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.
The progressive just-in-time preparation of the product backlog (requirements list) in agile software development approaches, such as Scrum, is also commonly described as refinement.
Data refinement is used to convert an abstract data model (in terms of sets for example) into implementable data structures (such as arrays). Operation refinement converts a specification of an operation on a system into an implementable program (e.g., a procedure). The postcondition can be strengthened and/or the precondition weakened in this process. This reduces any nondeterminism in the specification, typically to a completely deterministic implementation.
For example, x ∈ {1,2,3} (where x is the value of the variable x after an operation) could be refined to x ∈ {1,2}, then x ∈ {1}, and implemented as x := 1. Implementations of x := 2 and x := 3 would be equally acceptable in this case, using a different route for the refinement. However, we must be careful not to refine to x ∈ {} (equivalent to false) since this is unimplementable; it is impossible to select a member from the empty set.
The term reification is also sometimes used (coined by Cliff Jones). Retrenchment is an alternative technique when formal refinement is not possible. The opposite of refinement is abstraction.
Refinement calculus is a formal system (inspired from Hoare logic) that promotes program refinement. The FermaT Transformation System is an industrial-strength implementation of refinement.
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In computer science, formal specifications are mathematically based techniques whose purpose are to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning tools. These specifications are formal in the sense that they have a syntax, their semantics fall within one domain, and they are able to be used to infer useful information.
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We introduce formal verification as an approach for developing highly reliable systems. Formal verification finds proofs that computer systems work under all relevant scenarios. We will learn how to u
We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...
Covers the basics of writing and verifying Scala code using the Demo.scala file.
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EPFL2015
Statically typed languages verify programs at compile-time. As a result many programming mistakes are detected at an early stage of development. A programmer does not have to specify types for every single term manually, however. Many programming languages ...