Nuprl - mb_event_system_7 Citations of lsrc

mb event system 7 Sections EventSystems Doc

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Def source(l) == 1of(l)

is mentioned by

Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|.
Thm* bi-graph(G;to;from)  ((inverse(e)  to(i))  source(e) = i) [edge-inv-to]

Thm* G:(Id), to,from:(|G|(IdLnk List)), e:Edge(G), i:|G|.
Thm* bi-graph(G;to;from)  ((e  from(i))  source(e) = i) [edge-from]

Thm* T:(Id), to,from:(|T|(IdLnk List)), u:Edge(T).
Thm* bi-graph(T;to;from)  source(u)  |T| [src-edge]

Thm* a:Id, f:(AT), tg:Id, l:IdLnk, x:Id.
Thm* "done" = x
Thm*
Thm* A
Thm*
Thm* T
Thm*
Thm* loc.(send-once(loc;T;A;a;f;tg;l;x))
Thm* realizes es.(vartype(source(l);x) r A)
Thm* realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* realizes es.& (e:E.
Thm* realizes es.& (kind(e) = rcv(l; tg)  Knd
Thm* realizes es.& (& val(e) = f((x when sender(e)))  T
Thm* realizes es.& (& & kind(sender(e)) = locl(a)  Knd
Thm* realizes es.& (& & (e':E.
Thm* realizes es.& (& & (kind(e') = rcv(l; tg)  Knd
Thm* realizes es.& (& & (
Thm* realizes es.& (& & (kind(sender(e')) = locl(a)  Knd  e' = e  E)) [send-once__realizes]

Thm* L:Knd List, l:IdLnk, tg:Id.
Thm* @source(l): only L sends on (l with tg)  Dsys
Thm* & (D:Dsys.
Thm* & (@source(l): only L sends on (l with tg)  D
Thm* & (
Thm* & (D
Thm* & (realizes es.e:E.
Thm* & (realizes es.loc(e) = destination(l)  Id
Thm* & (realizes es.
Thm* & (realizes es.kind(e) = rcv(l; tg)  Knd  (kind(sender(e))  L)) [better-sframe-rule]

Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type.
Thm* (rcv(l; tg) = k  T = B)
Thm*
Thm* (f:(ABT), c:(AB).
Thm* (@source(l): ma-single-sends1(A;
Thm* (@source(l): ma-single-sends1(B;
Thm* (@source(l): ma-single-sends1(T;
Thm* (@source(l): ma-single-sends1(x;
Thm* (@source(l): ma-single-sends1(k;
Thm* (@source(l): ma-single-sends1(l;
Thm* (@source(l): ma-single-sends1(tg;
Thm* (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi))
Thm* ( Dsys
Thm* (& (D:Dsys.
Thm* (& (@source(l): ma-single-sends1(A;
Thm* (& (@source(l): ma-single-sends1(B;
Thm* (& (@source(l): ma-single-sends1(T;
Thm* (& (@source(l): ma-single-sends1(x;
Thm* (& (@source(l): ma-single-sends1(k;
Thm* (& (@source(l): ma-single-sends1(l;
Thm* (& (@source(l): ma-single-sends1(tg;
Thm* (& (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi)
Thm* (& (@source(l): ma-single-sends1()  D
Thm* (& (
Thm* (& (D
Thm* (& (realizes es.(vartype(source(l);x) r A)
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd  (valtype(e) r B))
Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd
Thm* (& (realizes es.& (
Thm* (& (realizes es.& ((c((x when e),val(e))
Thm* (& (realizes es.& ((
Thm* (& (realizes es.& (((e':E.
Thm* (& (realizes es.& (((kind(e') = rcv(l; tg)  Knd
Thm* (& (realizes es.& (((& sender(e') = e  E
Thm* (& (realizes es.& (((& & (e'':E.
Thm* (& (realizes es.& (((& & (kind(e'') = rcv(l; tg)  Knd
Thm* (& (realizes es.& (((& & (
Thm* (& (realizes es.& (((& & (sender(e'') = e  E  e'' = e'  E)
Thm* (& (realizes es.& (((& & val(e') = f((x when e),val(e))  T))
Thm* (& (realizes es.& (& (c((x when e),val(e))
Thm* (& (realizes es.& (& (
Thm* (& (realizes es.& (& ((e':E.
Thm* (& (realizes es.& (& ((kind(e') = rcv(l; tg)  Knd
Thm* (& (realizes es.& (& ((& sender(e') = e  E))))) [conditional-send1-rule]

Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type.
Thm* (rcv(l; tg) = k  T = B)
Thm*
Thm* (f:(ABT).
Thm* (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))]))
Thm* ( Dsys
Thm* (& (D:Dsys.
Thm* (& (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))])
Thm* (& (@source(l): ma-single-sends1()  D
Thm* (& (
Thm* (& (D
Thm* (& (realizes es.(vartype(source(l);x) r A)
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd  (valtype(e) r B))
Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* (& (realizes es.& (e:E.
Thm* (& (realizes es.& (loc(e) = source(l)  Id
Thm* (& (realizes es.& (
Thm* (& (realizes es.& (kind(e) = k  Knd
Thm* (& (realizes es.& (
Thm* (& (realizes es.& ((e':E.
Thm* (& (realizes es.& ((kind(e') = rcv(l; tg)  Knd
Thm* (& (realizes es.& ((& sender(e') = e  E
Thm* (& (realizes es.& ((& & (e'':E.
Thm* (& (realizes es.& ((& & (kind(e'') = rcv(l; tg)  Knd
Thm* (& (realizes es.& ((& & (
Thm* (& (realizes es.& ((& & (sender(e'') = e  E  e'' = e'  E)
Thm* (& (realizes es.& ((& & val(e') = f((x when e),val(e))  T)))) [s-unconditional-send1-rule]

Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type, f:(AB(T List)).
Thm* (rcv(l; tg) = k  T = B)
Thm*
Thm* @source(l): ma-single-sends1(A; B; T; x; k; l; tg; f)  Dsys
Thm* & (D:Dsys.
Thm* & (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; f)  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(source(l);x) r A)
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = source(l)  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k  Knd  (valtype(e) r B))
Thm* & (realizes es.& (e:E. kind(e) = rcv(l; tg)  Knd  (valtype(e) r T))
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = source(l)  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = k  Knd
Thm* & (realizes es.& (
Thm* & (realizes es.& ((L:{e':E| kind(e') = rcv(l; tg)  Knd } List.
Thm* & (realizes es.& (((e':E.
Thm* & (realizes es.& ((((e'  L)
Thm* & (realizes es.& (((
Thm* & (realizes es.& (((kind(e') = rcv(l; tg)  Knd & sender(e') = e  E)
Thm* & (realizes es.& ((& (e1,e2:E. e1 before e2  L  (e1 <loc e2))
Thm* & (realizes es.& ((& map(e'.val(e');L) = f((x when e),val(e))  T List))) [s-sends-rule1]

Def bi-graph(G;to;from)
Def == i:|G|.
Def == (lto(i).destination(l) = i
Def == & (G(source(l)))
Def == & (l  from(source(l)))
Def == & (lnk-inv(l)  from(i)))
Def == & (lfrom(i).source(l) = i
Def == & & (G(destination(l)))
Def == & & (l  to(destination(l)))
Def == & & (lnk-inv(l)  to(i))) [bi-graph]

Def p(i) == source(in(i)) [rprev]

Def ring(R;in;out)
Def == (i:|R|.
Def == ((R(source(in(i)))) & (R(destination(out(i))))
Def == (& source(out(i)) = i
Def == (& & destination(in(i)) = i
Def == (& & in(destination(out(i))) = out(i)  IdLnk
Def == (& & out(source(in(i))) = in(i)  IdLnk)
Def == & (i,j:|R|. k:. x.destination(out(x))^k(i) = j  Id)
Def == & |R| [ring]

Def send-once(loc;T;A;a;f;tg;l;x)
Def == [(once(loc;a;source(l)));
Def == [if loc = source(l)
Def == [if ma-single-sends1(A; Unit; T; x; locl(a); l; tg; (a,b. [(f(a))]))
Def == [else  fi] [send-once]

