Nuprl - mb_event_system_7 Citations of assert

mb event system 7 Sections EventSystems Doc

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Def

b == if b

True else False fi

is mentioned by

Thm* P:(AT), i:Id, k:Knd, a,x:Id.
Thm* A
Thm*
Thm* T
Thm*
Thm* x = "trigger"
Thm*
Thm* locl(a) = k
Thm*
Thm* loc.(trigger1(loc;T;A;P;i;k;a;x))
Thm* realizes es.(vartype(i;x) r A)
Thm* realizes es.& e@i.kind(e) = k  Knd  (valtype(e) r T)
Thm* realizes es.& e'@i.kind(e') = locl(a)
Thm* realizes es.& e'@i.
Thm* realizes es.& (e:E.
Thm* realizes es.& ((e <loc e') & kind(e) = k  Knd & P((x when e),val(e)))
Thm* realizes es.& e@i.kind(e) = k  Knd
Thm* realizes es.& e@i.
Thm* realizes es.& P((x when e),val(e))  e'@i.kind(e') = locl(a)  Knd [trigger1__realizes]

Thm* P:(AT), k:Knd, i,r,x:Id.
Thm* A
Thm*
Thm* T
Thm*
Thm* x = r
Thm*
Thm* loc.(recognizer1(loc;T;A;P;k;i;r;x))
Thm* realizes es.e@i.kind(e) = k  Knd  (valtype(e) r T)
Thm* realizes es.& (vartype(i;x) r A)
Thm* realizes es.& e@i.first(e)  (r when e) = false
Thm* realizes es.& e'@i.(r after e')
Thm* realizes es.& e'@i.
Thm* realizes es.& e'@i.(e:E.
Thm* realizes es.& e'@i.((e <loc e')  e = e'  E
Thm* realizes es.& e'@i.(& kind(e) = k  Knd
Thm* realizes es.& e'@i.(& P((x when e),val(e))) [recognizer1__realizes]

Thm* a:Id, T:Top, ds:x:Id fp-> Type, P:Top, init:x:Id fp-> ds(x)?Void, x:Id,
Thm* t:Type, v:t.
Thm* ds || x : t
Thm*
Thm* (x  dom(init)  init(x) = v  t)
Thm*
Thm* (with ds: ds
Thm* (init: init
Thm* action a:T
Thm* aprecondition a(v) is
Thm* aP) ||+ x : t initially x = v [ma-single-pre-init-ma-single-init-compatible]

Thm* i:Id, L:Knd List, l:IdLnk, tg:Id.
Thm* @i: only L sends on (l with tg)  Dsys
Thm* & (D:Dsys.
Thm* & (@i: only L sends on (l with tg)  D
Thm* & (
Thm* & (D
Thm* & (realizes es.e:E.
Thm* & (realizes es.loc(e) = i  Id  null(sends(l,tg,e))  (kind(e)  L)) [s-sframe-rule]

Thm* i,a,x:Id, A,T:Type, c:A, P:(ATProp).
Thm* @i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v))  Dsys
Thm* & (D:Dsys.
Thm* & (@i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v))  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(i;x) r A)
Thm* & (realizes es.& (e:E. loc(e) = i  Id  first(e)  (x when e) = c  A)
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = i  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = locl(a)  Knd  (valtype(e) r T))
Thm* & (realizes es.& (e:E.
Thm* & (realizes es.& (loc(e) = i  Id
Thm* & (realizes es.& (
Thm* & (realizes es.& (kind(e) = locl(a)  Knd  P((x when e),val(e)))
Thm* & (realizes es.& & ((v:T. P(c,v))
Thm* & (realizes es.& & (
Thm* & (realizes es.& & ((e:E.
Thm* & (realizes es.& & ((loc(e) = i  Id
Thm* & (realizes es.& & ((& kind(e) = locl(a)  Knd
Thm* & (realizes es.& & ((&  (v:T. P((x after e),v))))) [s-pre-init-rule1]

Thm* i:Id, T:Type, v:T, x:Id.
Thm* @i: x : T initially x = v  Dsys
Thm* & (D:Dsys.
Thm* & (@i: x : T initially x = v  D
Thm* & (
Thm* & (D
Thm* & (realizes es.(vartype(i;x) r T)
Thm* & (realizes es.& (e:E. loc(e) = i  Id  first(e)  (x when e) = v  T)) [s-init-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]

Def spanner-root(f;T;to;from;i) == l:Edge(T). (l  to(i))  (f(l)) [spanner-root]

