Haut PDF Normalisation & Equivalence in Proof Theory & Type Theory
Normalisation & Equivalence in Proof Theory & Type Theory
... plémentaires de la logique classique. Chapitre 11 Tenter d’introduire des raisonnements classiques plus loin dans les théories des types dévelopées en seconde partie (par exemple avec des types dépendants) se heurte au ...
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A Calculus of Substitutions for Incomplete-Proof Representation in Type Theory
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ...
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Lawvere-Tierney sheafification in Homotopy Type Theory
... ] in Isabelle and HOL Light. One advantage of type theory over set theory is the computation property of type theory: any term is identified with its normal ...a proof ...
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Extending type theory with syntactic models
... Dybjer in [ Dyb95 ], see also [ Hof97 ] for a good ...Families in a very pedestrian way, and let the reader refer to the presentations of Dybjer and Hofmann for a more abstract point of ...]. In this ...
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Setoid type theory - a syntactic translation
... Keywords: type theory · function extensionality · proof irrelevance · univalence 1 Introduction Extensional type theory (ETT [23]) is a convenient setting for formalising math- ematics: ...
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Unsolvability of the Quintic Formalized in Dependent Type Theory
... { in root (p ^^ ratr), ∀ x, ∃ f : algterm rat, algR_eval ratr f = ...reasoning in a constructive setting ...Galois theory The present contribution takes over the main design choices deployed ...
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A Nelson-Oppen based Proof System using Theory Specific Proof Systems
... EUF proof verifier, which aims at maxi- mum factorisation of ...The proof forest maintained by our proof-producing prover is a compact array-based structure, on which it is very easy and efficient to ...
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Formalising Real Numbers in Homotopy Type Theory
... • isP ositive 0 = ⊥ Proof. By lemmas 6.11 and 6.12 and computation. 7. Conclusion We have defined a Cauchy completion operation which is a monad on the category of premetric spaces with an appropriate closeness ...
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Generic Proof Tools and Finite Group Theory
... equality type argument passed to the order relation oA , with the one used in the lattice specification itself ( eA ...Unfortunately, in mathematical developments, thin-slicing a concept hi- erarchy ...
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Type Theory and Decision Procedures
... (of type @pn : ...(of type @pn n 1 : natq, list n Ñ list n 1 Ñ list pn 9 n 1 ...The proof sketch is simple: it su ces to apply as many times as needed the lemma reversepl@l 1 q reversepl 1 q@ ...
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On the homotopy groups of spheres in homotopy type theory
... duced in homotopy type theory because defining the set of singular cochains requires taking the underlying set of a topological space which is not an operation invariant un- der homotopy ...
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Extending Type Theory with Forcing
... subset type for dependent sums whose second component is a ...subset type specially in the conversion rule, allowing to transparently move an object between different subset ...of type T can ...
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Eliminating Reflection from Type Theory
... 1997]. In particular, the work of Hofmann provides a categor- ical answer to the question of consistency and conservativity of ET T over IT T with UIP and functional ...the proof and shows that there merely ...
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A Reasonably Exceptional Type Theory
... exceptions in type theories for proof assistants have severe drawbacks from both a programming and a reasoning ...exceptional type theory is interpreted by a translation into CIC, ...
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Dependent Type Theory in Polarised Sequent Calculus (abstract)
... logic in proof theory, it is now well-established that continuation- passing style (CPS) translations in call by name and call by value correspond to different polarisations of formulae ( ...
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Categorical Structures for Type Theory in Univalent Foundations
... split type-categories). Hofmann also mentions that – in our terminology – going from q-morphism structures to term-structures and back yields the original q-morphism ...working in set-theoretic ...
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Implementing Type Theory in Higher Order Constraint Logic Programming
... a proof step that opens a new goal (corresponding to Q ...elaborator. In ad- dition to that, the set of suspended goals implicitly kept by the language interpreter represents faithfully the metas-env data ...
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Regular Language Representations in the Constructive Type Theory of Coq
... formulas. In addition to the mathematical redesign, we implement all concepts in a manner that is both faithful to the mathematical development and easy to work ...elided in the ...least in ...
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DEEPSEC: Deciding Equivalence Properties in Security Protocols Theory and Practice
... deployed in 3G telephony networks [AMR + 12], the Passive Authentication and Basic Access Control (BAC) protocols implemented in the European passport [For04], as well as the Prˆ et-` a-Voter (PaV) [RS06] ...
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Induction principles as the foundation of the theory of normalisation: Concepts and Techniques
... In this se
tion we prove that if a λ -term t is strongly normalising for β -redu
tions, then i (t) is weakly normalising in λI ...The proof simply onsists in simulating an adequate redu
tion ...
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