rewrite, which should be considered a new language that shares a name and tradition.
Total functional programming is a programming paradigm that restricts the range of programs to those that are provably terminating.
In programming language semantics, normalisation by evaluation (NBE) is a style of obtaining the normal form of terms in the λ calculus by appealing to their denotational semantics. A term is first interpreted into a denotational model of the λ-term structure, and then a canonical representative is extracted by reifying the denotation. Such an essentially semantic approach differs from the more traditional syntactic description of normalisation as a reductions in a term rewrite system where β-reductions are allowed deep inside λ-terms.
F* is a functional programming language inspired by ML and aimed at program verification. Its type system includes dependent types, monadic effects, and refinement types. This allows expressing precise specifications for programs, including functional correctness and security properties. The F* type-checker aims to prove that programs meet their specifications using a combination of SMT solving and manual proofs. Programs written in F* can be translated to OCaml, F#, and C for execution. Previous versions of F* could also be translated to JavaScript.