| | Some definitions of interest. |
|
| append | Def as @ bs == Case of as; nil  bs ; a.as' [a / (as' @ bs)] (recursive) |
| | | Thm*  T:Type, as,bs:T List. (as @ bs)  T List |
|
| connect | Def x-the_graph- > *y ==  p:Vertices(the_graph) List. path(the_graph;p) & p[0] = x & last(p) = y |
| | | Thm* For any graph
x,y:V. x-the_graph- > *y Prop |
|
| graphobj | Def GraphObject(the_graph) == eq:Vertices(the_graph)  Vertices(the_graph)  (x,y:Vertices(the_graph).  (eq(x,y))   x = y)(eacc:( T:Type. (TVertices(the_graph)T)TVertices(the_graph)T)(T:Type, s:T, x:Vertices(the_graph), f:(TVertices(the_graph)T). L:Vertices(the_graph) List. (y:Vertices(the_graph). x-the_graph- > y (y L)) & eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L))(vacc:(T:Type. (TVertices(the_graph)T)TT)(T:Type, s:T, f:(TVertices(the_graph)T). L:Vertices(the_graph) List. no_repeats(Vertices(the_graph);L) & (y:Vertices(the_graph). (y L)) & vacc(f,s) = list_accum(s',x'.f(s',x');s;L))Top)) |
| | | Thm* the_graph:Graph. GraphObject(the_graph) Type{i'} |
|
| traversal | Def traversal(G) == (Vertices(G)+Vertices(G)) List |
| | | Thm* For any graph
Traversal Type |
|
| gr_v | Def Vertices(t) == 1of(t) |
| | | Thm* t:Graph. Vertices(t) Type |
|
| graph | Def Graph == v:Typee:Type(evv)Top |
| | | Thm* Graph Type{i'} |
|
| iff | Def P Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| l_member | Def (x l) == i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| not | Def  A == A False |
| | | Thm* A:Prop. (A) Prop |
