12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Sunday May 05, 2024
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Propositions As Types (view source)
Revision as of 20:42, 26 March 2009
, 20:42, 26 March 2009→Basic Concepts from Lambek and Scott (1986)
===Graph===
===Graph===
<pre>
{| align="center" cellpadding="8" width="90%" <!--QUOTE-->
|
|
<p>'''Definition 1.2.''' A ''graph'' (usually called a ''directed graph'') consists of two classes: the class of ''arrows'' (or ''oriented edges'') and the class of ''objects'' (usually called ''nodes'' or ''vertices'') and two mappings from the class of arrows to the class of objects, called ''source'' and ''target'' (often also ''domain'' and ''codomain'').</p>
<br><pre>
o--------------o source o--------------o
| | ----------------> | |
| Arrows | | Objects |
| | ----------------> | |
o--------------o target o--------------o
</pre><br>
</pre>
<p>One writes <math>^{\backprime} f : A \to B \, ^{\prime}</math> for <math>^{\backprime} \operatorname{source}~ f = A</math> and <math>\operatorname{target}~ f = B \, ^{\prime}.</math> A graph is said to be ''small'' if the classes of objects and arrows are sets.</p>
<p>(Lambek & Scott, 5).</p>
|}
===Deductive System===
===Deductive System===
