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A Mechanised Proof of the Time Invariance Thesis for the Weak Call-By-Value λ-Calculus

Yannick Forster, Fabian Kunze, Gert Smolka, Maximilian Wuttke, Liron Cohen, Cezary Kaliszyk
2021
The weak call-by-value λ-calculus Łand Turing machines can simulate each other with a polynomial overhead in time.  ...  The present paper presents a mechanised proof of the time invariance thesis for L, constituting the first mechanised equivalence proof between two standard models of computation covering time complexity  ...  The call-by-value λ-calculus L The call-by-value λ-calculus was introduced by Plotkin [21] as variant of Church's λcalculus [5] .  ... 
doi:10.4230/lipics.itp.2021.19 fatcat:dl6dgs6szvhzjojjwng3ij7fsq

Beta Reduction is Invariant, Indeed (Long Version) [article]

Beniamino Accattoli, Ugo Dal Lago
2014 arXiv   pre-print
Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is λ-calculus a reasonable machine?  ...  This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modelled after linear logic and proof-nets and admitting a decomposition of leftmost-outermost derivations  ...  While there is room for finer analyses (e.g. studying call-by-value or call-by-need evaluation), we consider the understanding of time invariance essentially achieved.  ... 
arXiv:1405.3311v1 fatcat:7zueginxfbgorlcd6poyz4wi7m

Hilbert's Tenth Problem in Coq (Extended Version) [article]

Dominique Larchey-Wendling, Yannick Forster
2022 arXiv   pre-print
To do so, we give the first full mechanisation of the Davis-Putnam-Robinson-Matiyasevich theorem, stating that every recursively enumerable problem – in our case by a Minsky machine – is Diophantine.  ...  We obtain an elegant and comprehensible proof by using a synthetic approach to computability and by introducing Conway's FRACTRAN language as intermediate layer.  ...  The first author was partially supported by the TICAMORE project (ANR grant 16-CE91-0002).  ... 
arXiv:2003.04604v5 fatcat:xstpu6zkovh7zpoki3rlkkeedu

Psi-Calculi in Isabelle

Jesper Bengtson, Joachim Parrow, Tjark Weber
2015 Journal of automated reasoning  
This paper presents a mechanisation of psi-calculi, a parametric framework for modelling various dialects of process calculi including (but not limited to) the pi-calculus, the applied pi-calculus, and  ...  To our knowledge, this is the most extensive formalisation of process calculi mechanised in a proof assistant to date.  ...  Acknowledgements We want to convey our sincere thanks to Stefan Berghofer for his hard work on enhancing Nominal Isabelle to include the features that we needed for this formalisation.  ... 
doi:10.1007/s10817-015-9336-2 fatcat:6xd44jmybzftljt2j3zc7kadzm

Automated Verification of Reactive and Concurrent Programs by Calculation [article]

Simon Foster, Kangfeng Ye, Ana Cavalcanti, Jim Woodcock
2021 arXiv   pre-print
Of note is our reasoning support for iterative programs with reactive invariants, based on Kleene algebra, and for parallel composition. We illustrate our strategy by verifying a reactive buffer.  ...  With this we can calculate a reactive program's denotational semantics, and thereby facilitate automated proof.  ...  We would like to thank the anonymous reviewers of our article for their diligent and helpful feedback, which has greatly improved the presentation of our results.  ... 
arXiv:2007.13529v2 fatcat:v2xwbwr7pvc3de5m7gp53gbv44

A Semantic Theory of the Internet of Things [article]

Valentina Castiglioni, Ruggero Lanotte, Massimo Merro
2016 arXiv   pre-print
We propose a process calculus for modelling systems in the Internet of Things paradigm.  ...  The calculus is equipped with a standard notion of bisimilarity which is a fully abstract characterisation of a well-known contextual equivalence.  ...  Acknowledgements We thank Ilaria Castellani and Matthew Hennessy for their precious comments on an early draft.  ... 
arXiv:1510.04854v3 fatcat:tknvwi2iencgfm2z2l46qrbvpa

Customised induction rules for proving correctness of imperative programs

O. Olsson, A. Wallenburg
2005 Third IEEE International Conference on Software Engineering and Formal Methods (SEFM'05)  
This time, we make use of failed proof attempts in a theorem prover to gain information about the problem structure and create the partition.  ...  The second part of the thesis continues with a more thorough development of the method.  ...  This work was also supported by a STINT (the Swedish Foundation for International Cooperation in Research and Higher Education) grant.  ... 
doi:10.1109/sefm.2005.15 dblp:conf/sefm/OlssonW05 fatcat:ucqksavqsvhwnackkdjpjhhfui

