A theoretical basis for stepwise refinement and the programming calculus
Science of Computer Programming
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A calculus of refinements for program derivations
Acta Informatica
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Programming in Martin-Lo¨f's type theory: an introduction
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Computation and reasoning: a type theory for computer science
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Functional Procedures in Higher-Order Logic
Functional Procedures in Higher-Order Logic
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Modelling general recursion in type theory
Mathematical Structures in Computer Science
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This paper describes a formalization of the weakest precondition, wp, for general recursive programs using the type-theoretical proof assistant Coq. The formalization is a deep embedding using the computational power intrinsic to type theory. Since Coq accepts only structural recursive functions, the computational embedding of general recursive programs is non-trivial. To justify the embedding, an operational semantics is defined and the equivalence between wp and the operational semantics is proved. Three major healthiness conditions, namely: Strictness, Monotonicity and Conjunctivity are proved as well.