In prior sections: mb event system 2 mb event system 3 mb event system 5 mb event system 6 mb event system 4

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mb event system 7 Sections EventSystems Doc

Thm* G:(Id), to,from:(\|G\|(IdLnk List)), e:Edge(G), i:\|G\|. Thm* bi-graph(G;to;from) ((inverse(e) to(i)) source(e) = i)	[edge-inv-to]
Thm* G:(Id), to,from:(\|G\|(IdLnk List)), e:Edge(G), i:\|G\|. Thm* bi-graph(G;to;from) ((e from(i)) source(e) = i)	[edge-from]
Thm* T:(Id), to,from:(\|T\|(IdLnk List)), u:Edge(T). Thm* bi-graph(T;to;from) source(u) \|T\|	[src-edge]
Thm* a:Id, f:(AT), tg:Id, l:IdLnk, x:Id. Thm* "done" = x Thm* Thm* A Thm* Thm* T Thm* Thm* loc.(send-once(loc;T;A;a;f;tg;l;x)) Thm* realizes es.(vartype(source(l);x) r A) Thm* realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* realizes es.& (e:E. Thm* realizes es.& (kind(e) = rcv(l; tg) Knd Thm* realizes es.& (& val(e) = f((x when sender(e))) T Thm* realizes es.& (& & kind(sender(e)) = locl(a) Knd Thm* realizes es.& (& & (e':E. Thm* realizes es.& (& & (kind(e') = rcv(l; tg) Knd Thm* realizes es.& (& & ( Thm* realizes es.& (& & (kind(sender(e')) = locl(a) Knd e' = e E))	[send-once__realizes]
Thm* L:Knd List, l:IdLnk, tg:Id. Thm* @source(l): only L sends on (l with tg) Dsys Thm* & (D:Dsys. Thm* & (@source(l): only L sends on (l with tg) D Thm* & ( Thm* & (D Thm* & (realizes es.e:E. Thm* & (realizes es.loc(e) = destination(l) Id Thm* & (realizes es. Thm* & (realizes es.kind(e) = rcv(l; tg) Knd (kind(sender(e)) L))	[better-sframe-rule]
Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type. Thm* (rcv(l; tg) = k T = B) Thm* Thm* (f:(ABT), c:(AB). Thm* (@source(l): ma-single-sends1(A; Thm* (@source(l): ma-single-sends1(B; Thm* (@source(l): ma-single-sends1(T; Thm* (@source(l): ma-single-sends1(x; Thm* (@source(l): ma-single-sends1(k; Thm* (@source(l): ma-single-sends1(l; Thm* (@source(l): ma-single-sends1(tg; Thm* (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi)) Thm* ( Dsys Thm* (& (D:Dsys. Thm* (& (@source(l): ma-single-sends1(A; Thm* (& (@source(l): ma-single-sends1(B; Thm* (& (@source(l): ma-single-sends1(T; Thm* (& (@source(l): ma-single-sends1(x; Thm* (& (@source(l): ma-single-sends1(k; Thm* (& (@source(l): ma-single-sends1(l; Thm* (& (@source(l): ma-single-sends1(tg; Thm* (& (@source(l): ma-single-sends1((a,b. if c(a,b) [(f(a,b))] else nil fi) Thm* (& (@source(l): ma-single-sends1() D Thm* (& ( Thm* (& (D Thm* (& (realizes es.(vartype(source(l);x) r A) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd (valtype(e) r B)) Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd Thm* (& (realizes es.& ( Thm* (& (realizes es.& ((c((x when e),val(e)) Thm* (& (realizes es.& (( Thm* (& (realizes es.& (((e':E. Thm* (& (realizes es.& (((kind(e') = rcv(l; tg) Knd Thm* (& (realizes es.& (((& sender(e') = e E Thm* (& (realizes es.& (((& & (e'':E. Thm* (& (realizes es.& (((& & (kind(e'') = rcv(l; tg) Knd Thm* (& (realizes es.& (((& & ( Thm* (& (realizes es.& (((& & (sender(e'') = e E e'' = e' E) Thm* (& (realizes es.& (((& & val(e') = f((x when e),val(e)) T)) Thm* (& (realizes es.& (& (c((x when e),val(e)) Thm* (& (realizes es.& (& ( Thm* (& (realizes es.& (& ((e':E. Thm* (& (realizes es.& (& ((kind(e') = rcv(l; tg) Knd Thm* (& (realizes es.& (& ((& sender(e') = e E)))))	[conditional-send1-rule]
Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type. Thm* (rcv(l; tg) = k T = B) Thm* Thm* (f:(ABT). Thm* (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))])) Thm* ( Dsys Thm* (& (D:Dsys. Thm* (& (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; (a,b. [(f(a,b))]) Thm* (& (@source(l): ma-single-sends1() D Thm* (& ( Thm* (& (D Thm* (& (realizes es.(vartype(source(l);x) r A) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd (valtype(e) r B)) Thm* (& (realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* (& (realizes es.& (e:E. Thm* (& (realizes es.& (loc(e) = source(l) Id Thm* (& (realizes es.& ( Thm* (& (realizes es.& (kind(e) = k Knd Thm* (& (realizes es.& ( Thm* (& (realizes es.& ((e':E. Thm* (& (realizes es.& ((kind(e') = rcv(l; tg) Knd Thm* (& (realizes es.& ((& sender(e') = e E Thm* (& (realizes es.& ((& & (e'':E. Thm* (& (realizes es.& ((& & (kind(e'') = rcv(l; tg) Knd Thm* (& (realizes es.& ((& & ( Thm* (& (realizes es.& ((& & (sender(e'') = e E e'' = e' E) Thm* (& (realizes es.& ((& & val(e') = f((x when e),val(e)) T))))	[s-unconditional-send1-rule]
Thm* x,tg:Id, k:Knd, l:IdLnk, T,A,B:Type, f:(AB(T List)). Thm* (rcv(l; tg) = k T = B) Thm* Thm* @source(l): ma-single-sends1(A; B; T; x; k; l; tg; f) Dsys Thm* & (D:Dsys. Thm* & (@source(l): ma-single-sends1(A; B; T; x; k; l; tg; f) D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(source(l);x) r A) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = source(l) Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = k Knd (valtype(e) r B)) Thm* & (realizes es.& (e:E. kind(e) = rcv(l; tg) Knd (valtype(e) r T)) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = source(l) Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = k Knd Thm* & (realizes es.& ( Thm* & (realizes es.& ((L:{e':E\| kind(e') = rcv(l; tg) Knd } List. Thm* & (realizes es.& (((e':E. Thm* & (realizes es.& ((((e' L) Thm* & (realizes es.& ((( Thm* & (realizes es.& (((kind(e') = rcv(l; tg) Knd & sender(e') = e E) Thm* & (realizes es.& ((& (e1,e2:E. e1 before e2 L (e1 <loc e2)) Thm* & (realizes es.& ((& map(e'.val(e');L) = f((x when e),val(e)) T List)))	[s-sends-rule1]
Def bi-graph(G;to;from) Def == i:\|G\|. Def == (lto(i).destination(l) = i Def == & (G(source(l))) Def == & (l from(source(l))) Def == & (lnk-inv(l) from(i))) Def == & (lfrom(i).source(l) = i Def == & & (G(destination(l))) Def == & & (l to(destination(l))) Def == & & (lnk-inv(l) to(i)))	[bi-graph]
Def p(i) == source(in(i))	[rprev]
Def ring(R;in;out) Def == (i:\|R\|. Def == ((R(source(in(i)))) & (R(destination(out(i)))) Def == (& source(out(i)) = i Def == (& & destination(in(i)) = i Def == (& & in(destination(out(i))) = out(i) IdLnk Def == (& & out(source(in(i))) = in(i) IdLnk) Def == & (i,j:\|R\|. k:. x.destination(out(x))^k(i) = j Id) Def == & \|R\|	[ring]
Def send-once(loc;T;A;a;f;tg;l;x) Def == [(once(loc;a;source(l))); Def == [if loc = source(l) Def == [if ma-single-sends1(A; Unit; T; x; locl(a); l; tg; (a,b. [(f(a))])) Def == [else fi]	[send-once]