# HG changeset patch
# User Christian Urban <christian dot urban at kcl dot ac dot uk>
# Date 1386239375 0
# Node ID 70198792c2aa29f3d229152fc5b4b13b52984e89
# Parent  e4b29b57f6a3240d065be53924d824e07aa9b9d4
added

diff -r e4b29b57f6a3 -r 70198792c2aa progs/defs.rec
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/defs.rec	Thu Dec 05 10:29:35 2013 +0000
@@ -0,0 +1,76 @@
+
+def zero(x) = 0;
+
+def suc(x) = x + 1;
+
+def pred(x) = if x == 0 then x else x - 1;
+
+def add(x, y) = if x == 0 then y else suc(add(x - 1, y));
+
+def mult(x, y) = if x == 0 then 0 else add(y, mult(x - 1, y));
+
+def pow(x, y) = if y == 0 then 1 else mult(x, pow(x, y - 1));
+
+def fib(n) = if n == 0 then 0 
+             else if n == 1 then 1 
+             else fib(n - 1) + fib(n - 2);
+
+def fact(n) = if n == 0 then 1 else n * fact(n - 1);
+
+def ack(m, n) = if m == 0 then n + 1
+                else if n == 0 then ack(m - 1, 1)
+                else ack(m - 1, ack(m, n - 1));
+
+def stack_test(x) = x + 1 + 2 + 3 + 4 + 5;
+
+def div(x, y) = x / y;   //integer division
+
+def rem(x, y) = x % y;   //remainder
+
+def gcd(a, b) = if b == 0 then a else gcd(b, a % b);
+
+def is_prime_aux(n, i) = 
+  if n % i == 0 then 0
+  else if (i * i) <= n then is_prime_aux(n, i + 1)  
+  else 1;
+
+def is_prime(n) = if n == 2 then 1 else is_prime_aux(n, 2);
+
+def primes(n) = 
+  if n == 0 then 0
+  else if is_prime(n) == 1 then (write n; primes(n - 1)) 
+  else primes(n - 1);
+
+def is_collatz(n) =
+  if n == 1 then 1
+  else if n % 2 == 0 then is_collatz(n / 2)
+  else is_collatz(3 * n + 1);  
+
+def collatz_aux(n, i) = 
+  if i > n then 0
+  else if is_collatz(i) == 1 then (write i; collatz_aux(n, i + 1)) 
+  else collatz_aux(n, i + 1);
+
+def collatz(n) = collatz_aux(n, 1);
+
+def facT(n, acc) = if n == 0 then acc else facT(n - 1, n * acc);
+
+
+//zero(3)
+//suc(8)
+//pred(7)
+//add(3, 4)
+//mult(4,5)
+//pow(2, 3)
+//fib(20)
+//(write(fact(5)) ; fact(6))
+//(write(1) ; 2)
+//ack(2, 3)
+//stack_test(0)
+//(write (div(11, 3)); rem(11, 3))
+//gcd(54, 24)
+//is_prime(2)
+primes(1000000)
+//collatz(5000)
+//facT(6, 1)
+
diff -r e4b29b57f6a3 -r 70198792c2aa progs/fact.rec
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/fact.rec	Thu Dec 05 10:29:35 2013 +0000
@@ -0,0 +1,8 @@
+def fact(n) = if n == 0 then 1 else n * fact(n - 1);
+
+def facT(n, acc) = if n == 0 then acc else facT(n - 1, n * acc);
+
+facT(15, 1)
+
+//fact(15)
+
diff -r e4b29b57f6a3 -r 70198792c2aa slides/slides10.pdf
Binary file slides/slides10.pdf has changed
diff -r e4b29b57f6a3 -r 70198792c2aa slides/slides10.tex
--- a/slides/slides10.tex	Wed Dec 04 01:51:22 2013 +0000
+++ b/slides/slides10.tex	Thu Dec 05 10:29:35 2013 +0000
@@ -615,8 +615,7 @@
 \begin{frame}[c]
 
 \Large\bf
-There are more problems, than there are programs.\bigskip\bigskip\pause\\
-
+There are more problems, than there are programs.\bigskip\bigskip\\
 There must be a problem for which there is no program.
 \end{frame}}
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