# Lambda Blues

## Wednesday, 20 September 2017

### Message to my younger self.

(Yes I know this doesn't work)

In your life you will have time to do exactly ONE thing.

So decide soon what your one thing is going to be and stick to it.

Don't be tempted to bite off more than you can chew, and don't let them feed you more than you can chew.

Don't starve with your mouth so full you can't swallow.

When you have to, spit.

Focus.

## Monday, 27 March 2017

## Friday, 24 March 2017

## 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?

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, 23 December 2016

## Friday, 9 December 2016

### Plots have I laid, inductions dangerous

Time to do some F#.

First I want a function that will

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

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

Now to

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

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

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.

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.

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