11 Search Results for "Brady, Edwin"


Artifact
Software
kontheocharis/erasure-impl

Authors: Constantine Theocharis


Abstract

Cite as

Constantine Theocharis. kontheocharis/erasure-impl (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@misc{dagstuhl-artifact-26954,
   title = {{kontheocharis/erasure-impl}}, 
   author = {Theocharis, Constantine},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:18b74b13bf47b1740130031fe2cc393db1e95615;origin=https://github.com/kontheocharis/erasure-impl;visit=swh:1:snp:22f5796592ed642a59bdfc83787df0dd25d3d07e;anchor=swh:1:rev:b33efb7ac1b24535cdd4b1a6c13072f30ca9383b}{\texttt{swh:1:dir:18b74b13bf47b1740130031fe2cc393db1e95615}} (visited on 2026-07-15)},
   url = {https://github.com/kontheocharis/erasure-impl},
   doi = {10.4230/artifacts.26954},
}
Artifact
Software
kontheocharis/erasure-agda

Authors: Constantine Theocharis


Abstract

Cite as

Constantine Theocharis. kontheocharis/erasure-agda (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@misc{dagstuhl-artifact-26955,
   title = {{kontheocharis/erasure-agda}}, 
   author = {Theocharis, Constantine},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:985bed7fde164c22db65b5fc19c69f7ad8896270;origin=https://github.com/kontheocharis/erasure-agda;visit=swh:1:snp:abe007c225313601adc0da7a9844de1a8cc993e0;anchor=swh:1:rev:b840465809e71c5fc469fcd8b267a8191e931341}{\texttt{swh:1:dir:985bed7fde164c22db65b5fc19c69f7ad8896270}} (visited on 2026-07-15)},
   url = {https://github.com/kontheocharis/erasure-agda},
   doi = {10.4230/artifacts.26955},
}
Document
Type Theory with Erasure

Authors: Constantine Theocharis and Edwin Brady

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)


Abstract
Erasure enriches type theory with a distinction between runtime relevant and irrelevant data, allowing the compilation step to safely erase the latter. Versions of this feature are implemented by many systems, including Agda, Idris, and Rocq. We present a structural version of type theory with erasure, formulated as a second-order generalised algebraic theory (SOGAT). Erasure is encoded as a phase distinction between runtime and erased terms, in the form of a proposition that can appear in a context. This formulation has several advantages: it has models based on categories with families, is compatible with other structural features such as staging, and provides a better guideline for implementation. Through the model theory of SOGATs, we study the semantics of type theory with erasure in families of sets, which generalises to any Grothendieck topos equipped with a tiny proposition. We establish conservativity over Martin-Löf type theory (MLTT) in both phases. For code extraction, we construct a presheaf model that produces untyped lambda calculus programs and prove its correctness through gluing. Our results are formalised in Agda and we provide a toy elaborator implementation.

Cite as

Constantine Theocharis and Edwin Brady. Type Theory with Erasure. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 31:1-31:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{theocharis_et_al:LIPIcs.FSCD.2026.31,
  author =	{Theocharis, Constantine and Brady, Edwin},
  title =	{{Type Theory with Erasure}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{31:1--31:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.31},
  URN =		{urn:nbn:de:0030-drops-263816},
  doi =		{10.4230/LIPIcs.FSCD.2026.31},
  annote =	{Keywords: Type theory, erasure, dependent types, compilation, synthetic phase distinction, higher-order abstract syntax, logical frameworks}
}
Document
Towards the Type Safety of Pure Subtype Systems

Authors: Valentin Pasquale and Álvaro García-Pérez

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)


Abstract
Hutchins' Pure Subtype Systems (PSS) offer a unified framework for types and terms, promising significant advancements in language design for features like dependent types and higher-order subtyping. However, the theory has been hampered by a critical gap: a proof of type safety has remained an open problem for over a decade. The original attempt to prove this property relied on the conjectured commutativity of two fundamental reduction relations, equivalence and subtyping. Proving transitivity elimination, however, requires this commutativity, a property that is notoriously difficult to establish for higher-order subtyping systems. In this paper, we address this issue by introducing Machine-Based PSS (MPSS), a novel reformulation of the original system. MPSS integrates a continuation stack mechanism, reminiscent of the Krivine Abstract Machine, to keep track of arguments that are passed during function application, enabling more fine-grained reductions. This architectural change exposes crucial intermediate reduction steps that were absent in the original PSS. The primary contribution of our work is a direct proof that the equivalence and subtyping reductions in MPSS commute. This result formally establishes transitivity elimination, which is the cornerstone of the inversion lemma required for type safety. We conclude by outlining a pathway from our foundational result to a complete, type-safe system, thereby paving the way for the practical realization of PSS-based languages.

Cite as

Valentin Pasquale and Álvaro García-Pérez. Towards the Type Safety of Pure Subtype Systems. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{pasquale_et_al:LIPIcs.CSL.2026.37,
  author =	{Pasquale, Valentin and Garc{\'\i}a-P\'{e}rez, \'{A}lvaro},
  title =	{{Towards the Type Safety of Pure Subtype Systems}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.37},
  URN =		{urn:nbn:de:0030-drops-254626},
  doi =		{10.4230/LIPIcs.CSL.2026.37},
  annote =	{Keywords: Lambda calculus, Pure subtype systems, Dependent types, Higher-order subtyping, Type safety}
}
Document
Short Paper
LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean (Short Paper)

Authors: Eric Vin, Kyle A. Miller, and Daniel J. Fremont

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)


Abstract
We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with arbitrary Lean expressions, making it straightforward to define properties involving numerical or other types. We prove that standard flavors of LTL can be embedded in our framework. The library also provides automation for reasoning about LeanLTL formulas in a way that facilitates using Lean’s existing tactics. Finally, we provide examples illustrating the utility of the library in reasoning about systems that come from applications.

Cite as

Eric Vin, Kyle A. Miller, and Daniel J. Fremont. LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean (Short Paper). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 37:1-37:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{vin_et_al:LIPIcs.ITP.2025.37,
  author =	{Vin, Eric and Miller, Kyle A. and Fremont, Daniel J.},
  title =	{{LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{37:1--37:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.37},
  URN =		{urn:nbn:de:0030-drops-246356},
  doi =		{10.4230/LIPIcs.ITP.2025.37},
  annote =	{Keywords: Linear Temporal Logic, Interactive Theorem Proving, Lean 4}
}
Document
Program Logics for Ledgers

Authors: Orestis Melkonian, Wouter Swierstra, and James Chapman

Published in: OASIcs, Volume 129, 6th International Workshop on Formal Methods for Blockchains (FMBC 2025)


Abstract
Distributed ledgers nowadays manage substantial monetary funds in the form of cryptocurrencies such as Bitcoin, Ethereum, and Cardano. For such ledgers to be safe, operations that add new entries must be cryptographically sound - but it is less clear how to reason effectively about such ever-growing linear data structures. This paper demonstrates how distributed ledgers may be viewed as computer programs, that, when executed, transfer funds between various parties. As a result, familiar program logics, such as Hoare logic, are applied in a novel setting. Borrowing ideas from concurrent separation logic, this enables modular reasoning principles over arbitrary fragments of any ledger. All of our results have been mechanised in the Agda proof assistant.

