Hardware Verification Using Co-induction in COQ

Coupet-Grimal, Solange; Jakubiec, Line

doi:10.1007/3-540-48256-3_7

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…For example, in [29] it is shown that quite often the final coalgebra Z −→ Z as an algebra. This happens for example in the formalisation of "coinductive types" (final coalgebras) in the theorem prover Coq [32] (and used for instance in [59,121]). However, this may lead to rather complicated formulations of coinduction, distracting from the coalgebraic essentials.…”

Section: Coalgebras As Algebrasmentioning

confidence: 99%

Introduction to Coalgebra

Jacobs

2016

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The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.

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Section: Coalgebras As Algebrasmentioning

confidence: 99%

Introduction to Coalgebra

Jacobs

2016

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“…Several synchronous languages have been formalized in ITPs, including a subset of Lustre in Coq using coinductive types [21], an Esterel-like language in HOL with a focus on program proof [62], a shallow embedding of Lucid Synchrone in Coq with a focus on its higher-order features and clock calculus [12], and a denotational semantics of Kahn networks in Coq [51]. Similarly, work on synchronous compilers in ITPs has remained close to the dataflow model: an unpublished report [24] for a Scade 3 compiler focused on semantic and clocking definitions; the Gene-Auto project showed the correctness of equation scheduling for a Simulink to C code generator [34].…”

Section: Related Workmentioning

confidence: 99%

A formally verified compiler for Lustre

BourkeTimothy¹,

BrunLélio²,

DagandPierre-Evariste³

et al. 2017

SIGPLAN Not.

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The correct compilation of block diagram languages like Lustre, Scade, and a discrete subset of Simulink is important since they are used to program critical embedded control software. We describe the specification and verification in an Interactive Theorem Prover of a compilation chain that treats the key aspects of Lustre: sampling, nodes, and delays. Building on CompCert, we show that repeated execution of the generated assembly code faithfully implements the dataflow semantics of source programs. We resolve two key technical challenges. The first is the change from a synchronous dataflow semantics, where programs manipulate streams of values, to an imperative one, where computations manipulate memory sequentially. The second is the verified compilation of an imperative language with encapsulated state to C code where the state is realized by nested records. We also treat a standard control optimization that eliminates unnecessary conditional statements.

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“…The corecursive 10 functions zr, sc, mv : Cgn ∞ × IN + (×IN + ) → Cgn ∞ alter the configurations, as pre- 10 Corecursion is defined in Section 2. Note that these functions would be recursive working with finite configurations.…”

Section: Full Computationmentioning

confidence: 99%

“…There are several contributions in the literature exploiting the potential of coinductive definitions and proofs within CC (Co)Ind to master the fundamental concept of non-terminating computation. Some of these approaches concern transition systems [10,3], linear temporal logic [9,3] and process algebras [18,20].…”

Section: Other Work Related To Divergence or Low-level Languagesmentioning

confidence: 99%

A coinductive semantics of the Unlimited Register Machine

Ciaffaglione

2011

Electron. Proc. Theor. Comput. Sci.

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We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type theory. Our formalization allows us to certify the implementation of partial functions, thus it can be regarded as a ﬁrst step towards the development of a workbench for the formal analysis and verification of both converging and diverging computations

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Hardware Verification Using Co-induction in COQ

Cited by 5 publications

References 9 publications

Introduction to Coalgebra

Introduction to Coalgebra

A formally verified compiler for Lustre

A coinductive semantics of the Unlimited Register Machine

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