Agda - A dependently typed programming language
Webpage:Agda wiki
Theory:Dependent Type Theory
Implementation:Haskell (GHC)
Authors:Ulf Norell, Nils Anders Danielsson, Andreas Abel, and many more

My contributions to Agda: termination checker, sized types, copatterns, irrelevance, efficient projections, some improvements to unification, many improvements to user experience (UX), many bug fixes, ...


Correct-By-Construction Programming in Agda
14 January 2019, Tutorial at the 46th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2019), Hotel Cascais Miragem, Lisbon, Portugal
Introduction to Dependent Types and Agda
2 lectures during the 8th Summer School on Formal Techniques, Menlo College, Atherton, California, USA, 21-25 May 2018.
Agda Tutorial at Proof and Computation 2016
Autumn School Proof and Computation
3-8 October 2016, Aurachhof, Fischbachau, Bayern, Germany

Tutorial material for live coding: Prelude.agda TreeSortBool.agda TreeSortOrd.agda Copatterns.agda
Solutions: TreeSortOrdSolution.agda CopatternsSolution.agda
Solutions pretty: TreeSortOrdSolution.html CopatternsSolution.html

How to Keep Your Neighbors in Order
An Agda tutorial using Conor McBride's beautiful representation of binary search trees
30 June 2016, guest lecture in Computer Aided Formal Reasoning, class by Gordon Cichon and Martin Hofmann, Institut für Informatik, Ludwig-Maximilians-Universität München
Agda code: .html .zip
Agda Tutorial at FLOPS 2016
13th International Symposium of Functional and Logic Programming (FLOPS 2016)
6 March 2016, Kochi, Japan
Slides: .pdf Start: .agda Solution: .agda Solution pretty: .html
An Introduction to Dependent Types and Agda
Lecture notes (7 pages) for class on functional programming. Uses examples of vectors and sorted lists.
Source code Agda code
Agda: Equality
Lecture notes (6 pages) explaining definitional and propositional equality plus syntax for equality chains.
Source code
Verifying Program Optimizations in Agda. Case Study: List Deforestation
Lecture notes (4 pages) demonstrating provably correct fold-unfold fusion for lists.
Source code

Code Snippets

Parallel substitution for the untyped lambda calculus encoded with de Bruijn indices, plus correctness for substitution composition.
.agda .html
A normalizer for simply typed lambda terms using hereditary substitution. (2017-12-02)
.agda .html
Application of β-normal simply typed lambda terms using parallel hereditary substitution. (2019-10-30)
Description: .pdf Code: .agda .html
A normalizer for full Intuitionistic Propositional Logic (IPL) using hereditary substitution. Basically extends HereditarySubstitutionSTLC.agda to sum types with permutative conversions (and product types and the empty type). The normal form is not unique (no eta). (2018-05-21)
.agda .html
A trick I remember from Conor McBride how to use instance search to get a weak higher-order abstract syntax (WHOAS) interface on top of a de Bruijn representation.
.agda .html


MiniAgda - Termination checking using sized types
Webpage:MiniAgda homepage
Theory:Dependent Type Theory
Implementation:Haskell (GHC ≥ 7.6)
Authors:Andreas Abel, Karl Mehltretter

A Haskell implementation of a core dependently typed language with sized types and recursive and corecursive functions. Every well-typed program is terminating.
See MiniAgda homepage for further information and latest release, and a blog with examples. (The better looking MiniAgda blog has been abandoned).


Helf - Haskell implementation of the Edinburgh Logical Framework
Webpage: Helf repo on github
Theory:Logical Framework (λΠ)
Implementation:Haskell (GHC ≥ 7.8)
Authors:Andreas Abel, Nicolai Kraus

Helf is an implementation of the Edinburgh Logical Framework (LF) in Haskell. The purpose is to compare term representations with regard to their efficiency in practice.

A Lambda Term Representation Based on Linear Ordered Logic
Andreas Abel and Nicolai Kraus (2011)
6th International Workshop on Logical Frameworks and Meta-languages: Theory and Practice, LFMTP 2011, Nijmegen, the Netherlands, August 26, 2011.
.pdf .ps.gz .dvi .bib
Background literature:



Completed Projects

These projects have been completed until 2003:
  • Type checking Fω: Fomega and Church.
  • Tool for teaching natural deduction and dependent types: Proof checker Tutch.
  • Termination checker based on structural ordering: Foetus.


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