Algorithmic logic: Różnice pomiędzy wersjami
Z Lem
| Linia 9: | Linia 9: | ||
----------------- | ----------------- | ||
class Node | class Node | ||
| − | { | + | { |
Node l,r; | Node l,r; | ||
Key k; | Key k; | ||
| − | |||
Node( Key _k ) : k(_k) {} | Node( Key _k ) : k(_k) {} | ||
| − | } | + | } |
| − | + | ||
| − | void insert( Node n, Key k ) | + | void insert( Node n, Key k ) |
| − | { | + | { |
loop | loop | ||
{ | { | ||
| Linia 40: | Linia 39: | ||
return; | return; | ||
} | } | ||
| − | } | + | } |
| − | + | ||
| − | bool contains( Node n, Key k ) | + | bool contains( Node n, Key k ) |
| − | { | + | { |
while( n ) | while( n ) | ||
{ | { | ||
| Linia 55: | Linia 54: | ||
} | } | ||
return false; | return false; | ||
| − | } | + | } |
| + | ----------------- | ||
Wersja z 21:43, 7 sty 2015
Algorithmic logic is a logical calculus. More than this it is also a calculus of programs.
We begin with an example ot its usefulness.
Are you ready?
A challenge
Given the piece of software NIC consisting of a class Node and two functions insert and contains (see below) prove or disprove the following formula
[math] NIC \vdash \forall_{n_0 \in Node} \forall_{e \in T}\,[\textbf{call } insert(n_0,e)]contains(n_0,e) [/math]
i.e. it is a logical consequence of admitting declarations of class Node and functions insert and contains, that for every object [math]n_0 [/math], and for every element [math]e [/math] of type [math]T [/math], after execution of command [math]insert(n_),e) [/math] holds [math]contains(n_0,e) [/math].
class Node
{
Node l,r;
Key k;
Node( Key _k ) : k(_k) {}
}
void insert( Node n, Key k )
{
loop
{
if( k < n.k )
if( n.l )
n := n.l;
else
{
n.l := new Node( k );
return;
}
else
if( n.k < k )
if( n.r )
n := n.r;
else
{
n.r := new Node( k );
return;
}
else
return;
}
}
bool contains( Node n, Key k )
{
while( n )
{
if( k < n.k )
n := n.l;
else
if( n.k < k )
n := n.r;
else
return true;
}
return false;
}
