arraysuch

Arraysuch is a theoretical construct in computer science and programming that denotes a class of array-like data structures defined by a predicate that determines the value at each index. The name combines 'array' with 'such that,' echoing mathematical notation in which a property specifies each element. In an Arraysuch, the domain of valid indices is defined, and each element a(i) is specified by a rule or function that must hold for all valid i. Implementations may be eager, computing all elements upfront, or lazy, evaluating elements on access. Some designs support partial definitions, where only certain indices have defined values until constraints are completed, after which a solver or evaluation procedure fills in the rest.

Design and characteristics: Arraysuch emphasizes a declarative specification over explicit storage. Elements are not purely stored but derived from a constraint system or functional definition. This enables compact representations of large or infinite domains and allows formal reasoning about properties of the array. Update semantics vary: in some models, updates modify the defining rule; in others, they constrain a set of permissible values.

Examples: An Arraysuch of size 10 with a(i) = i^2 demonstrates a simple, computable definition. A more constraint-oriented example defines a(i) to be the smallest nonnegative integer such that a(i) % 3 = i % 3, illustrating a dependency on both index and value.

Applications and limitations: Arraysuch concepts appear in discussions of lazy evaluation, dependent types, and constraint programming. They are mainly theoretical tools or educational devices, useful for exploring how constraints shape data representations. Practical implementations must balance evaluation cost, constraint solving, and predictable performance.