Sage-Tips

What is Hoare logic used for?

Proof Rules. The goal of Hoare logic is to provide a compositional method for proving the validity of specific Hoare triples. That is, we want the structure of a program’s correctness proof to mirror the structure of the program itself.

Is Hoare triple valid?

If there is a complete proof system for proving assertions in the underlying logic, then all valid Hoare triples have a proof.

What makes a Hoare triple valid?

Hoare Triples, Informally If command c begins execution in a state satisfying assertion P, and if c eventually terminates in some final state, then that final state will satisfy the assertion Q.

What is formal Hoare logic method?

Hoare Logic is a formalism for reasoning about the behaviour of programs by relating their initial and terminal state. It uses an assertion logic based on first-order logic to reason about program states and extends this with Hoare triples to reason about the programs.

What is the central feature of Hoare logic?

Hoare logic provides axioms and inference rules for all the constructs of a simple imperative programming language. In addition to the rules for the simple language in Hoare’s original paper, rules for other language constructs have been developed since then by Hoare and many other researchers.

What is Hoare?

Hoare is an English surname derived from Middle English hor(e) meaning grey- or white-haired.

What is the formula and semantic of Hoare logic?

The rules of Hoare logic are (almost) syntax-directed and automate all those aspects of the proof that are concerned with program execution. The formulas of Hoare logic are the Hoare triples {P} c {Q}, where P is called the precondition and Q the postcondition.

What are the features of Hoare logic?

The central feature of Hoare logic is the Hoare triple. A triple describes how the execution of a piece of code changes the state of the computation. A Hoare triple is of the form

What is the Hoare triple?

Hoare triple. The central feature of Hoare logic is the Hoare triple. A triple describes how the execution of a piece of code changes the state of the computation.

What is the intuitive reading of a Hoare triple?

There are rules for concurrency, procedures, jumps, and pointers . Using standard Hoare logic, only partial correctness can be proven, while termination needs to be proved separately. Thus the intuitive reading of a Hoare triple is: Whenever does not terminate. In the latter case, there is no “after”, so can be any statement at all.

What is the Hoare rule for assignment?

The rule for assignment is the most fundamental of the Hoare logic proof rules. Here’s how it works. Consider this (valid) Hoare triple: In English: if we start out in a state where the value of Y is 1 and we assign Y to X, then we’ll finish in a state where X is 1.