Recursive data typeIn computer programming languages, a recursive data type (also known as a recursively-defined, inductively-defined or inductive data type) is a data type for values that may contain other values of the same type. Data of recursive types are usually viewed as directed graphs. An important application of recursion in computer science is in defining dynamic data structures such as Lists and Trees. Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; in contrast, a static array's size requirements must be set at compile time.
Proof assistantIn 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. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
EveEve (ˈiːv; ; Ḥawwāʾ; Heúa; Eva, Heva; Syriac: ܚܰܘܳܐ romanized: ) is a figure in the Book of Genesis in the Hebrew Bible. According to the origin story of the Abrahamic religions, she was the first woman, yet some debate within Judaism has also given that position to Lilith. Eve is known also as Adam's wife. According to the second chapter of Genesis, Eve was created by God (Yahweh) by taking her from the rib of Adam, to be Adam's companion.
Generalized algebraic data typeIn functional programming, a generalized algebraic data type (GADT, also first-class phantom type, guarded recursive datatype, or equality-qualified type) is a generalization of parametric algebraic data types. In a GADT, the product constructors (called data constructors in Haskell) can provide an explicit instantiation of the ADT as the type instantiation of their return value. This allows defining functions with a more advanced type behaviour.
Data typeIn computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data.
Adam and EveAdam and Eve, according to the creation myth of the Abrahamic religions, were the first man and woman. They are central to the belief that humanity is in essence a single family, with everyone descended from a single pair of original ancestors. They also provide the basis for the doctrines of the fall of man and original sin that are important beliefs in Christianity, although not held in Judaism or Islam. In the Book of Genesis of the Hebrew Bible, chapters one through five, there are two creation narratives with two distinct perspectives.
Automated theorem provingAutomated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics.
Primitive data typeIn computer science, primitive data types are a set of basic data types from which all other data types are constructed. Specifically it often refers to the limited set of data representations in use by a particular processor, which all compiled programs must use. Most processors support a similar set of primitive data types, although the specific representations vary. More generally, "primitive data types" may refer to the standard data types built into a programming language (built-in types).
Isabelle (proof assistant)The Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As an LCF-style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring yet supporting explicit proof objects. Isabelle is available inside a flexible system framework allowing for logically safe extensions, which comprise both theories as well as implementations for code-generation, documentation, and specific support for a variety of formal methods.
Algebraic data typeIn computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types. Two common classes of algebraic types are product types (i.e., tuples and records) and sum types (i.e., tagged or disjoint unions, coproduct types or variant types). The values of a product type typically contain several values, called fields. All values of that type have the same combination of field types.
R (programming language)R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. The core R language is augmented by a large number of extension packages containing reusable code and documentation. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages in data mining.
EvalIn some programming languages, eval , short for the English evaluate, is a function which evaluates a string as though it were an expression in the language, and returns a result; in others, it executes multiple lines of code as though they had been included instead of the line including the eval. The input to eval is not necessarily a string; it may be structured representation of code, such as an abstract syntax tree (like Lisp forms), or of special type such as code (as in Python).
Read–eval–print loopA read–eval–print loop (REPL), also termed an interactive toplevel or language shell, is a simple interactive computer programming environment that takes single user inputs, executes them, and returns the result to the user; a program written in a REPL environment is executed piecewise. The term usually refers to programming interfaces similar to the classic Lisp machine interactive environment. Common examples include command-line shells and similar environments for programming languages, and the technique is very characteristic of scripting languages.
Operational semanticsOperational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its terms (denotational semantics).
Proof theoryProof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
Array (data type)In computer science, array is a data type that represents a collection of elements (values or variables), each selected by one or more indices (identifying keys) that can be computed at run time during program execution. Such a collection is usually called an array variable or array value. By analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively. More generally, a multidimensional array type can be called a tensor type, by analogy with the physical concept, tensor.
Python (programming language)Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library.
Composite data typeIn computer science, a composite data type or compound data type is any data type which can be constructed in a program using the programming language's primitive data types and other composite types. It is sometimes called a structure or aggregate type, although the latter term may also refer to arrays, lists, etc. The act of constructing a composite type is known as composition. Composite data types are often contrasted with scalar variables. A struct is C's and C++'s notion of a composite type, a datatype that composes a fixed set of labeled fields or members.
Denotational semanticsIn computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called denotations) that describe the meanings of expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics and operational semantics. Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do.
Boolean data typeIn computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the two truth values of logic and Boolean algebra. 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 statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false.
