Concepts inOperational semantics using the partiality monad
Monad (functional programming)
In functional programming, a monad is a programming structure that represents computations. Monads are a kind of abstract data type constructor that encapsulate program logic instead of data in the domain model. A defined monad allows the programmer to chain actions together and build different pipelines that process data in various steps, in which each action is decorated with additional processing rules provided by the monad.
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Operational semantics
In computer science, operational semantics is a way to give meaning to computer programs in a mathematically rigorous way. Operational semantics are classified into two categories: structural operational semantics (or small-step semantics) formally describe how the individual steps of a computation take place in a computer-based system. By opposition natural semantics (or big-step semantics) describe how the overall results of the executions are obtained.
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Dependent type
In computer science and logic, a dependent type is a type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS, Agda and Epigram. An example is the type of n-tuples of real numbers. This is a dependent type because the type depends on the value n. Deciding equality of dependent types in a program may require computations.
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Type safety
In computer science, type safety is the extent to which a programming language discourages or prevents type errors. A type error is erroneous or undesirable program behaviour caused by a discrepancy between differing data types.
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Agda (programming language)
Agda is a proof assistant, i.e. a computer program that can check mathematical proofs. More specifically, it is an interactive system for developing constructive proofs based on the Curry-Howard correspondence in a variant of Per Martin-Löf's Type Theory. It can also be seen as a functional programming language with dependent types. Agda was developed by Ulf Norell, a postdoctoral researcher at Chalmers University of Technology.
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In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state. Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate function definition, function application, and recursion.
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Coinduction
In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects. Coinduction is the mathematical dual to structural induction. Coinductively defined types are known as codata and are typically infinite data structures, such as streams. As a definition or specification, coinduction describes how an object may be "observed", "broken down" or "destructed" into simpler objects.
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