© 1996-2021

| | | ||

| ## 3.3 ITL library for Isabelle/HOLIsabelle/HOL is a generic proof assistant. It allows mathematical formulas to be expressed in a formal language and provides tools for proving those formulas in a logical calculus. We have given a deep embedding of propositional ITL and a shallow embedding of ﬁrst order ITL in Isabelle/HOL. A shallow embedding represents ITL using Isabelle/HOL predicates, while a deep embedding would represent ITL formulas as mutually inductive datatypes. See, e.g., [100] for a discussion about deep vs. shallow embeddings in Isabelle/HOL. The shallow embedding of ﬁrst order ITL uses techniques developed by Stefan Merz [183, 22] for the shallow embedding of Temporal Logic of Actions (TLA) in Isabelle/HOL.
## 3.3.1 Shallow embedding- Intervals are denoted by non-empty coinductive lists. These are a subtype of coinductive lists formalised by Andreas Lochbihler [24].
- First Order ﬁnite ITL, both quantiﬁcation over state variables, temporal variables (current, next, ﬁnal, penultimate), syntax, semantics, and axioms and proof rules. The encoding is similar to that of Stephan Merz [183, 22] used for TLA in Isabelle/HOL.
- The lemmas from Imperative Reasoning in Interval Temporal Logic by Ben Moszkowski.
- The until operator for ﬁnite and inﬁnite ITL and extensive list of lemmas from [180].
- The Pi operator [77, 2] for ﬁnite and inﬁnite ITL.
- Finite and Inﬁnite Interval Temporal Algebra. This work is based on Interval Temporal Algebra (Section 3.4) but now re-encoded in Isabelle/HOL. So the work on ITL and Prover9 and PVS has now been superseded by the Isabelle/HOL library. ITA is related to Kleene and Omega Algebras [11].
Download: - Version 3.0 (09/04/2021, ﬁrst public release) gzipped tar ﬁle
- First Order ﬁnite ITL, both quantiﬁcation over state variables, temporal variables (current, next, ﬁnal, penultimate), syntax, semantics, and axioms and proof rules. The encoding is similar to that of Stephan Merz [183, 22] used for TLA in Isabelle/HOL.
- The lemmas from Imperative Reasoning in Interval Temporal Logic by Ben Moszkowski.
- Time Reversal operator and an extensive list of lemmas included. Time reversal operator is also deﬁned for temporal variables and quantiﬁcation.
- First operator and Monitors. All key theorems/lemmas/semantics in David Smallwood PhD thesis “ITL Monitor: Compositional Runtime Analysis with Interval Temporal Logic” [158] have been veriﬁed.
- The projection operator [131] for ﬁnite ITL.
- Finite Interval Temporal Algebra. This work is based on Interval Temporal Algebra (Section 3.4) but now re-encoded in Isabelle/HOL. So the work on ITL and Prover9 and PVS has now been superseded by the Isabelle/HOL library. ITA is related to Kleene Algebras [11].
- The until and since operator for ﬁnite ITL and extensive list of lemmas from [180].
- The Pi operator [77, 2] for ﬁnite ITL.
- Forward and backward executability of ITL formula.
Download: - Version 2.7 (28/02/2021) gzipped tar ﬁle
Changes: - Added theory on executability of ITL formulae.
- Naming of deﬁnitions and lemmas is more consistent, all operations on intervals are starting with i.
- Removed inﬁnite ITL, i.e., this version only deals with ﬁnite ITL. Inﬁnite and ﬁnite ITL are now in the upcoming version 3.X which uses a uniform representation for ﬁnite and inﬁnite intervals using coinductive lists.
- Version 2.6 (16/04/2020) gzipped tar ﬁle
Changes: - Added projection operator (for ﬁnite ITL), axioms and proof rules.
- Added ﬁlter operator on ﬁnite intervals and extensive list of lemmas.
- Added until and since operator (for ﬁnite ITL) and extensive list of lemmas.
- Added Pi operator (for ﬁnite ITL), axiom and proof rules.
- Added Interval Temporal Algebra (for ﬁnite ITL) from version 1.
- Version 2.5 (21/07/2019, more polished version), axioms gzipped tar ﬁle.
Changes: - Added Inﬁnite intervals, semantics, axioms and proof rules, and extensive list of lemmas.
- Version 2.4 (11/06/2019, still work in progress), gzipped tar ﬁle.
Changes: - Replaced notation deprecated in Isabelle/HOL 2019.
- Version 2.3 (16/03/2019, still work in progress), gzipped tar ﬁle.
Changes: - Use Intensional.thy from Isabelle/HOL distribution.
- Restructure First and Monitor Theories.
- Added equivalence relation on monitors.
- Restructure Example Theory.
- See ChangeLog for detailed changes.
- Version 2.2 (08/12/2018, warning this is work in progress), gzipped tar ﬁle.
## 3.3.2 Deep embedding- Propositional ITL, syntax, semantics (ﬁnite intervals), and axioms and proof rules.
- The lemmas from Imperative Reasoning in Interval Temporal Logic by Ben Moszkowski.
- Time Reversal operator and an extensive list of lemmas.
- First operator and Monitors. All key theorems/lemmas/semantics in David Smallwood PhD thesis “ITL Monitor: Compositional Runtime Analysis with Interval Temporal Logic” [158] have been veriﬁed.
- Interval Temporal Algebra for ﬁnite interval. This work is based on Interval Temporal Algebra (Section 3.4) but now re-encoded in Isabelle/HOL. So the work on ITL and Prover9 and PVS has now been superseded by the Isabelle/HOL library. ITA is related to Kleene Algebras [11].
Download: - Version 1.10 (11/06/2019), gzipped tar ﬁle.
Changes: - Replaced notation deprecated in Isabelle/HOL 2019.
- Version 1.9 (16/03/2019), gzipped tar ﬁle.
Changes: - Restructure First and Monitor Theories.
- Added equivalence relation on monitors.
- See ChangeLog for detailed changes.
- Version 1.8 (08/12/2018, ﬁrst public release), gzipped tar ﬁle.
| | ||

| |