Concepts inProgram verification through characteristic formulae
Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics . Complete formal verification is the only known way to guarantee that a system is free of programming errors. ¿ ¿ From abstract of paper presented to ACM symposium
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Caml
Caml (originally an acronym for Categorical Abstract Machine Language) is a dialect of the ML programming language family, developed at INRIA and formerly at ENS. Like many descendants of ML, Caml is statically typed, strictly evaluated, and uses automatic memory management. The first Caml implementation in Lisp was nicknamed "Heavy CAML" because of its memory and CPU requirements relative to its successor Caml Light that was implemented in C by Xavier Leroy and Damien Doligez.
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In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a 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.
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Coq
In computer science, Coq is an interactive theorem prover. It allows 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.
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Well-formed formula
In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word which is part of a formal language. A formal language can be considered to be identical to the set containing all and only its formulas. A formula is a syntactic formal object that can be informally given a semantic meaning.
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Validity
In logic, an argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form (or schema) is valid if and only if every argument of that logical form is valid.
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Logic
Logic (from the Greek ¿¿¿¿¿¿ logik¿) is the philosophical study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, ontology, epistemology, and ethics.
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