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A Mechanised Proof of the Time Invariance Thesis for the Weak Call-By-Value λ-Calculus
2021
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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]
2014
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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
2015
Journal of automated reasoning
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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]
2021
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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
2005
Third IEEE International Conference on Software Engineering and Formal Methods (SEFM'05)
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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
2011
Electronic Proceedings in Theoretical Computer Science
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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 ...
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]
2021
arXiv
pre-print
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2021 pre-print arXiv:2103.15292v1 fatcat:knljsvqn7beaxcaqjwmfm5xgxu
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]
2009
Philosophy of Mathematics
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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]
2018
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
1998
ACM Transactions on Design Automation of Electronic Systems
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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]
2014
arXiv
pre-print
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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]
2002
Lecture Notes in Computer Science
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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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