QOTD

I consider it extremely important–perhaps vital, even–to spend time engaging others intelligently who have diverging views from one’s own. I think that this is, on the whole, one of the most valuable uses of one’s time that exists. Whether it’s consulting a disagreeable book or a person, somehow at the intersection of intelligence and difference lies a “something” that is mind-expanding.

From Sealed Abstract - Why I stopped reading HN via @conal

Single exponential smoothing and foldl

Recently I looked at simple techniques for time series smoothing and forecasting. One such primitive method is the single exponentially weighted moving average (SEWMA), defined as



where the sequences are indexed from 1. denotes an observed value of the time series and a SEWMA value. In words, this recursive definition expresses that the next SEWMA value is a weighted average of the curent observed and SEWMA values.

If I pose the question "What is the predicted value for the next time series observation?" we just apply the formula.


A typical imperative implementation

sewma <- function (alp, y) {
  S <- y[1]
  for (t in 2:length(y)) { S <- alp * y[t] + (1-alp) * S }
  S
}

This is R code, but it should look familiar enough to anyone who has written Java, C#, etc.


Haskell implementation
In Haskell, a fold is a way of recursively iterating a data structure, accumulating a return value. The left fold has type

foldl :: (a -> b -> a) -> a -> [b] -> a
foldl f s y = ...

Denote one of the values from the conceptual sequence of accumulator values as . The function f maps from the current accumulator and list values to the next accumulator value



which is the form of the SEWMA equation above. The foldl1 function is a specialisation of foldl that uses the first value of the list as the initial accumulator value, yielding the implementation

sewma alp = foldl1 (\s y -> alp * y + (1-alp) * s)

Revisiting R
R has the Reduce function for performing folds.

sewma <- function (alp, ys) {
  Reduce(function (S, y) { S <- alp * y + (1-alp) * S }, ys[2:length(ys)], ys[1])
}

Summary
If accumulating a value over a data structure can be represented with a step function of the form



then a left fold captures the recursive implementation.

Haskell mode in MacVim

I set up Haskell mode (haskellmode-20100622.vba) in MacVim 7.3 (53). As a Vim newbie I found this page useful, even though it says pretty much the same thing as the Haskell mode project page.

I followed the instructions and created $HOME/.vimrc with these contents.

" use ghc functionality for haskell files
au Bufenter *.hs compiler ghc

" switch on syntax highlighting
set syntax on

" enable filetype detection, plus loading of filetype plugins
set filetype plugin on

" Configure browser for haskell_doc.vim
let g:haddock_browser = "open"
let g:haddock_browser_callformat = "%s %s"

Unfortunately when I edited a Haskell file none of the Haddock integration was working. I assume the haskell_doc.vim filetype plugin wasn't being loaded because the :DocSettings command failed with E492: Not an editor command.

After some hours I changed the line set filetype plugin on to :filetype plugin on and Haddock integration now works (don't know why). I am using the Haskell Platform which includes the documentation.

After reading A minimal Vim configuration I have switched from $HOME/.vimrc to $HOME/.gvimrc with these contents.

" line numbers
set number

" show the cursor line and column number
set ruler

" turn off blinking cursor in normal mode
set gcr=n:blinkon0

" hide the toolbar
set go-=T

" switch on syntax highlighting
set syntax

" highlight matches in a search (hls)
" show the current matching pattern as you search (is),
" ignore case (ic) unless you are searching for both upper and lowercase letters (scs)
set hls is ic scs

" use ghc functionality for haskell files
au Bufenter *.hs compiler ghc

" enable filetype detection, plus loading of filetype plugins
:filetype plugin indent on

" Configure browser for haskell_doc.vim
let g:haddock_browser = "open"
let g:haddock_browser_callformat = "%s %s"