Dependent Type Archives - Page 2 of 2 - niche computing science

Well-Founded Recursion and Accessibility

April 20, 2008 September 30, 2008 / Agda, Dependent Type, Termination

Given a relation < that has been shown to be well-founded, we know that a recursively defined function is terminating if its arguments becomes “smaller” with respect to < at each recursive call. We can encode such well-founded recursion in Agda’s style of structural recusion.

Terminating Unfolds (2)

April 13, 2008 May 5, 2008 / Agda, Dependent Type, Termination

After seeing our code, Nils Anders Danielsson suggested two improvements. Firstly, to wrap the bound in the seed. Secondly, to define unfoldT↓ using well-founded recursion.

Terminating Unfolds (1)

April 8, 2008 April 13, 2008 / Agda, Dependent Type, Termination

I hope to come up with a variation of unfoldr which, given a proof of well-foundedness, somehow passes the termination check.

AoPA — Algebra of Programming in Agda

March 30, 2008 March 30, 2015 / Agda, Dependent Type, Optimisation Problems, Program Derivation

The AoPA library allows one to encode Algebra of Programming style program derivation, both functional and relational, in Agda, accompanying the paper Algebra of Programming Using Dependent Types (MPC 2008) developed in co-operation with Hsiang-Shang Ko and Patrik Jansson.

Agda Exercise: Proving that Mergesort Returns Ordered Lists

September 28, 2007 November 27, 2007 / Agda, Dependent Type

This time I am implementing the example in another section of Why Dependent Types Matter by Altenkirch, McBride, and McKinna in Agda: proving that mergesort returns an ordered list.

Agda Exercise: Sized Mergesort

September 27, 2007 November 27, 2007 / Agda, Dependent Type

Continuing with my Adga programming practice. Part of the mergesort example became easy once Max showed me how I should perform the pattern matching in insert.

My First Agda Program: Append, Reverse, and Merge

September 19, 2007 November 27, 2007 / Agda, Curry-Howard, Dependent Type

During the WG 2.1 meeting, my attention was brought to Agda. So, here is my first Agda program. I am merely repeating some simple exercises on lists, which I tried using Haskell in a previous entry Developing Programs and Proofs Spontaneously using GADT.

Developing Programs and Proofs Spontaneously using GADT

August 6, 2007 November 27, 2007 / Curry-Howard, Dependent Type, GADT, Haskell, Types

I am curious about the possibility of developing Haskell programs spontaneously with proofs about their properties and have the type checker verify the proofs for us, in a way one would do in a dependently typed language. I tried to redo part of the merge-sort example in Altenkirch, McBride, and McKinna’s introduction to Epigram: deal the input list into a binary tree, and fold the tree by the function merging two sorted lists into one.