Making the java memory model safe

Automated Deduction - CADE-25

2015

Abstract. We present a decision procedure that combines reasoning about datatypes and codatatypes. The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. The procedure decides universal problems and is composable via the Nelson-Oppen method. It has been implemented in CVC4, a state-of-the-art SMT solver. An evaluation based on problems generated from theories developed with Isabelle demonstrates the potential of the procedure.

Section: Introductionmentioning

confidence: 99%

A Decision Procedure for (Co)datatypes in SMT Solvers

Reynolds

Automated Deduction - CADE-25

2015

“…Until then, Isabelle/HOL and the other main systems based on higher-order logic (HOL4, HOL Light, and ProofPower-HOL) provided at most (inductive) datatypes, recursive functions, and (co)inductive predicates. Our aim was to support formalizations such as Lochbihler's verified compiler for a Java-like language [32] and his mathematization of the Java memory model [33], both of which rely on codatatypes to represent infinite traces.…”

Section: Introductionmentioning

confidence: 99%

Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

Julian

Frontiers of Combining Systems

Bouzy³

et al. 2017

Self Cite

Abstract. We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach.

“…Isabelle/HOL provides a few manually derived codatatypes (e.g., lazy lists) in the Coinductive entry of the Archive of Formal Proofs [18]. This library forms the basis of JinjaThreads [19], a verified compiler for a Java-like language, and of the formalization of the Java memory model [21]. The manual constructions are heavy, requiring hundreds of lines for each codatatype.…”

Section: Introductionmentioning

confidence: 99%

Truly Modular (Co)datatypes for Isabelle/HOL

Interactive Theorem Proving

Hölzl

Lochbihler

et al. 2014

Self Cite

Abstract. We extended Isabelle/HOL with a pair of definitional commands for datatypes and codatatypes. They support mutual and nested (co)recursion through well-behaved type constructors, including mixed recursion-corecursion, and are complemented by syntaxes for introducing primitive (co)recursive functions and by a general proof method for reasoning coinductively. As a case study, we ported Isabelle's Coinductive library to use the new commands, eliminating the need for tedious ad hoc constructions.