Related papers: Presentable signatures and initial semantics
An important property of programming language semantics is that they should be compositional. However, unstructured low-level code contains goto-like commands making it hard to define a semantics that is compositional. In this paper, we…
Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
In previous work ("From signatures to monads in UniMath"), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant. In the present work, we…
Mathematical documents written in LaTeX often contain ambiguities. We can resolve some of them via semantic markup using, e.g., sTeX, which also has other potential benefits, such as interoperability with computer algebra systems, proof…
Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…
Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Both syntactic and semantic structures are key linguistic contextual clues, in which parsing the latter has been well shown beneficial from parsing the former. However, few works ever made an attempt to let semantic parsing help syntactic…
The paper presents a constraint based semantic formalism for HPSG. The syntax-semantics interface directly implements syntactic conditions on quantifier scoping and distributivity. The construction of semantic representations is guided by…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Early stages of system development involve outlining desired features such as functionality, availability, or usability. Specifications are derived from these features that concretize vague ideas presented in natural languages. The…
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 present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
Effective program synthesis requires a way to minimise the number of candidate programs being searched. A type signature, for example, places some small restrictions on the structure of potential candidates. We introduce and motivate a…
In this paper we provide a semantic and syntactic analysis of parametrised natural numbers object in coherent categories, or pr-coherent categories. Semantically, we show the definable functions in the initial pr-coherent category are…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
SYNTAGMA is a rule-based parsing system, structured on two levels: a general parsing engine and a language specific grammar. The parsing engine is a language independent program, while grammar and language specific rules and resources are…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…