[PDF] Top 20 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 ... Voir le document complet

... 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] ... Voir le document complet

... ] 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 ... Voir le document complet

... 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 ... Voir le document complet

... Keywords: type theory · function extensionality · proof irrelevance · univalence 1 Introduction Extensional type theory (ETT [23]) is a convenient setting for formalising math- ematics: ... Voir le document complet

... { 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 ... Voir le document complet

... 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 ... Voir le document complet

... • 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 ... Voir le document complet

... 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 ... Voir le document complet

... (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 suces to apply as many times as needed the lemma reversepl@l 1 q  reversepl 1 q@ ... Voir le document complet

... 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 ... Voir le document complet

... 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 ... Voir le document complet

... 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 ... Voir le document complet

... 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, ... Voir le document complet

... 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 ( ... Voir le document complet

... 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 ... Voir le document complet

... 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 ... Voir le document complet

... 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 ... Voir le document complet

... 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] ... Voir le document complet

... 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 ... Voir le document complet