#+Title: Today

* Kernel
#+BEGIN_SRC C
int x;

// fine; statement
if (1 < 2) x = 3; else x = 5;

// not; expression
x = if (1 < 2) 3 else 5;

// instead you must remember
x = (1 < 2)? 3 : 5;

// no else!
if (1 < 2) printf("noice");

// Often
#define skip      // This does nothing

   if B then S₁;
≈  if B then S₁ else skip;

// What do⁉
int y = if (9 < 2) then 3;

// C# may do something like this
// using the “default” keyword
   if B then S₁;
≈  if B then S₁ else default(T);
   ⇐ provided S₁ is of type T
#+END_SRC
Likewise in Haskell using ~mempty~.


* Monoids

A Monoid is a set C with a binary operation ⊕ and an element ε
such that
+ Identity: x ⊕ ε ≈ x ≈ ε ⊕ x
+ Associtivity: x ⊕ y ⊕ z is “unambiguous”
  - Exercise: What does this mean?

Prime example:
+ Set: Programs
+ Operation: Sequencing
+ Element: skip
+ S₁ ⨾ S₂ ⨾ S₃  with no trouble

#+BEGIN_SRC haskell
➪ Do Nothing: skip
➪ Sequencing: S₁⨾S₂  “do S₁ then do S₂”
#+END_SRC

+ Mother of computation: The Fold!
  - Look it up!
+ Filter, map, fold
  - Exercise: Define sum, max, min, mult, factorial, map, filter, reverse
    in terms of fold.

* Oz

(message-box "woah")

#+BEGIN_SRC oz
{Browse 'noice'}
{Browse 'again'}
#+END_SRC

#+BEGIN_SRC oz
{Show "woah"}
{Show 'explicitly me'}

#+END_SRC

#+RESULTS: