intervaltyyppinen

Intervaltyyppinen (literally “interval-type” in Finnish) is a concept in type systems describing types whose values are restricted to a numeric interval. It is commonly encountered in languages that support refinement or dependent types, where the bounds of the interval become part of the type itself and are checked statically.

Definition: For an integer base type, an interval type I(min, max) denotes all integers v with min ≤ v ≤ max. In languages with refinement syntax this can be written as { v : Int | min ≤ v ∧ v ≤ max } or as a parametrized type IntervalInt(min, max).

Usage: Intervaltyyppinen types encode invariants directly in the type, enabling compile-time verification of numeric constraints and reducing runtime guard checks. They are used in safety-critical software, numerical libraries, and validation-heavy domains where invariants such as non-negativity or bounded ranges are essential.

Relation to other concepts: Interval types are related to refinement types and dependent types. They differ from simple bounded data types in that the bounds can be parameterized and may depend on other values or proofs. Some languages require explicit proof terms, while others strive for type inference with subtyping.

Limitations and considerations: Implementing interval types can increase type-system complexity and complicate type inference. Overly granular intervals can lead to verbose code or brittle interfaces, and performance may be affected by extra checks or proof obligations in some toolchains.

See also: refinement type, dependent type, bounded type, range type, static verification.