A construction of nondomain models for various type systems such as Martin-Löf’s type theory with intensional identity types, the polymorphic lambda calculus and other extensions of the simply typed lambda calculus is presented. These extensions include nearly all calculi in Barendregt’s lambda cube enriched by strong sums. The models can be arranged in such a way that the universal type Πα. α ...

We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λ-calculi. In particular, we focus on special Linear Combinatory Algebras of partial involutions, and we present PER models ov...

We argue that symmetric (semi)monoidal comonads provide a means to structure context-dependent notions of computation such as notions of dataflow computation (computation on streams) and of tree relabelling as in attribute evaluation. We propose a generic semantics for extensions of simply typed lambda calculus with context-dependent operations analogous to the Moggi-style semantics for effectf...

This paper explores the surprisingly rich design space for the simply typed lambda calculus with casts and a dynamic type. Such a calculus is the target intermediate language of the gradually typed lambda calculus but it is also interesting in its own right. In light of diverse requirements for casts, we develop a modular semantic framework, based on Henglein’s Coercion Calculus, that instantia...

A denotational semantics of simply typed lambda calculus with a basic type Dynamic, modelling values whose type is to be inspected at run-time, has been given by Abadi e.a..1]. We extend this interpretation to cover (formally contractive) recursive types as well. Soundness of typing rules and freeness of run-time type errors for well-typed programs hold. The interpretation works also for implic...

This paper deals with knowledge-based text processing which aims at an intuitive notion of textual similarity. Entities and relations relevant for a particular domain are identified and disambiguated by means of semi-supervised machine learning techniques and resulting annotations are applied for computing typedsimilarity of individual texts. The work described in this paper particularly shows ...

Abstract We run a series of experiments involving over 4,000 online participants and 10,000 school-aged youth. When individuals are asked to subjectively describe their performance on male-typed task relating math science, we find large gender gap in self-evaluations. This arises when self-evaluations provided potential employers, thus measure self-promotion, not driven by incentives promote. T...

A model-theoretic operation is characterised that preserves the property of being a model of typed λ-calculus. (i.e., the result of applying it to a model of typed λ-calculus is another model of typed λ-calculus.) An expression is well-typed iff the class of its models is closed under this operation.

Typed Clojure is an optional type system for Clojure, a dynamic language in the Lisp family that targets the JVM. Typed Clojure’s type system build on the design of Typed Racket, repurposing in particular occurrence typing, an approach to statically reasoning about predicate tests. However, in adapting the type system to Clojure, changes and extensions are required to accommodate additional lan...

In this paper, we elucidate how Korean temporal markers, OE and DONGAN contribute to specifying the event time and formalize it in terms of typed lambda calculus. We also present a computational method for constructing temporal representation of Korean sentences on the basis of G grammar proposed by [Renaud, 1992;1996].