Overview

Higher-order logic (HOL) is presented in the evidence as a major logic supported by the Isabelle proof-assistant framework. Isabelle is described as customizable to multiple logics, including first-order logic (FOL), Zermelo-Fraenkel set theory (ZF), and, most notably, higher-order logic (HOL).

Role in Isabelle/HOL

The HOL instance of Isabelle is described as providing components for specification constructs such as type definitions, recursive function definitions with termination proofs, and inductive set definitions. Isabelle itself is described as an interactive development environment with immediate feedback for proof attempts and symbolic computations, as well as automated reasoning support such as term rewriting and decision procedures.

Use in testing and verification workflows

The evidence connects HOL to model-based testing through HOL-TestGen. HOL-TestGen is built on top of Isabelle/HOL, and its test specifications are expressed in higher-order logic. This allows test generation to reuse existing Isabelle/HOL verification models. In the cited microprocessor case study, a formal VAMP processor model developed in Isabelle/HOL is adapted and reused to generate test cases for checking hardware conformance to the VAMP model.

Related tooling

• Isabelle/HOL: A tool environment using higher-order logic in the evidence, including support for specification constructs and as the basis for HOL-TestGen.