Reference. Categorial and categorical grammars

Joachim Lambek · · categorial-grammar · DOI
Having been under the impression that categorial grammars in general and the so-called syntactic calculus in particular had been swept away by the tide of transformational grammar, I was very surprised to learn of the recent revival of interest in these matters, as, for example, by Buszkowski in Poland and by van Benthem in the Netherlands. Stimulated by the renewed activity in this area, I decided to take another look at it, and in particular, to explore the categorical connection, which had been at the back of my mind all along.

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Cite as @lambek1988categorial (helia, typst) · \cite{lambek1988categorial} (LaTeX)
BibTeX
bibtex · 16 lines
@inbook{lambek1988categorial,
 title = {Categorial and Categorical Grammars},
 author = {Lambek, J.},
 year = {1988},
 isbn = {978-94-015-6878-4},
 doi = {10.1007/978-94-015-6878-4_11},
 url = {https://doi.org/10.1007/978-94-015-6878-4_11},
 booktitle = {Categorial Grammars and Natural Language Structures},
 editor = {Oehrle, Richard T.
and Bach, Emmon
and Wheeler, Deirdre},
 pages = {297--317},
 publisher = {Springer Netherlands},
 address = {Dordrecht},
 abstract = {Having been under the impression that categorial grammars in general and the so-called syntactic calculus in particular had been swept away by the tide of transformational grammar, I was very surprised to learn of the recent revival of interest in these matters, as, for example, by Buszkowski in Poland and by van Benthem in the Netherlands. Stimulated by the renewed activity in this area, I decided to take another look at it, and in particular, to explore the categorical connection, which had been at the back of my mind all along.}
}
hayagriva YAML (typst)
yaml · 21 lines
lambek1988categorial:
  type: chapter
  title: Categorial and Categorical Grammars
  author: Lambek, J.
  date: 1988
  editor:
  - Oehrle, Richard T.
  - Bach, Emmon
  - Wheeler, Deirdre
  page-range: 297-317
  url: https://doi.org/10.1007/978-94-015-6878-4_11
  serial-number:
    doi: 10.1007/978-94-015-6878-4_11
    isbn: 978-94-015-6878-4
  abstract: Having been under the impression that categorial grammars in general and the so-called syntactic calculus in particular had been swept away by the tide of transformational grammar, I was very surprised to learn of the recent revival of interest in these matters, as, for example, by Buszkowski in Poland and by van Benthem in the Netherlands. Stimulated by the renewed activity in this area, I decided to take another look at it, and in particular, to explore the categorical connection, which had been at the back of my mind all along.
  parent:
    type: book
    title: Categorial Grammars and Natural Language Structures
    publisher:
      name: Springer Netherlands
      location: Dordrecht
Cited by (2)

Intrinsic Verification of Parsers and Formal Grammar Theory in Dependent Lambek Calculus intrinsic-verification-of-parsers

We present Dependent Lambek Calculus (Lambek𝙳), a domain-specific dependent type theory for verified parsing and formal grammar theory. In Lambek𝙳, linear types are used as a syntax for formal grammars, and parsers can be written as linear terms. The linear typing restriction provides a form of intrinsic verification that a parser yields only valid parse trees for the input string. We demonstrate the expressivity of this system by showing that the combination of inductive linear types and dependency on non-linear data can be used to encode commonly used grammar formalisms such as regular and context-free grammars as well as traces of various types of automata. Using these encodings, we define parsers for regular expressions using deterministic automata, as well as examples of verified parsers of context-free grammars.

We present a denotational semantics of our type theory that interprets the linear types as functions from strings to sets of abstract parse trees and terms as parse transformers. Based on this denotational semantics, we have made a prototype implementation of Lambek𝙳 using a shallow embedding in the Agda proof assistant. All of our examples parsers have been implemented in this prototype implementation.

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Closed Categories and Categorial Grammar dougherty-1993

DOI
Cites 22 works (4 here)
With notes (4)

Introduction to Higher-Order Categorical Logic lambek_scott_1986

Web

Formal Philosophy: Selected Papers of Richard Montague Montague1974-MONFPS

Web

Categories for the Working Mathematician maclane_1971

Web

The mathematics of sentence structure lambek58

DOI
External (18)
lambek1988categorial reference entries/refs/lambek1988categorial/lambek1988categorial.hel