# Haut PDF Normalisation & Equivalence in Proof Theory & Type Theory

### Normalisation & Equivalence in Proof Theory & Type Theory

377

### A Calculus of Substitutions for Incomplete-Proof Representation in Type Theory

161

### 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**...

107

### Extending type theory with syntactic models

**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 ...

141

### Setoid type theory - a syntactic translation

**type**

**theory**· function extensionality ·

**proof**irrelevance · univalence 1 Introduction Extensional

**type**

**theory**(ETT [23]) is a convenient setting for formalising math- ematics: ...

42

### 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 ...

19

### A Nelson-Oppen based Proof System using Theory Specific Proof Systems

**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 ...

15

### Formalising Real Numbers in Homotopy Type Theory

**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 ...

14

### Generic Proof Tools and Finite Group Theory

**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 ...

157

### Type Theory and Decision Procedures

**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@ ...

102

### On the homotopy groups of spheres in homotopy type theory

**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 ...

188

### Extending Type Theory with Forcing

**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 ...

11

### Eliminating Reflection from Type Theory

**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 ...

20

### A Reasonably Exceptional Type Theory

**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, ...

30

### Dependent Type Theory in Polarised Sequent Calculus (abstract)

**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 ( ...

4

### Categorical Structures for Type Theory in Univalent Foundations

**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 ...

17

### Implementing Type Theory in Higher Order Constraint Logic Programming

**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 ...

27

### Regular Language Representations in the Constructive Type Theory of Coq

**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**...

34

### DEEPSEC: Deciding Equivalence Properties in Security Protocols Theory and Practice

**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] ...

92

### 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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