Well-Foundedness and Reductivity
It seems that reductivity of Doornbos and Backhouse is in fact accessibility, which is often taken by type theorists to be an alternative definition of well-foundedness.
Agda
Well-Founded Recursion and Accessibility
Given a relation
Terminating Unfolds (2)
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)
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
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.
Maximum Segment Sum, Agda Approved
To practise using the Logic.ChainReasoning module in Agda, Josh proved the foldr-fusion theorem, and I thought it would be an small exercise over the weekend to start off where he finished…
Agda Exercise: Proving that Mergesort Returns Ordered Lists
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
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
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.