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Scaling Language Features for Program Verification

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System programming language

A system programming language is a programming language used for system programming; such languages are designed for writing system software, which usually requires different development approaches when compared with application software. Edsger Dijkstra refers to these languages as machine oriented high order languages, or mohol. General-purpose programming languages tend to focus on generic features to allow programs written in the language to use the same code on different platforms.

Programming paradigm

Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, such as allowing side effects, or whether the sequence of operations is defined by the execution model. Other paradigms are concerned mainly with the way that code is organized, such as grouping a code into units along with the state that is modified by the code.

Map (higher-order function)

In many programming languages, map is the name of a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning the results in a collection of the same type. It is often called apply-to-all when considered in functional form. The concept of a map is not limited to lists: it works for sequential containers, tree-like containers, or even abstract containers such as futures and promises. Suppose we have a list of integers [1, 2, 3, 4, 5] and would like to calculate the square of each integer.

Pure function

In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable reference arguments or input streams), and the function has no side effects (no mutation of local static variables, non-local variables, mutable reference arguments or input/output streams). Some authors, particularly from the imperative language community, use the term "pure" for all functions that just have the above property 2 (discussed below).

Higher-order logic

In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic.

Passive data structure

In computer science and object-oriented programming, a passive data structure (PDS), also termed a plain old data structure or plain old data (POD), is a record, in contrast with objects. It is a data structure that is represented only as passive collections of field values (instance variables), without using object-oriented features. Passive data structures are appropriate when there is a part of a system where it should be clearly indicated that the detailed logic for data manipulation and integrity are elsewhere.

Matita

Matita is an experimental proof assistant under development at the Computer Science Department of the University of Bologna. It is a tool aiding the development of formal proofs by man-machine collaboration, providing a programming environment where formal specifications, executable algorithms and automatically verifiable correctness certificates naturally coexist. Matita is based on a dependent type system known as the Calculus of (Co)Inductive Constructions (a derivative of Calculus of Constructions), and is compatible, to some extent, with Coq.

Lua (programming language)

Lua (ˈluːə ; from lua ˈlu(w)ɐ meaning moon) is a lightweight, high-level, multi-paradigm programming language designed primarily for embedded use in applications. Lua is cross-platform, since the interpreter of compiled bytecode is written in ANSI C, and Lua has a relatively simple C API to embed it into applications. Lua originated in 1993 as a language for extending software applications to meet the increasing demand for customization at the time.

Idris (programming language)

Idris is a purely-functional programming language with dependent types, optional lazy evaluation, and features such as a totality checker. Idris may be used as a proof assistant, but is designed to be a general-purpose programming language similar to Haskell. The Idris type system is similar to Agda's, and proofs are similar to Coq's, including tactics (theorem proving functions/procedures) via elaborator reflection. Compared to Agda and Coq, Idris prioritizes management of side effects and support for embedded domain-specific languages.

Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be identified with the set of formulas in the language. A formula is a syntactic object that can be given a semantic meaning by means of an interpretation. Two key uses of formulas are in propositional logic and predicate logic.