# Write a denotational semantics mapping function for the following statements ada for This is the claim we are making about the statement, but we don't yet know that it's actually true. The loop terminates. Axiomatic Semantics Based on formal logic predicate calculus Informal program verification How do you know you made all the right tests? Can we prove that this is really what the program does? For a given program or just a sequence of statementsconstruct a set of logic expressions, describing the state of the program values of variables, etc. For each statement type in the language, define a set of axioms or inference rules that describe the statement's behavior.

This is program-independent.

### Compute the weakest precondition for each of the following assignment statements and postconditions:

That seems really obvious, but we still need to make it more definite, which is where the axioms and inference rules come in. The loop terminates. This works in two directions. The denotational semantics of a language defines the meanings of You don't need to do both, of course. The second method is the one to use when trying to prove something about a program. What can you conclude to be true after the statement is executed? The logic expressions are assertions. If the precondition on the first statement is the same as the program specification, the program is correct. If "whatever is above the line" the antecedent is true, then "whatever is below the line" the consequent is true. Java Boolean expressions d. For a given program or just a sequence of statements , construct a set of logic expressions, describing the state of the program values of variables, etc.

You don't need to do both, of course. C switch If so, then you can prove that the desired claim is true. Java Boolean expressions d. An assertion before a statement is a precondition.

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