Digital Science Cambridge Retreat 2014 slides about "Fundamentals of Computing".

1. http://wedesoft.de/downloads/cambridge2014.pdf
Fundamentals of Computing
1/18c 2014 Jan Wedekind, Digital Science

2. http://wedesoft.de/downloads/cambridge2014.pdf
motivation
The Hundred-Year Language
2/18c 2014 Jan Wedekind, Digital Science
Paul Graham

3. http://wedesoft.de/downloads/cambridge2014.pdf
motivation
not fundamentals of computing
3/18c 2014 Jan Wedekind, Digital Science

4. http://wedesoft.de/downloads/cambridge2014.pdf
motivation
Building Your Own Dynamic Language
4/18c 2014 Jan Wedekind, Digital Science
Ian Piumarta
http://piumarta.com/papers/EE380-2007-slides.pdf

5. http://wedesoft.de/downloads/cambridge2014.pdf
motivation
Building Your Own Dynamic Language
5/18c 2014 Jan Wedekind, Digital Science
Application
System
Hardware
Libraries
Compiler
Syntax
SemanticsSource
Runtime
Language
Environment
malleable (under programmer control)
rigid (imposed fromoutside)
"black box" (hermetically sealed)
Pragmatics
UDP

6. http://wedesoft.de/downloads/cambridge2014.pdf
λ-calculus
core
6/18c 2014 Jan Wedekind, Digital Science
x, y, z, . . . ∈ L
M ∈ L ⇒ λx.M ∈ L
M, N ∈ L ⇒ (MN) ∈ L
recursive definition
x, y, z
lambda { |x| M }
M.call(N)
Ruby
x y z
(lambda (x) M)
(M N)
Scheme
abbreviations:
• λab.M ≡ λa.λb.M
• MNO . . . = ((. . . (MN)O) . . .)

7. http://wedesoft.de/downloads/cambridge2014.pdf
λ-calculus
Church encoding
7/18c 2014 Jan Wedekind, Digital Science
id ≡ λx.x
true ≡ λa.λb.a
nil ≡ false ≡ λa.λb.b
if1
≡ λabc.abc
and ≡ λmn.mnm
or ≡ λmn.mmn
not ≡ λm.λab.mba
=bool ≡ λab.ab(not b)
1lazy evaluation
pair ≡ λhtx.(if xht)
head ≡ λl.(l true)
tail ≡ λl.(l false)
empty ≡ λl.(l (λhtb.false) true)

8. http://wedesoft.de/downloads/cambridge2014.pdf
λ-calculus
binary numbers
8/18c 2014 Jan Wedekind, Digital Science
0 ≡ nil
1 ≡ (pair true nil)
2 ≡ (pair true (pair false nil))
3 ≡ (pair true (pair true nil))
...

9. http://wedesoft.de/downloads/cambridge2014.pdf
Scheme
variable definitions ⇔ λ-expressions
9/18c 2014 Jan Wedekind, Digital Science
Scheme uses eager evaluation
((lambda (f)
((lambda (x y)
(f x y))
2 3))
(lambda (a b) (+ a b)))
; 5
(let ((f (lambda (a b) (+ a b)))
(x 2) (y 3))
(f x y))
; 5
; (define f (lambda (a b) (+ a b)))
(define (f a b) (+ a b))
(define x 2) (define y 3)
(f x y)
; 5

10. http://wedesoft.de/downloads/cambridge2014.pdf
Scheme
recursion ⇔ higher-order function
10/18c 2014 Jan Wedekind, Digital Science
(define (neg l)
(if (null? l)
’()
(cons (- (car l))
(neg (cdr l)))))
(neg (list 1 2 3))
; (-1 -2 -3)
(sum (list 1 2 3))
(define (sum l)
(if (null? l)
0
(+ (car l)
(sum (cdr l)))))
(sum (list 1 2 3))
; 6
(use-modules (srfi srfi-1))
(map - (list 1 2 3))
; (-1 -2 -3)
(fold + 0 (list 1 2 3))
; 6

11. http://wedesoft.de/downloads/cambridge2014.pdf
Scheme
currying
11/18c 2014 Jan Wedekind, Digital Science
(use-modules (srfi srfi-1))
(use-modules (srfi srfi-26))
(map (cut + <> 1) (list 1 2 3))
; 2 3 4

12. http://wedesoft.de/downloads/cambridge2014.pdf
Scheme
quote, eval & apply
12/18c 2014 Jan Wedekind, Digital Science
(quote +)
; +
(quote (+ 1 2))
; (+ 1 2)
(car (quote (+ 1 2)))
; +
(eval (quote (+ 1 2)) (current-module))
; 3
(eval (car (quote (+ 1 2))) (current-module))
; #<procedure + (#:optional _ _ . _)>
(apply + (list 1 2))
; 3

13. http://wedesoft.de/downloads/cambridge2014.pdf
Scheme
(hygienic) macros ⇔ lazy evaluation
13/18c 2014 Jan Wedekind, Digital Science
(define-syntax-rule (lazy expr) (lambda () expr))
(define-syntax-rule (force expr) (expr))
(define y (let ((x 2)) (lazy (+ x 3))))
y
; #<procedure 105992de0 at <current input>:10:0 ()>
(force y)
; 5

14. http://wedesoft.de/downloads/cambridge2014.pdf
14/18c 2014 Jan Wedekind, Digital Science
closures, monads, prompts, delimited
continuations, combinators, reification, multiple
dispatch, generics using functions,
Y-combinator, Iota & Jot, reflection,
inspection, readers, Factor, Haskell

15. http://wedesoft.de/downloads/cambridge2014.pdf
More References
Binary Lambda Calculus
15/18c 2014 Jan Wedekind, Digital Science
John Tromp

16. http://wedesoft.de/downloads/cambridge2014.pdf
More References
Structure and Interpretation of Computer
Programs
16/18c 2014 Jan Wedekind, Digital Science
Harold Abelson & Gerald Sussman

17. http://wedesoft.de/downloads/cambridge2014.pdf
More References
Understanding Computation
17/18c 2014 Jan Wedekind, Digital Science
Tom Stuart

18. http://wedesoft.de/downloads/cambridge2014.pdf
More References
Schemer books
18/18c 2014 Jan Wedekind, Digital Science
The



Little
Seasoned
Reasoned



Schemer: Q&A-style books