| | Some definitions of interest. |
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| depthfirst | Def depthfirst(the_obj) == the_obj.vacc(( s,i. dfs(the_obj;s;i)),nil) |
| | | Thm* For any graph
 the_obj:GraphObject(the_graph). depthfirst(the_obj)  Traversal |
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| dfsl | Def dfsl(G;L) == list_accum(s,i.dfs(G;s;i);nil;L) |
| | | Thm* For any graph
the_obj:GraphObject(the_graph), L:V List. dfsl(the_obj;L) Traversal |
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| 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'} |
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| traversal | Def traversal(G) == (Vertices(G)+Vertices(G)) List |
| | | Thm* For any graph
Traversal Type |
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| gr_v | Def Vertices(t) == 1of(t) |
| | | Thm* t:Graph. Vertices(t) Type |
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| graph | Def Graph == v:Typee:Type(evv)Top |
| | | Thm* Graph Type{i'} |
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| l_all | Def (xL.P(x)) == x:T. (x L)  P(x) |
| | | Thm* T:Type, L:T List, P:(TProp). (xL.P(x)) Prop |
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| l_member | Def (x l) == i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
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| no_repeats | Def no_repeats(T;l) == i,j:. i < ||l|| j < ||l||  i = j l[i] = l[j] T |
| | | Thm* T:Type, l:T List. no_repeats(T;l) Prop |
