## Observations of Kirch’s comet 1680-81

The observations Newton used to calculate the orbit of Kirch’s comet can be found in the tables in http://www.newtonproject.ox.ac.uk/view/texts/diplomatic/NATP00301 page 491. Observations up to 5 February are by Flamsteed; later observations are by Newton. Different versions of these tables exist. This version is sufficient to demonstrate the calculation. I have not found the Newton Project’sContinue reading “Observations of Kirch’s comet 1680-81”

## Installing Diagrams

In preparation for my forthcoming series reproducing Newton’s calculation of the orbit of Kirch’s comet, I have been investigating Brent Yorgey’s Diagrams package. After successfully running the tutorial example in https://diagrams.github.io/doc/quickstart.html#your-first-diagram once, I had difficulties using it in new projects (and even reproducing the tutorial), for possibly related reasons: I usually use stack for development,Continue reading “Installing Diagrams”

## Countdown 2

In my previous post, I bodged a function to aggregate additions and multiplications into a program based on individual binary operations. This is what it looks like if it is designed to use Sum’ (the prime disambiguates it from the built-in monoid) and Prod from the beginning. It is only a little shorter, and muchContinue reading “Countdown 2”

## Countdown

This post is based on chapter 9 of https://www.cambridge.org/gb/academic/subjects/computer-science/programming-languages-and-applied-logic/programming-haskell-2nd-edition?format=PB. The game of countdown is to combine a list of integers using common operations to make a target. The allowed operations are +, -, * and /, with the restrictions that the result of a subtraction (even as an intermediate value) must not be negative, andContinue reading “Countdown”

## Jug Puzzles

Jug problems are a popular puzzle: given a set of jugs with distinct* integral capacities that are otherwise unmarked, measure out a specified integral volume of liquid. For example, you may have jugs with capacities of 5, 8 and 12 litres (Americans may substitute gallons, and Texans may substitute hats for jugs) and be askedContinue reading “Jug Puzzles”

## Free Monads

Free monads are monads with the bare minimum of properties. They are useful because they can be chained together and interpreted in different ways. The example below shows a program with two interpreters: one that executes the program and one that prints it out. The best introduction I have found is https://www.haskellforall.com/2012/06/you-could-have-invented-free-monads.html. Free monads areContinue reading “Free Monads”

## My first monad tutorial

Most books and web tutorials devote a lot of attention to deriving monads, and only briefly show how they are used in real life. For instance, here is Graham Hutton relabelling a tree with integers: Bear in mind that monads are supposed to make programming easier. Here, without confusing explanations, is how to do itContinue reading “My first monad tutorial”

## Permutations with constraints – magic square

Starting from my previous post, I add code to apply constraints as permutations are being generated. This is still faster than Tsoder’s brute force method, but slower than my list comprehension methods. I like the way permutations and constraints are separated I dislike the way the constraints are based on the recursion depth, which keepsContinue reading “Permutations with constraints – magic square”

## Permutations with constraints

In order to apply constraints while generating permutations, I needed a new algorithm. Haskell’s library function Data.List.permutations builds permutations using interleave, so each item added could end up anywhere in the list. I needed items to stay in the same place once chosen. Note that this performs much worse than Data.List.permutations, because it has toContinue reading “Permutations with constraints”

## Magic Square by brute force

This was inspired by Tsoder’s video https://www.youtube.com/watch?v=Qf4NyHiy0W8 where he generated all the 3×3 magic squares by brute force, generating all permutations of 1-9 and rejecting the ones which were not magic squares. My first reaction was that that was not brute force; this was brute force: This turned out to be faster than Tsoder’s method,Continue reading “Magic Square by brute force”

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