A coinductive semantics of the Unlimited Register Machine

Alberto Ciaffaglione
2011 Electronic Proceedings in Theoretical Computer Science  
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  ...  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  ...  Traces of execution. Leroy and Grall [22] adopt coinduction within CC (Co)Ind to capture both finite and infinite evaluations of a call-by-value λ -calculus.  ... 
doi:10.4204/eptcs.73.7 fatcat:6eztb747uvhc5m3heabqwmblmq

Deriving Laws for Developing Concurrent Programs in a Rely-Guarantee Style [article]

Ian J. Hayes and Larissa A. Meinicke and Patrick A. Meiring
2021 arXiv   pre-print
All the above constructs are defined in terms of a simple core language, based on four primitive commands and a handful of operators, and for which we have developed an extensive algebraic theory in Isabelle  ...  It provides a range of constructs for specifying concurrent programs and laws for refining these to code.  ...  Special thanks go to Cliff Jones for his continual feedback and encouragement during the course of developing this research.  ... 
arXiv:2103.15292v2 fatcat:4xp6l55gabcghjm2jjurdozpxe

ON COMPUTABILITY [chapter]

Wilfried Sieg
2009 Philosophy of Mathematics  
It could also be treated easily by the methods for proving the consistency of weak systems of arithmetic Herbrand had developed in his thesis.  ...  , ψ i l (x 1 , . . . , x n )), and (2) for every l-tuple of natural numbers the value of φ is "computable in a calculus".  ... 
doi:10.1016/b978-0-444-51555-1.50017-1 fatcat:7fjtsyt6izeizbzm4zgoastvuy

Adventures in Formalisation: Financial Contracts, Modules, and Two-Level Type Theory [article]

Danil Annenkov
2018 arXiv   pre-print
module system, including the ability to eliminate at compile time abstraction barriers introduced by the module system.  ...  The first project is about a certified compilation technique for a domain-specific programming language for financial contracts (the CL language).  ...  Normalisation in the Call-by-Value Simply-Typed Lambda Calculus In this section we present a well-known result that simply-typed lambda calculus (STLC) is normalising.  ... 
arXiv:1811.11317v1 fatcat:kuze4hglynh43eojv3juuxv2za

Change actions: from incremental computation to discrete derivatives [article]

Mario Alvarez-Picallo
2020 arXiv   pre-print
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation.  ...  Third, to give a theoretically sound calculus for this general setting.  ...  For brevity's sake, we omit it here, but a fully mechanised version of the proof using the Coq proof assistant is available.  ... 
arXiv:2002.05256v2 fatcat:o6zzymbz5rcgbgamuqve2fkyou

Semantics and verification of action diagrams with linear timing

K. Khordoc, E. Cerny
1998 ACM Transactions on Design Automation of Electronic Systems  
In this chapter, we postpone the choice for a time-domain and use an arbitrary time-domain T. The time-domain of choice for the rest of this thesis is R ≥0 .  ...  The notation ϑ[λ := 0] for a set λ ⊆ C is a short-hand for the valuation ϑ , defined as ϑ (c) = 0 for all c ∈ λ and ϑ (c) = ϑ(c) for all c ∈ C \ λ.  ...  If the condition of a time-lock can be reduced to false, using the invariants, we use the annotation f.  ... 
doi:10.1145/270580.270582 fatcat:bwnh5h3v7fgrdh7nypj3lybbze

Reasoning with !-Graphs [article]

Alexander Merry
2014 arXiv   pre-print
To this end, there is a project (Quantomatic) to build a proof assistant for string diagrams, at least for those based on categories with a notion of trace.  ...  Of particular note is the presentation of a form of graph-based induction, allowing the formal encoding of proofs that previously could only be represented as a mix of string diagrams and explanatory text  ...  Proof. Let A = im(fix G≈H ). We need to show that for each λ ∈ N A 0 and each concrete instance G ′ ≈ H ′ of X λ (G ≈ H), ∼ E λ ⊢ G ′ ≈ H ′ in the equational theory of string graphs.  ... 
arXiv:1403.7828v1 fatcat:knas4fdtkzg3phlmbz7vsxey7a

Proof Transformations for Evolutionary Formal Software Development [chapter]

Axel Schairer, Dieter Hutter
2002 Lecture Notes in Computer Science  
This thesis proposes to solve the problem by considering the state of a formal development consisting of (potentially buggy) specification and (potentially partial) proofs as one entity and transforming  ...  This leads to a separation of a framework for propagating transformations through development graphs and a reference instantiation that commits to concrete languages and proof representation.  ...  Proofs for these obligations are mechanised using a proof calculus for the institution, and proofs are represented using, e.g., proof objects or proof scripts. −→ n 2 with σ : Σ ′ → Σ is defined by obl  ... 
doi:10.1007/3-540-45719-4_30 fatcat:tm3npco76nasxabc73qicj2kv4
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