# What is hoare triple?

Last Update: April 20, 2022

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**Asked by: Hildegard Kub**

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

## What are Hoare triples?

A Hoare triple has three parts, **a precondition P, a program statement or series of statements S, and a postcondition Q**. It's usually written in the form. {P} S {Q} The meaning is "if P is true before S is executed, and if the execution of S terminates, then Q is true afterwards".

## What is Hoare logic used for?

The goal of Hoare logic is to **provide a formal system for reasoning about program correctness**. Hoare logic is based on the idea of a specification as a contract between the implementation of a function and its clients. The specification is made up of a precondition and a postcondition.

## What is Hoare?

Hoare is **an English surname derived from Middle English hor(e) meaning grey- or white-haired**. Notable people with the surname include: Albert Alfred Hoare, known as Bert Hoare (1874–1962), South Australian politician. Des Hoare (born 1934), Australian cricketer. ... John Gurney Hoare (1810–1875), English cricketer and ...

## Is Hoare logic complete?

The answer is yes, and it shows that **Hoare logic is sound**. Soundness is important because it says that Hoare logic doesn't allow us to derive partial correctness assertions that actually don't hold. The proof of soundness requires induction on the derivations in ⊢ {P} c {Q} (we omit this proof).

## Let's #TalkConcurrency with Sir Tony Hoare

**16 related questions found**

### How do you find the weakest precondition?

The weakest precondition P is simply **Q with all free occurrences of x replaced by e**. For example, to find wp(x=y+1, x > 0) we replace x with y+1 in the postcondition x > 0, obtaining the weakest precondition y+1 > 0.

### How do I find the strongest post condition?

Specifically, we could write a stronger postcondition, i.e. one that implies x > 0. For example, x > 5 ∧ x < 20 is stronger because it is more informative; it pins down the value of x more precisely than x > 0. The strongest postcondition possible is **x = 10**; this is the most useful postcondition.

### Is Hoare a word?

Hoare is **a surname**.

### What are components of Hoare notation?

Hoare's notation uses **formal logic notation to express conditions on the values of program variables**. This notation is described informally and illustrated with examples. In order to prove the correctness of a program mathematically one must first specify what it means for it to be correct.

### 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 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 is an assertion in axiomatic semantics?

Axiomatic semantics define **the meaning of a command in a program by describing its effect on assertions about the program state**. The assertions are logical statements—predicates with variables, where the variables define the state of the program.

### What does Hoar mean in slang?

The word hoar is derived from the Old English word har which means **venerable or old**. A whore is a prostitute or someone who has had many, indiscriminate sexual encounters. Whore usually refers to a woman. Whore is also used figuratively to mean someone who will do anything to get what he or she wants.

### What does hoarfrost mean in English?

hoarfrost in British English

(ˈhɔːˌfrɒst ) noun. a deposit of needle-like ice crystals formed on the ground by direct condensation at temperatures below freezing point. Also called: **white frost**.

### Is Hoare a Scrabble word?

**Yes**, hoar is in the scrabble dictionary.

### What is the meaning of weakest precondition?

The weakest precondition of S with respect to R, normally written wp (S,R) is **a predicate that characterizes this set of states**. Use of the adjective weakest explicitly indicates that the predicate must characterize all states that guarantee termination of S in a state for which R is true.

### What is a loop invariant how is a loop invariants used?

In computer science, a loop invariant is a **property of a program loop that is true before (and after) each iteration**. ... The loop invariants will be true on entry into a loop and following each iteration, so that on exit from the loop both the loop invariants and the loop termination condition can be guaranteed.

### What is precondition and postcondition?

A precondition is **a predicate that should hold upon entry into a function**. It expresses a function's expectation on its arguments and/or the state of objects that may be used by the function. A postcondition is a predicate that should hold upon exit from a function.

### What is WP's true for any statement s?

in the simple language. **The verification condition for a given program** S —which, recall, is a formula that is valid if and only if S is free of errors—is therefore the formula wp(S, true) .

### Why is it called hoarfrost?

Hoar frost derives **from the old English word “hoary,” meaning getting on in age**. With this thought in mind, many trees, especially evergreens did present a "hair-like" appearance resembling white, feathery beards.

### What is the difference between denotational and axiomatic semantics?

operational: related to the activities involved in doing or producing something. denotational: the main meaning of a word. axiomatic: obviously true and therefore not needing to **be proved**.

### How does axiomatic semantics verify the correctness of programs?

Axiomatic Semantics of Programming Languages

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

### What is operational language?

Operational semantics is **a category of formal programming language semantics in** which certain desired properties of a program, such as correctness, safety or security, are verified by constructing proofs from logical statements about its execution and procedures, rather than by attaching mathematical meanings to its ...

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

The precondition statement **indicates what must be true before the function is called**. The postcondition statement indicates what will be true when the function finishes its work.

### What is a post condition loop?

The second form of conditional loop is known as a post-condition loop. This **form of repetition will check the condition after the commands have been executed**, initiating another execution of the loop if the condition is not met.