Conditionshave

Conditionshave is a theoretical concept in formal methods used to describe when a given set of conditions guarantees a particular property. A conditionshave comprises a set C of conditions and a property P such that, in every model or computation where all conditions in C hold, the property P also holds. In formal notation, C have P can be expressed as the implication that the conjunction of conditions implies P: (∧c∈C c) → P.

Relation to existing formalisms: It is related to preconditions and postconditions in Hoare logic but emphasizes the guarantee provided by a specific trigger set. Unlike a programmatic precondition that may enable or disable execution, a conditionshave speaks to logical entailment: whenever the triggers are satisfied, the guarantee P follows.

Applications: It can be used to reason about safety properties, invariants, or contracts that depend on several simultaneous conditions. For example, in a data-processing pipeline, a conditionshave might state that if the input is well-formed and the system is in a non-overloaded state, the processing step will produce a valid result.

Variants and notation: Some authors treat C as a multi-guarded assertion; others abstract C as a single composite condition. The concept remains informal in many sources and is not widely standardized.

See also: preconditions, postconditions, Hoare logic, contract-based design, invariants.