Monday, 13 February 2017

Philosophy

I used to think that the only thing that matters in and of itself is coffee.  This weekend though I realised a case can also be made for a good smooth Merlot.  Hm.

Monday, 30 January 2017

The King of France

Bertrand Russell observed that sentence "The present King of France is bald"  is not true - - it can't be as France is no longer a monarchy. He also maintained that "The present king of France is not bald"  is also not true: certainly you can argue that the set of non-bald things does not contain a present king of France.

The law of excluded middle tells us that "For any proposition p, either p is true or not-p, the negation or denial of p, is true" - - and this seems to imply that there is no middle ground - - for any given sentence, either that sentence or its denial is true.  Clearly there is some inconsistency in progress here.

We could say that Russell is trying to run this test:

assert((France.getKing(present).isBald() == true) or 
    (France.getKing(present).isBald() == false))

However, his problem is that France.getKing(present) returns null, and so the call to isBald() throws a method-called-on-invalid-object exception.  Ah, dammit.  Now what?



Friday, 9 December 2016

Plots have I laid, inductions dangerous

Time to do some F#.

First I want a function that will tabulate a function f.

f is to be a function of two floats x and y returning a float. The table is to operate over an x-axis range and a y-axis range, each described by a tuple of floats.  So here is a sample function of the type I mean:

let testfun (x:float) (y:float) =
    let r = sqrt ((x * x) + (y * y))
    if r < 2.0
    then
        if r < 1.0
        then 7.0
        else 4.0
    else
        0.0

My tabulate function is to return a two-dimensional array of floats.  Here it is:

let tabulate funct (xrange : (float*float)) (yrange : (float*float)) : float[,]=
    let x0 = fst xrange
    let dx = (snd xrange - fst xrange) / 50.0
    let y0 = fst yrange
    let dy = (snd yrange - fst yrange) / 50.0
    Array2D.init 51 51 (fun i j -> funct (x0+(float i * dx)) (y0+(float j * dy)))

The function Array2D.init takes the size of the two dimensions of the array and a function that will populate each element in the array, given the indices I and j. I'm breaking my ranges into 50 parts so I want 51 elements in each direction.

Now to project this table of values as in isometric type sheet: create a new array of the same size but here each element is a tuple of values p and q that represent screen coordinates. p works down from the top left and q works across. So p and q depend on the index i and j, and p also depends on the value of the array that I've passed through.  I've scaled the value by 10.0 pixels quite arbitrarily. The grid is drawn by going right 5 pixels per cell and either up or down by 3.5 pixels for p and q axis, so:

let project (valueTable : float [,]) : (float * float)[,] =
    Array2D.init 51 51
        (fun (i:int) (j:int) ->
            let p = (float i * 5.0) + (float j * 5.0) + 20.0
            let q = (float i * 3.5) - (float j * 3.5) + 300.0 - (valueTable.[i,j] * 10.0)
            (p,q)) 

Right, now I want to plot out the projected table as an SVG element. After some research it looks like this is the thing to do:

let plot (a:(float * float)[,]) : unit =
    use file = System.IO.File.CreateText("plotout.svg")
    fprintfn file """<svg xmlns="http://www.w3.org/2000/svg" version="1.1">"""
    for j in 0..49 do
        for i in 0..49 do
            fprintf file """<polygon fill="#FFFFFF" """
            fprintf file """stroke="#000000" stroke-width="1" points="""
            fprintfn file "\"%.2f,%.2f %.2f,%.2f %.2f,%.2f %.2f,%.2f\" "
                (fst a.[i,j]) (snd a.[i,j])
                (fst a.[i,j+1]) (snd a.[i,j+1])
                (fst a.[i+1,j+1]) (snd a.[i+1,j+1])
                (fst a.[i+1,j]) (snd a.[i+1,j])
            fprintfn file """/>"""
    fprintfn file """</svg>"""

The SVG document contains a polygon element which has a fill colour and a stroke width and colour and a list of points - each point is represented by a two floats separated by a comma. For each element i, j I'm drawing a four sided shape with the points from i,j - i+1,j - i+1,j+1 - i,j+1.

So finally to tabulate and plot my test function in the range -3 to 3:

let main () =
    (tabulate testfun (-3.0, 3.0) (-3.0, 3.0)) |> project |> plot

Then you can open the resulting file in the browser:



This looks a bit rough round the back of the raised area.  Really I need to plot starting from the cells that are furthest away and then working forward, so get the hidden ones properly hidden. Still, nice first try.

