相关论文: Initiality for Typed Syntax and Semantics

Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…

These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…

We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…

Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model-value beyond mere comprehensible pictures. To…

Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…

Sentence simplification reduces semantic complexity to benefit people with language impairments. Previous simplification studies on the sentence level and word level have achieved promising results but also meet great challenges. For…

We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n),…

We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…

With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…

The lambda calculus, subject to typing restrictions, provides a syntax for the internal language of cartesian closed categories. This paper establishes a parallel result: staging annotations, subject to named level restrictions, provide a…

Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our…

Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

Syntax is fundamental to our thinking about language. Failing to capture the structure of input language could lead to generalization problems and over-parametrization. In the present work, we propose a new syntax-aware language model:…

In this essay, I present the advantages and, I dare say, the beauty of programming in a language with set-theoretic types, that is, types that include union, intersection, and negation type connectives. I show by several examples how…

We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meaningful physical…

Linguine is a natural-language-inspired programming language that enables users to write programs in a fluent, controlled subset of English while preserving formal semantics. The language introduces anaphoric constructs, such as pronoun…

Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…

Topological collections allow to consider uniformly many data structures in programming languages and are handled by functions defined by pattern matching called transformations. We present two type systems for languages with topological…