Cite as

Orestis Melkonian, Wouter Swierstra, and James Chapman. Program Logics for Ledgers. In 6th International Workshop on Formal Methods for Blockchains (FMBC 2025). Open Access Series in Informatics (OASIcs), Volume 129, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{melkonian_et_al:OASIcs.FMBC.2025.10,
  author =	{Melkonian, Orestis and Swierstra, Wouter and Chapman, James},
  title =	{{Program Logics for Ledgers}},
  booktitle =	{6th International Workshop on Formal Methods for Blockchains (FMBC 2025)},
  pages =	{10:1--10:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-371-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{129},
  editor =	{Marmsoler, Diego and Xu, Meng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FMBC.2025.10},
  URN =		{urn:nbn:de:0030-drops-230370},
  doi =		{10.4230/OASIcs.FMBC.2025.10},
  annote =	{Keywords: blockchain, distributed ledgers, UTxO separation logic, program semantics, formal verification, Agda}
}
Document
Type Theory as a Language Workbench

Authors: Jan de Muijnck-Hughes, Guillaume Allais, and Edwin Brady

Published in: OASIcs, Volume 109, Eelco Visser Commemorative Symposium (EVCS 2023)


Abstract
Language Workbenches offer language designers an expressive environment in which to create their Domain Specific Languages (DSLs). Similarly, research into mechanised meta-theory has shown how dependently typed languages provide expressive environments to formalise and study DSLs and their meta-theoretical properties. But can we claim that dependently typed languages qualify as language workbenches? We argue yes! We have developed an exemplar DSL called Vélo that showcases not only dependently typed techniques to realise and manipulate Intermediate Representations (IRs), but that dependently typed languages make fine language workbenches. Vélo is a simple verified language with well-typed holes and comes with a complete compiler pipeline: parser, elaborator, REPL, evaluator, and compiler passes. Specifically, we describe our design choices for well-typed IR design that includes support for well-typed holes, how CSE is achieved in a well-typed setting, and how the mechanised type-soundness proof for Vélo is the source of the evaluator.

Cite as

Jan de Muijnck-Hughes, Guillaume Allais, and Edwin Brady. Type Theory as a Language Workbench. In Eelco Visser Commemorative Symposium (EVCS 2023). Open Access Series in Informatics (OASIcs), Volume 109, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{demuijnckhughes_et_al:OASIcs.EVCS.2023.9,
  author =	{de Muijnck-Hughes, Jan and Allais, Guillaume and Brady, Edwin},
  title =	{{Type Theory as a Language Workbench}},
  booktitle =	{Eelco Visser Commemorative Symposium (EVCS 2023)},
  pages =	{9:1--9:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-267-9},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{109},
  editor =	{L\"{a}mmel, Ralf and Mosses, Peter D. and Steimann, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.EVCS.2023.9},
  URN =		{urn:nbn:de:0030-drops-177797},
  doi =		{10.4230/OASIcs.EVCS.2023.9},
  annote =	{Keywords: dependent types, language workbenches, idris2, dsl, edsl, intrinsically scoped, well typed, co-De Bruijn}
}
Document
Idris 2: Quantitative Type Theory in Practice

Authors: Edwin Brady

Published in: LIPIcs, Volume 194, 35th European Conference on Object-Oriented Programming (ECOOP 2021)


Abstract
Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run. This is promising, because it suggests the ability to design and reason about resource usage protocols, such as we might find in distributed and concurrent programming, where the state of a communication channel changes throughout program execution. As yet, however, there has not been a full-scale programming language with which to experiment with these ideas. Idris 2 is a new version of the dependently typed language Idris, with a new core language based on QTT, supporting linear and dependent types. In this paper, we introduce Idris 2, and describe how QTT has influenced its design. We give examples of the benefits of QTT in practice including: expressing which data is erased at run time, at the type level; and, resource tracking in the type system leading to type-safe concurrent programming with session types.

