Hall logic is a formal system with a set of logical rules for rigorous reasoning about the correctness of computer programs. It was proposed by British computer scientist and logician Tony Hall in 1969 and subsequently improved by Hall and other researchers.

What is a Hall triplet?

Hoare triples contain three parts, A precondition P, a program statement or sequence of statements S and a postcondition Q. It is usually written in the table. {P} S {Q} means « if P is true before the execution of S, then Q is true after that if the execution of S terminates ».

What is Hall Logic for?

The goal of Hall logic is to Provides a formal system for reasoning about program correctness. Hoare logic is based on the idea of ​​viewing a specification as a contract between a function implementation and its client. A specification consists of preconditions and postconditions.

What is Hall?

Hall is English surname from Middle English hor(e) meaning grey or white hairNotable persons with this surname include: Albert Alfred Hoare, known as Bert Hoare (1874-1962), a South Australian politician. Des Hoare (born 1934), Australian cricketer. …John Gurney Hoare (1810–1875), English cricketer and…

Is Hall logic complete?

The answer is yes, which shows that Hall logic is plausible. Robustness is important because it says that Hoare logic doesn’t allow us to derive partial correctness assertions that don’t actually hold. The proof of reliability requires induction on the derivation in ⊢ {P} c {Q} (we omit this proof).

Let’s #TalkConcurrency with Sir Tony Hall

16 related questions found

How do you find the weakest precondition?

The weakest precondition P is simple Q replaces all free-occurring x’s with e. For example, to find wp(x=y+1, x > 0), we replace x with y+1 in the postcondition x > 0, resulting in the weakest precondition y+1 > 0.

How to find the strongest postcondition?

Specifically, we can write a stronger postcondition that implies x > 0. For example, x > 5 ∧ x < 20 更强，因为它提供更多信息； 它比 x > 0 determines the value of x more precisely.The strongest possible postcondition is x = 10; This is the most useful postcondition.

Is Hall a word?

Hall is last name.

What are the components of the Hall symbol?

Hall symbol usage Formal logic symbols to express conditions for the values ​​of program variables. This symbol is described informally and illustrated by an example. In order to prove the correctness of a program mathematically, it must first be specified what it means correctly.

What are the core features of Hall logic?

Hall Logic provides Axioms and inference rules for all constructs of simple imperative programming languagesIn addition to the simple language rules in Hoare’s original paper, Hoare and many other researchers have since developed rules for other language structures.

What are the formulas and semantics of Hall logic?

The rules of Hoare logic are (almost) syntax-oriented and automate all aspects of proofs related to program execution. …the formula for Hall logic is Hoare triplet {P} c {Q}, where P is called the precondition and Q is called the postcondition.

What are assertions in axiomatic semantics?

Axiomatic Semantic Definition Understand the meaning of commands in a program by describing their effect on assertions about the state of the program. Assertions are logical statements – predicates with variables that define the state of the program.

What does hoar mean in slang?

The word hoar comes from the Old English word har, which means venerable or ancient. A prostitute is a prostitute or a person who has had multiple indiscriminate sexual encounters. A prostitute usually refers to a woman. A prostitute is also used as a metaphor for someone who is willing to do anything in order to get what he or she wants.

What does hoarfrost mean in english?

hoarfrost in British English

(ˈhɔːˌfrɒst) noun. Deposits of needle-like ice crystals that form directly on the ground at sub-freezing temperatures. Also known as: Hoarfrost.

Is Hall a Scrabble?

Yeshoar is in the Scrabble dictionary.

What does the weakest premise mean?

The weakest premise of S on R, usually written as wp(S,R) is the predicate that characterizes the set of states. The use of the adjective weakest makes it clear that the predicate must characterize all states that are guaranteed to terminate in a state where R is true.

What are loop invariants and how to use loop invariants?

In computer science, loop invariants are Properties of program loops that are true before (and after) each iteration..the loop invariant will be true upon entering the loop and after each iteration, so when exiting the loop, both the loop invariant and the loop termination condition are guaranteed.

What are preconditions and postconditions?

A premise is that Predicates that should hold when entering a function. It expresses the function’s expectations for its arguments and/or the object state that the function may use. A postcondition is a predicate that should persist when the function is exited.

For any statement s, what is the truth value of WP?

in simple language. Validation conditions for a given program S – recall that it is a formula that is valid if and only if S has no errors – hence the formula wp(S, true).

Why is it called hoarfrost?

Hoarfrost From the Old English word « hoary », meaning to be oldWith this in mind, many trees, especially evergreens, do exhibit a « hairy » appearance that resembles a white feathery beard.

What is the difference between denotative semantics and axiomatic semantics?

Actionable: Related to the activities involved in doing or producing something. denotational: The main meaning of a word.Axiomatic: Obviously true, so no need proved.

How does axiomatic semantics verify the correctness of a program?

Axiomatic Semantics of Programming Languages

When proving the correctness of the program, we use Applied predicate (first-order) logic with equality whose individual variables correspond to program variables and whose function symbols include all operations that occur in program expressions.

What is an operating language?

The operational semantics are A category of formal programming language semantics Certain desired properties of a program, such as correctness, safety, or security, are verified by constructing proofs from logical statements about its execution and process, not by attaching mathematical meaning to its…

What do the preconditions and postconditions of a given statement mean in axiomatic semantics?

Precondition Statement Indicates that must be true before calling the function. A postconditional statement indicates what happens when the function completes its work.

What is a postcondition loop?

The second form of conditional looping is called a postconditional loop.This The repeated form will check the condition after the command is executedif the condition is not met, start another execution of the loop.