Formalization of Properties of Functional Programs
Journal of the ACM (JACM)
Decidable Properties of Monadic Functional Schemas
Journal of the ACM (JACM)
Fixpoint approach to the theory of computation
Communications of the ACM
Inductive methods for proving properties of programs
Communications of the ACM
An axiomatic basis for computer programming
Communications of the ACM
The Mathematical Theory of Context-Free Languages
The Mathematical Theory of Context-Free Languages
Journal of Computer and System Sciences
25 Years of Model Checking
Generalised quantum weakest preconditions
Quantum Information Processing
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Manna's theorem on (partial) correctness of programs essentially states that in the statement of the Floyd inductive assertion method, ''A flow diagram is correct with respect to given initial and final assertions if suitable intermediate assertions can be found'', we may replace ''if'' by ''if and only if''. In other words, the method is complete. A precise formulation and proof for the flow chart case is given. The theorem is then extended to programs with (parameterless) recursion; for this the structure of the intermediate assertions has to be refined considerably. The result is used to provide a characterization of recursion which is an alternative to the minimal fixed point characterization, and to clarify the relationship between partial and total correctness. Important tools are the relational representation of programs, and Scott's induction.