Related papers: Type Inference for Bimorphic Recursion
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
In this paper, we argue that type inferencing incorrectly implements appropriateness specifications for typed feature structures, promote a combination of type resolution and unfilling as a correct and efficient alternative, and consider…
In this note we introduce several instructive examples of bijections found between several different combinatorially defined sequences of sets. Each sequence has cardinalities given by the Catalan numbers. Our results answer some questions…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…
It is an established assumption that pattern-based models are good at precision, while learning based models are better at recall. But is that really the case? I argue that there are two kinds of recall: d-recall, reflecting diversity, and…
Inferring semantic types for entity mentions within text documents is an important asset for many downstream NLP tasks, such as Semantic Role Labelling, Entity Disambiguation, Knowledge Base Question Answering, etc. Prior works have mostly…
We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation; this leads to a Bayesian recurrent unit…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…
The decidability of the reachability problem for finitary PCF has been used as a theoretical basis for fully automated verification tools for functional programs. The reachability problem, however, often becomes undecidable for a slight…
Deep neural networks are revolutionizing the way complex systems are developed. However, these automatically-generated networks are opaque to humans, making it difficult to reason about them and guarantee their correctness. Here, we propose…
We build a dual-way neural dictionary to retrieve words given definitions, and produce definitions for queried words. The model learns the two tasks simultaneously and handles unknown words via embeddings. It casts a word or a definition to…
We address the problem of local type inference for a language based on System F with context-free session types. We present an algorithm that leverages the bidirectional type checking approach to propagate type information, enabling first…
Bimorphic lenses are a simplification of polymorphic lenses that (like polymorphic lenses) have a type defined by 4 parameters, but which are defined in a monomorphic type system (i.e. an ordinary category with finite products). We show…