• Open Access IconOpen Access
  • Cite Icon38
  • https://doi.org/10.1145/2500365.2500587Copy DOI Icon

Modular monadic meta-theory

  • Sep 25, 2013
  • Benjamin Delaware +3 more
Show More
  • Abstract
  • Literature Map
  • References
  • Citations
  • Similar Papers
Abstract

This paper presents 3MT, a framework for modular mechanized meta-theory of languages with effects. Using 3MT, individual language features and their corresponding definitions -- semantic functions, theorem statements and proofs-- can be built separately and then reused to create different languages with fully mechanized meta-theory. 3MT combines modular datatypes and monads to define denotational semantics with effects on a per-feature basis, without fixing the particular set of effects or language constructs. One well-established problem with type soundness proofs for denotational semantics is that they are notoriously brittle with respect to the addition of new effects. The statement of type soundness for a language depends intimately on the effects it uses, making it particularly challenging to achieve modularity. 3MT solves this long-standing problem by splitting these theorems into two separate and reusable parts: a feature theorem that captures the well-typing of denotations produced by the semantic function of an individual feature with respect to only the effects used, and an effect theorem that adapts well-typings of denotations to a fixed superset of effects. The proof of type soundness for a particular language simply combines these theorems for its features and the combination of their effects. To establish both theorems, 3MT uses two key reasoning techniques: modular induction and algebraic laws about effects. Several effectful language features, including references and errors, illustrate the capabilities of 3MT. A case study reuses these features to build fully mechanized definitions and proofs for 28 languages, including several versions of mini-ML with effects.

Similar Papers
  • PDF
  • Research Article
  • Citations3

Perceptual and semantic maps in individual humans share structural features that predict creative abilities

  • Feb 24, 2025
  • Communications Psychology
  • Johannes P.-H Seiler +4
  • Supplementary Content

Co-Contextual Type Systems: Contextless Deductive Reasoning for Correct Incremental Type Checking

  • Mar 02, 2020
  • TUbilio (Technical University of Darmstadt)
  • Edlira Kuci
  • Dissertation

Domínios conceituais das construções locativas, existenciais, comitativas e possessivas em línguas bantas

  • Jan 01, 2013
  • Paulo Jeferson Pilar Araújo
  • Research Article
  • Citations2

A Theory of Symbolic Dynamics for Hybrid Systems

  • Jan 01, 2011
  • IFAC Proceedings Volumes
  • Manuela L Bujorianu +1
  • Research Article

Language support for parallel and distributed computing

  • Apr 27, 2021
  • ACM SIGAda Ada Letters
  • Kyle Chard +3
  • Research Article
  • Citations15

Self-Assessment Procedure XXIII

  • May 01, 1995
  • Communications of the ACM
  • Mitchell H Clifton
  • PDF
  • Research Article
  • Citations15

New avenues and challenges in semantic map research (with a case study in the semantic field of emotions)

  • Jun 09, 2022
  • Zeitschrift für Sprachwissenschaft
  • Thanasis Georgakopoulos +1
  • Single Book
  • Citations14

Assessing Chinese Learners of English

  • Jan 01, 2016
  • Guoxing Yu +1
  • Research Article

A Virtual Class Calculus

  • Jan 01, 2005
  • DAIMI Report Series
  • Erik Ernst +2
  • Research Article
  • Citations29

Scoped types and aspects for real-time Java memory management

  • May 23, 2007
  • Real-Time Systems
  • Chris Andreae +5
  • Research Article

Gendered Discourse in The Ballad of Songbirds and Snakes (2023): A Comparative Analysis of Male and Female Language Features

  • Feb 05, 2026
  • JETLEE : Journal of English Language Teaching, Linguistics, and Literature
  • Kharisma Tri Fajarwati +2
  • PDF
  • Research Article

Some peculiar features of military articles headlines in English press

  • Jun 01, 2023
  • World of Science. Series: Sociology, Philology, Cultural Studies
  • Ekaterina Zhuk
  • Book Chapter
  • Citations7

A Hoare Logic Contract Theory: An Exercise in Denotational Semantics

  • Jan 01, 2018
  • Dilian Gurov +1
  • Research Article
  • Citations1176

A Syntactic Approach to Type Soundness

  • Nov 01, 1994
  • Information and Computation
  • A.K Wright +1
  • Book Chapter
  • Citations9

Denotational Semantics of Hybrid Automata

  • Jan 01, 2006
  • Abbas Edalat +1
Cactus Communications logo

Copyright 2026 Cactus Communications. All rights reserved.