Friday, 25 November 2016

Random Questions

  • What is "Black Friday", and why?
  • What is a "comfort zone" and where do I get one?  Can I rent or do I buy it?
  • Is a "steep learning curve" one where I get from the bottom to the top quickly and easily or one where the route from the bottom to the top is difficult? (It's a lousy metaphor if it works two contradictory ways).
  • How much exactly is "most if not all"? Most? All? Which? Either? On the same note how hard is "difficult if not impossible"? So difficult it's effectively impossible? Or very difficult but not actually impossible? Or either difficult or impossible but you don't know which? Why not find out and tell us instead of leaving us dangling with an "if"...? What if I said, "The answer to your question is yes if not no"... How informed would you be?

Friday, 4 November 2016

F Sharp for Pleasure and well just pleasure really

The language F# has its origins at Microsoft and is now available in the latest versions of Visual Studio - but looking at fsharp.org I see there is an option to use F# on Linux.

But first you need Mono for it to run on... which I did basically by following the instructions on the Mono site.  The instructions are nice and clear so I resist the inclination to copy them here.

Then to test.  Create a file called hello.cs containing this code:

using System;

public class HelloWorld
{
    static public void Main ()
    {
        Console.WriteLine ("Hello Mono World");
    }
}

Then on the command line (you can come out of super user mode now) compile with this command:

mcs hello.cs

This creates a file called hello.exe that you can execute:

$ mcs hello.cs
$ ls h*
hello.cs  hello.exe
$ ./hello.exe
Hello Mono World
$ mono hello.exe
Hello Mono World


You can execute with the command mono but I didn't spot this and I find you can invoke the hello.exe directly. What have I just done? Blimey I've typed in and compiled a C# program almost without realising it.

So anyway that does demonstrate that Mono is installed... jolly good.

So I next need

apt-get install fsharp

Looks ok.  This installs fsharpc (the compiler) and fsharpi (the interactive REPL)

Possibly at this point... install Visual Studio Code...?

OK go on then.

Had to log off and log on as administrator to get this to work. It's a download from the Visual Studio Code web site.

However this seems to be in place.  Then you add the F-Sharp mode to the editor by going

Ctrl-P
ext install Ionide-fsharp


Then you select the right one, opt to install and then activate.

So that was very successful - the F Sharp site and the Mono site have excellent instructions for getting set up.

Now also there is an F-Sharp mode for Emacs.  I'll look into that another day.

Thursday, 3 November 2016

Crossing the Bridge

And having started from that left hand end of the bridge in an engineering role I have tried to explore some of the delights that await as you cross to the other side.

One of the odd pleasures of this challenge is seeing how difficult things become clear... but if anything even more delightful is to find how obvious things start to become problems.

A processor has executed an instruction. What can it do next? Just three things.

It can move on to the next instruction: and so the idea of a sequence is natural and obvious.

It can jump back to a previous instruction. And so the idea of a loop is present, but not yet obvious. We know that to jump back just anywhere is the road to madness. The jump has to be educated, trained to fit into the pattern. I write lots of flowcharts. To apply the pattern I have a rule that jumps back from the main flow must go to the right (anticlockwise) and furthermore no line is allowed to cross another.  So this is allowed:

But this is not:

Stick to the discipline and you have created the logic of the loop from the potential chaos of the jump.

And what is the other option? The processor can jump forward. Therefore it has opted to omit some part of the process, we are creating the conditional if / else construction. Here again my jumps need to submit to the discipline: all jumps down must go to the right, and no line is allowed to cross another. So this is allowed:

But not this:

This is what a proper if / else brings out in a higher level language.

And so given the sequence, the loop, and the conditional, we have the essence of structured programming. Everything we need.

What could be more obvious?

But then we start to wander across this enchanted bridge and soon we discover mysteries.

I clearly remember when I was learning Scheme, just about the first thing I wanted to write was the table of Celsius to Fahrenheit conversion from somewhere near the start of Kernighan & Ritchie. And I sat there thinking... just a minute, hold it right there, how exactly do I write a FOR loop? Surely there's got to be a way to write a FOR loop, otherwise...

Then of course you encounter the delights of looping by recursion, and the more mature delight of realising that your loops dissolve in functions that operate on collections directly, you discover MAP and FOLD and FILTER and so on. So the loop, which seemed so obviously essential to programming, becomes a stage that you leave behind. Odd. Disturbing and yet illuminating.

How truly it is written, In the search of the Way, every day something is left behind (Tao Te Ching Ch.48)

Next you discover pattern matching and see how a function can fork according to the structure of its arguments and you start to realise that you can make conditions without going through IF... in fact do you need IF at all? Can all your decisions be made on the basis of pattern matching with the odd guard or two here and there? Does IF go in the bin next to LOOP?

Then the final stage of your enlightenment comes when you discover that the sequence has now... gone. That most obvious thing of all, the increment of the program counter, becomes a problem that the Masters have to invoke arcane spells from mathematics to solve.

It turns out that even


is no longer allowed...