typeinterval2

Typeinterval2 is a formal construct used in programming language theory and static analysis to model the range of values a variable may assume, with an emphasis on the associated type information. It extends the basic interval concept by attaching a base type (such as int or real) and by supporting lattice-like operations that are compatible with type systems and abstract interpretation.

A typeinterval2 representation typically consists of a lower and upper bound, each bound possibly inclusive or exclusive, and a type tag indicating the underlying domain. Bounds can be finite or unbounded, and the structure may include metadata to handle special values such as infinities or NaN in floating point domains. This enables precise reasoning about arithmetic, comparisons, and over-approximation in analyses while preserving type correctness.

Key operations include containment tests, intersection, union, and difference, as well as arithmetic operators that safely propagate bounds. In a static analysis setting, typeinterval2 is used to approximate the set of possible values a variable may take at a program point, enabling optimizations, error detection, and proof obligations without executing the program.

The designation “2” signals a second-generation variant that improves precision and robustness over an earlier version. Improvements may cover edge-case handling, canonical normalization, and better integration with other abstract domains used in the analyzer.

Related concepts include interval arithmetic, abstract interpretation, and range analysis in type inference and optimization.