CID Outreach at Aston University

Overview

Web-based exact function/fractal plotter

Visualise rigorous approximationsArbitrary accuracySome obviously infinite behaviours

Short talks for 16-17 year olds

Computing with infinite data is coolInfinite data simplifies programs and reasoning

Project on verification of numerical software

50% funded by AdaCoreFocus on SPARK/Ada and FP

Junaid Rasheed's PhD project

https://github.com/michalkonecny/exact-function-plotter

Short talks for 16-17 year olds 30 min talkto 30 selected school studentsin a 4/5-day programming workshop

- Appreciate infinity in computation- Infinite structures simplify programs, their specifications and reasoning

Goals of talk

sqrt(s) = sqrtB(10,s)sqrtB(0, s) = 1sqrtB(n, s) =

let x = sqrtB(n-1, s)in (x + s/x) / 2

sqrt(s) ~

for all s ...around 4 billion values of s

is the program correct?

take 10 sqdiv11 =[1,10,12,21,23,32,34,43,45,54]

demo

divisible by 11

sqdiv11 = [x|x<-[1..], (x*x-1) `mod` 11 == 0]

Short talks for 16-17 year olds 30 min talkto 30 selected school studentsin a 4/5-day programming workshop

- Appreciate infinity in computation- Infinite structures simplify programs, their specifications and reasoning- See how computation involving infinite lists works

Goals of talk

[1,2,3] = 1 : (2 : (3 : []))

take 3 [1..] = take 3 (1:(2:(3:(from 4)))) = 1:(2:(3:[])) = [1,2,3]

from n = n : (from (n + 1))

[1..] = from 1 = 1 : (from 2) = 1 : (2 : (from 3)) = 1 : (2 : (3 : (from 4))) = ... = 1 : (2 : (3 : (4 : ... )))

Short talks for 16-17 year olds 30 min talkto 30 selected school studentsin a 4/5-day programming workshop

- Appreciate infinity in computation- Infinite structures simplify programs, their specifications and reasoning- See how computation involving infinite lists works- Observe exact real computation

Goals of talk

Real numbers are infinite = 3.14159265358979323846264338327950288419716939937510582097494459230781 640628620899862803482534211706798214808651328230664709384460955058223

172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986...

inifinitely many digitsno "simple" patternbut a "complex" pattern:a computer program

(by Jens Blanck, https://github.com/jensblanck/cdar)

π

Short talks for 16-17 year olds 30 min talkto 30 selected school studentsin a 4/5-day programming workshop

- Appreciate infinity in computation- Infinite structures simplify programs, their specifications and reasoning- See how computation involving infinite lists works- Observe exact real computation

- Observe and reflect on reliable approximations of numbers, real functions, 2D curves, simple fractals

Goals of talk

1. Specifications using real numbers2. 3.

1.

1. Specifications using real numbers2. Better prover support3.

1.

2.

1. Specifications using real numbers2. Better prover support3. Executable specifications with reals

1.

2.

SPARKintervalarithmetic

3.