Related papers: Normalisation of a Non-deterministic Type Isomorph…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
In the folklore of linear logic, a common intuition is that the structure of finiteness spaces, introduced by Ehrhard, semantically reflects the strong normalization property of cut-elimination. We make this intuition formal in the context…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
This paper extends the dual calculus with inductive types and coinductive types. The paper first introduces a non-deterministic dual calculus with inductive and coinductive types. Besides the same duality of the original dual calculus, it…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We give a type system in which the universe of types is closed by reflection into it of the logical relation defined externally by induction on the structure of types. This contribution is placed in the context of the search for a natural,…
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
System I is a recently introduced simply-typed lambda calculus with pairs where isomorphic types are considered equal. In this work we propose a variant of System I with the type Top, and present a complete formalization of this calculus in…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.
We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory of cubical type theory. Our normalization result is reduction-free, in the sense of yielding a bijection…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed $\lambda$-calculus, i.e. to solve the equation a = b where a and b are simply typed $\lambda$-terms and b is…
We present the system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence,…
We introduce Classification with Alternating Normalization (CAN), a non-parametric post-processing step for classification. CAN improves classification accuracy for challenging examples by re-adjusting their predicted class probability…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…