Contextual modal type theory

Authors:
Aleksandar Nanevski;Frank Pfenning;Brigitte Pientka
Affiliations:
Harvard University, Cambridge, MA;Carnegie Mellon University, Pittsburgh, PA;McGill University, Montreal, P. Q., Canada
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2008

Citing 42
Cited 45

Generality in artificial intelligence

Communications of the ACM
Explicit substitutions

POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A framework for defining logics

Journal of the ACM (JACM)
Multilanguage hierarchical logics, or: how we can do without modal logics

Artificial Intelligence
Logic programming in a fragment of intuitionistic linear logic

Papers presented at the IEEE symposium on Logic in computer science
Enriching the lambda calculus with contexts: toward a theory of incremental program construction

Proceedings of the first ACM SIGPLAN international conference on Functional programming
Multi-stage programming with explicit annotations

PEPM '97 Proceedings of the 1997 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
A lambda-calculus for dynamic binding

Theoretical Computer Science - Special issue: theoretical aspects of coordination languages
Run-time code generation and modal-ML

PLDI '98 Proceedings of the ACM SIGPLAN 1998 conference on Programming language design and implementation
Modal types as staging specifications for run-time code generation

ACM Computing Surveys (CSUR) - Special issue: electronic supplement to the September 1998 issue
Structural cut elimination

Information and Computation
A modal analysis of staged computation

Journal of the ACM (JACM)
A typed context calculus

Theoretical Computer Science
A Calculus of Lambda Calculus Contexts

Journal of Automated Reasoning
ML Systems: A Proof Theory for Contexts

Journal of Logic, Language and Information
Environment classifiers

POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Computing with Contexts

Higher-Order and Symbolic Computation
A Simply Typed Context Calculus with First-Class Environments

FLOPS '01 Proceedings of the 5th International Symposium on Functional and Logic Programming
Tradeoffs in the Intensional Representation of Lambda Terms

RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Open Proofs and Open Terms: A Basis for Interactive Logic

CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Absolute Explicit Unification

RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
A linear logical framework

Information and Computation
Higher-order Unification via Explicit Substitutions

LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
A temporal-logic approach to binding-time analysis

LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory

LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
From dynamic binding to state via modal possibility

Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
A judgmental reconstruction of modal logic

Mathematical Structures in Computer Science
Dependent types and explicit substitutions: a meta-theoretical development

Mathematical Structures in Computer Science
A modal foundation for meta-variables

MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Comparing formal theories of context in AI

Artificial Intelligence
A Symmetric Modal Lambda Calculus for Distributed Computing

LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Functional programming with names and necessity

Functional programming with names and necessity
Staged computation with names and necessity

Journal of Functional Programming
Explicit Environments

Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
Tabled higher-order logic programming

Tabled higher-order logic programming
Holes with binding power

TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Natural deduction and context as (constructive) modality

CONTEXT'03 Proceedings of the 4th international and interdisciplinary conference on Modeling and using context
Dynamic contextual intensional logic: logical foundations and an application

CONTEXT'03 Proceedings of the 4th international and interdisciplinary conference on Modeling and using context
Quantificational logic of context

AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
The ∇-calculus. functional programming with higher-order encodings

TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
A Formalization Of Viewpoints

Fundamenta Informaticae
Metamathematics Of Contexts

Fundamenta Informaticae

Polymorphism and separation in hoare type theory

Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming
Mechanizing metatheory in a logical framework

Journal of Functional Programming
Closing the stage: from staged code to typed closures

PEPM '08 Proceedings of the 2008 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Focusing and higher-order abstract syntax

Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A type-theoretic foundation for programming with higher-order abstract syntax and first-class substitutions

Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Focusing the Inverse Method for LF: A Preliminary Report

Electronic Notes in Theoretical Computer Science (ENTCS)
A Bidirectional Refinement Type System for LF

Electronic Notes in Theoretical Computer Science (ENTCS)
Programming with proofs and explicit contexts

Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
Bidirectional Decision Procedures for the Intuitionistic Propositional Modal Logic IS4

CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
A Conditional Logical Framework

LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Explicit Contexts in LF (Extended Abstract)

Electronic Notes in Theoretical Computer Science (ENTCS)
Case Analysis of Higher-Order Data

Electronic Notes in Theoretical Computer Science (ENTCS)
A semantics for context-oriented programming with layers

International Workshop on Context-Oriented Programming
A Logical Foundation for Environment Classifiers

TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Two-level Lambda-calculus

Electronic Notes in Theoretical Computer Science (ENTCS)
A universe of binding and computation

Proceedings of the 14th ACM SIGPLAN international conference on Functional programming
Higher-order term indexing using substitution trees

ACM Transactions on Computational Logic (TOCL)
Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages

Journal of Functional Programming
On a logical foundation for explicit substitutions

TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
On a logical foundation for explicit substitutions

RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Higher-order representation of substructural logics

Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
VeriML: typed computation of logical terms inside a language with effects

Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Justification logic and history based computation

ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
Programming inductive proofs: a new approach based on contextual types

Verification, induction termination analysis
Programming inductive proofs: a new approach based on contextual types

Verification, induction termination analysis
Higher-order dynamic pattern unification for dependent types and records

TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Cut-free Gentzen calculus for multimodal CK

Information and Computation
Hybrid

Journal of Automated Reasoning
Programming with binders and indexed data-types

POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Beluga: programming with dependent types, contextual data, and contexts

FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
Staged computation with staged lexical scope

ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Permissive-nominal logic: First-order logic over nominal terms and sets

ACM Transactions on Computational Logic (TOCL)
Trace matching in a concurrent logical framework

Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
LFP: a logical framework with external predicates

Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice
Explicitly heterogeneous metaprogramming with MetaHaskell

Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
Compiling contextual objects: bringing higher-order abstract syntax to programmers

PLPV '13 Proceedings of the 7th workshop on Programming languages meets program verification
Higher-Order processes, functions, and sessions: a monadic integration

ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Cut elimination in nested sequents for intuitionistic modal logics

FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Mtac: a monad for typed tactic programming in Coq

Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
Names for free: polymorphic views of names and binders

Proceedings of the 2013 ACM SIGPLAN symposium on Haskell
First-class substitutions in contextual type theory

Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Coeffects: unified static analysis of context-dependence

ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Combinators for impure yet hygienic code generation

Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation
J-Calc: A Typed Lambda Calculus for Intuitionistic Justification Logic

Electronic Notes in Theoretical Computer Science (ENTCS)
Intuitionistic Hypothetical Logic of Proofs

Electronic Notes in Theoretical Computer Science (ENTCS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

The intuitionistic modal logic of necessity is based on the judgmental notion of categorical truth. In this article we investigate the consequences of relativizing these concepts to explicitly specified contexts. We obtain contextual modal logic and its type-theoretic analogue. Contextual modal type theory provides an elegant, uniform foundation for understanding metavariables and explicit substitutions. We sketch some applications in functional programming and logical frameworks.