Cite as

Edwin Brady. Idris 2: Quantitative Type Theory in Practice. In 35th European Conference on Object-Oriented Programming (ECOOP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 194, pp. 9:1-9:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{brady:LIPIcs.ECOOP.2021.9,
  author =	{Brady, Edwin},
  title =	{{Idris 2: Quantitative Type Theory in Practice}},
  booktitle =	{35th European Conference on Object-Oriented Programming (ECOOP 2021)},
  pages =	{9:1--9:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-190-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{194},
  editor =	{M{\o}ller, Anders and Sridharan, Manu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2021.9},
  URN =		{urn:nbn:de:0030-drops-140527},
  doi =		{10.4230/LIPIcs.ECOOP.2021.9},
  annote =	{Keywords: Dependent types, linear types, concurrency}
}
Document
Artifact
Idris 2: Quantitative Type Theory in Practice (Artifact)

Authors: Edwin Brady

Published in: DARTS, Volume 7, Issue 2, Special Issue of the 35th European Conference on Object-Oriented Programming (ECOOP 2021)


Abstract
Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run. This is promising, because it suggests the ability to design and reason about resource usage protocols, such as we might find in distributed and concurrent programming, where the state of a communication channel changes throughout program execution. Idris 2 is a new version of Idris, implemented in itself, and based on Quantitative Type Theory. The paper introduces Idris 2 and describes how QTT has influenced its design, as well as giving several examples of how to use QTT in practice. The artifact, correspondingly, provides an implementation of Idris 2, running on a virtual machine, along with runnable examples from the paper. This document explains how to install the artifact, how to run the examples, and suggests some small ways to experiment with and modify the examples.

Cite as

Edwin Brady. Idris 2: Quantitative Type Theory in Practice (Artifact). In Special Issue of the 35th European Conference on Object-Oriented Programming (ECOOP 2021). Dagstuhl Artifacts Series (DARTS), Volume 7, Issue 2, pp. 10:1-10:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@Article{brady:DARTS.7.2.10,
  author =	{Brady, Edwin},
  title =	{{Idris 2: Quantitative Type Theory in Practice (Artifact)}},
  pages =	{10:1--10:7},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2021},
  volume =	{7},
  number =	{2},
  editor =	{Brady, Edwin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.7.2.10},
  URN =		{urn:nbn:de:0030-drops-140342},
  doi =		{10.4230/DARTS.7.2.10},
  annote =	{Keywords: Dependent types, linear types, concurrency}
}
Document
Pearl
A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl)

Authors: Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)


Abstract
Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold.

Cite as

Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede. A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 20:1-20:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{demuijnckhughes_et_al:LIPIcs.ECOOP.2020.20,
  author =	{de Muijnck-Hughes, Jan and Brady, Edwin and Vanderbauwhede, Wim},
  title =	{{A Framework for Resource Dependent EDSLs in a Dependently Typed Language}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{20:1--20:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.20},
  URN =		{urn:nbn:de:0030-drops-131773},
  doi =		{10.4230/LIPIcs.ECOOP.2020.20},
  annote =	{Keywords: Dependent Types, Algebraic Effect Handlers, Domain-Specific Languages, Embedded Domain Specific Languages, Idris, Substructural Type-Systems}
}
Document
Artifact
A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Artifact)

Authors: Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede

Published in: DARTS, Volume 6, Issue 2, Special Issue of the 34th European Conference on Object-Oriented Programming (ECOOP 2020)


Abstract
Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold.

Cite as

Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede. A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Artifact). In Special Issue of the 34th European Conference on Object-Oriented Programming (ECOOP 2020). Dagstuhl Artifacts Series (DARTS), Volume 6, Issue 2, pp. 2:1-2:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@Article{demuijnckhughes_et_al:DARTS.6.2.2,
  author =	{de Muijnck-Hughes, Jan and Brady, Edwin and Vanderbauwhede, Wim},
  title =	{{A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Artifact)}},
  pages =	{2:1--2:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2020},
  volume =	{6},
  number =	{2},
  editor =	{de Muijnck-Hughes, Jan and Brady, Edwin and Vanderbauwhede, Wim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.6.2.2},
  URN =		{urn:nbn:de:0030-drops-131995},
  doi =		{10.4230/DARTS.6.2.2},
  annote =	{Keywords: Dependent Types, Algebraic Effect Handlers, Domain-Specific Languages, Embedded Domain Specific Languages, Idris, Substructural Type-Systems}
}
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