fragmentary ideas ䷿ intellectual what-nots ䷷ and haskell programming ䷴

I’ve just started trying to learn and debug Template Haskell and found it a bit rough trying to explore TH interactively, but a couple of things have helped.

First and most obvious, we can use runQ to see the abstract TH syntax which a quasi-quoted expression expands to:

Prelude> :set -XTemplateHaskell
Prelude> :m + Language.Haskell.TH
Prelude Language.Haskell.TH> runQ [| \a -> a+1 |]
LamE [VarP a_1] (InfixE (Just (VarE a_1)) (VarE GHC.Num.+) (Just (LitE (IntegerL 1))))

Read the rest of this article »

Note: this is part of a series of posts is related to the “17×17 Challenge” posted by Bill Gasarch. The goal is to color cells of a 17 by 17 grid, using only four colors, such that no rectangle is formed from four cells of the same color.

Just a few follow-ups to my previous post in which I use a simulated annealing-type algorithm to find a good (hopefully complete) cover of a grid by swapping rows and columns from four identical sub-grids of 74 colors.

Easing into new thresholds

I modified my algorithm so that the likelihood of jumping into the highest permitted energy level is decreased over time; thus instead of having an abrupt transition to a new threshold, resulting in a steep dive, we instead ease into the new energy level.

Here is a graph of a run with the adjusted meta-heuristic (in blue) alongside a previous abrupt threshold transition run (in black). You can check compare it to the graph from the previous post:

Read the rest of this article »

Note: this is part of a series of posts is related to the “17×17 Challenge” posted by Bill Gasarch. The goal is to color cells of a 17 by 17 grid, using only four colors, such that no rectangle is formed from four cells of the same color.

In my last post I noticed that all of the smaller optimal single-colorings I generated showed diagonal symmetry, meaning that row 1 is the same as column 1, row 8 is the same as column 8, etc. It’s my hypothesis that all complete single-colorings are symmetrical in this way.

I decided to play with making the known 74-cell subset symmetrical by applying rotations and came up with this:

Read the rest of this article »