type theory
Normalisation by evaluation for type theory, in type theory
... We are working in intensional Martin-L¨ of Type Theory with postulated extensionality principles using Agda as a vehicle [1, 27]. We make use of quotient inductive inductive types (QIITs, see section 6 of ...
26
Probabilistic Type Theory for Incremental Dialogue Processing
... in type theory s ∶ T (that a given object s is of type T ) is extended in TTR so that s can be a (potentially complex) record and T can be a record type – ...state type (Ginzburg, 2012; ...
9
Spatial Descriptions in Type Theory with Records
... a type theory with records which leads to a view of meaning which is tightly linked to perception and ...of type T (written as a : T ...A type T is “true” just in case there is something a ...
6
HoTT-Crypt : A Study in Homotopy Type Theory based on Cryptography
... inductive type representing a graphical model in a topological ...inductive type acts as an abstract model for the encoded cryptographic system and enables us to specify the correctness proper- ties as ...
16
Extending homotopy type theory with strict equality
... unspecified type theory containing a “connective” for strict equality ...2-level theory does not (yet) exist, we cannot formalise our constructions exactly as they are ...homotopy type ...
17
Collection Principles in Dependent Type Theory
... logic-enriched type theory it will be necessary to include two rules in the type theory corresponding to the two collection schemes of CZF, Strong Collection and Subset ...original type ...
24
Comprehensive parametric polymorphism : categorical models and type theory
... The proof-relevant setting of dependent type theory, however, requires mod- ifications to our semantic framework. In particular the relational property of parametricity graphs must be relaxed. Ongoing work ...
17
A Probabilistic Rich Type Theory for Semantic Interpretation
... our type theoretical semantics are extracted. Our type theory is, then, the interface between observation-based learning of classifiers for objects and the situations in which they figure on one ...
8
Homotopy-initial algebras in type theory
... the type universe U. This is because these type theories are intended as background theories for our study of inductive ...The type theory H does not include any global extensionality ...
42
Towards a cubical type theory without an interval
... inductive type with only one ...each type (as described in chapter 2 of [17]): equality of pairs is a pair of equalities, equality of functions is given by a function and equality of types is given by ...
27
Model Theories of Set Theories and Type Theory
... We are quite far from having fully exploited the potential of Leonard’s definition of an existence predicate. The present pa- per gives a limited account of that potential within first-order logic. The system that we ...
5
Abstract Predicates and Mutable ADTs in Hoare Type Theory
... predicates, type-comparisons require some procedure for determining equality of terms and implication of predicates, which is generally ...dependent type system ...Hoare Type Theory or HTT ...
46
Free higher groups in homotopy type theory
... The central and guiding question of this paper was the problem of showing that the free ∞ -group F(A) over a set is a set as well. We have proved a first approximation of this, namely that F(A) has trivial fundamental ...
10
A relationally parametric model of dependent type theory
... The most exciting avenue for future work is in comparing the reflexive graph model we have presented here with the strikingly similar groupoid and ∞-groupoid models of type theory [32]. Re- flexive graphs ...
14
The vertical unity of concepts in mathematics through the lens of homotopy type theory
... homotopy type theory (Schreiber ...homotopy type theory can express this gluing process straightforwardly, as it can the geometric constructions needed to formulate gauge field ...
15
Type Theory & Functional Programming
... This section forms the heart of our development of type theory. In it we look at a remarkable correspondence, or isomorphism, linking the typed lambda calculus and constructive logic. It has become known as ...
378
MoL 2014 12: A Model Of Type Theory In Cubical Sets With Connections
... homotopy theory can be ...of type theory in model categories have motivated the composite field homotopy type theory as well as the univalent foundations research programme ...of ...
132
Type theory in type theory using quotient inductive types
... dependent type theory which only features typed ...rudimentary type the- ory here, mainly for reasons of ...other type constructors, ...
12
A Synopsis of Morphoid Type Theory
... Homotopy type theory (HoTT) and mor- phoid type theory (MTT) are intended as type- theoretic foundations for mathematics supporting a concept of ...L¨of type the- ory ...
12
Visual TTR Modelling Visual Question Answering in Type Theory with Records
... rich type universe of Type Theory with Records (TTR) to model utterances about the image, the image itself, and classifications made relating the outcomes of these two ...
6