Def spanner(f;T;to;from)
Def == (l:Edge(T). f(l) = f(inverse(l)))
Def == & (i:|T|, l1,l2:Edge(T).
Def == & ((l1  to(i))
Def == & (
Def == & ((l2  to(i))  l1 = l2  IdLnk  (f(l1))  (f(l2))) [spanner]

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 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 |R| == {i:Id| (R(i)) } [rset]

Def trigger1(loc;T;A;P;i;k;a;x)
Def == [(recognizer1(loc;T;A;P;k;i;"trigger";x));
Def == [if loc = i ma-single-pre1("trigger";;a;Unit;x,v.x) else  fi] [trigger1]

Def once(loc;a;i)
Def == if loc = i
Def == if [ma-single-pre-init1("done";;false;a;Unit;x,v.x);
Def == if [only members of [locl(a)] affect "done" :;
Def == if [ma-single-effect0("done";;locl(a);Unit;x,v. true)]
Def == else nil fi [once]

In prior sections: bool 1 list 1 union mb nat mb list 1 mb list 2 mb event system 1 mb event system 2 mb event system 3 mb event system 4 mb event system 5 mb event system 6 rel 1

Try larger context: EventSystems IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html

mb event system 7 Sections EventSystems Doc

Thm* P:(AT), i:Id, k:Knd, a,x:Id. Thm* A Thm* Thm* T Thm* Thm* x = "trigger" Thm* Thm* locl(a) = k Thm* Thm* loc.(trigger1(loc;T;A;P;i;k;a;x)) Thm* realizes es.(vartype(i;x) r A) Thm* realizes es.& e@i.kind(e) = k Knd (valtype(e) r T) Thm* realizes es.& e'@i.kind(e') = locl(a) Thm* realizes es.& e'@i. Thm* realizes es.& (e:E. Thm* realizes es.& ((e <loc e') & kind(e) = k Knd & P((x when e),val(e))) Thm* realizes es.& e@i.kind(e) = k Knd Thm* realizes es.& e@i. Thm* realizes es.& P((x when e),val(e)) e'@i.kind(e') = locl(a) Knd	[trigger1__realizes]
Thm* P:(AT), k:Knd, i,r,x:Id. Thm* A Thm* Thm* T Thm* Thm* x = r Thm* Thm* loc.(recognizer1(loc;T;A;P;k;i;r;x)) Thm* realizes es.e@i.kind(e) = k Knd (valtype(e) r T) Thm* realizes es.& (vartype(i;x) r A) Thm* realizes es.& e@i.first(e) (r when e) = false Thm* realizes es.& e'@i.(r after e') Thm* realizes es.& e'@i. Thm* realizes es.& e'@i.(e:E. Thm* realizes es.& e'@i.((e <loc e') e = e' E Thm* realizes es.& e'@i.(& kind(e) = k Knd Thm* realizes es.& e'@i.(& P((x when e),val(e)))	[recognizer1__realizes]
Thm* a:Id, T:Top, ds:x:Id fp-> Type, P:Top, init:x:Id fp-> ds(x)?Void, x:Id, Thm* t:Type, v:t. Thm* ds \|\| x : t Thm* Thm* (x dom(init) init(x) = v t) Thm* Thm* (with ds: ds Thm* (init: init Thm* action a:T Thm* aprecondition a(v) is Thm* aP) \|\|+ x : t initially x = v	[ma-single-pre-init-ma-single-init-compatible]
Thm* i:Id, L:Knd List, l:IdLnk, tg:Id. Thm* @i: only L sends on (l with tg) Dsys Thm* & (D:Dsys. Thm* & (@i: only L sends on (l with tg) D Thm* & ( Thm* & (D Thm* & (realizes es.e:E. Thm* & (realizes es.loc(e) = i Id null(sends(l,tg,e)) (kind(e) L))	[s-sframe-rule]
Thm* i,a,x:Id, A,T:Type, c:A, P:(ATProp). Thm* @i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v)) Dsys Thm* & (D:Dsys. Thm* & (@i: ma-single-pre-init1(x;A;c;a;T;x,v.P(x,v)) D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(i;x) r A) Thm* & (realizes es.& (e:E. loc(e) = i Id first(e) (x when e) = c A) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = i Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = locl(a) Knd (valtype(e) r T)) Thm* & (realizes es.& (e:E. Thm* & (realizes es.& (loc(e) = i Id Thm* & (realizes es.& ( Thm* & (realizes es.& (kind(e) = locl(a) Knd P((x when e),val(e))) Thm* & (realizes es.& & ((v:T. P(c,v)) Thm* & (realizes es.& & ( Thm* & (realizes es.& & ((e:E. Thm* & (realizes es.& & ((loc(e) = i Id Thm* & (realizes es.& & ((& kind(e) = locl(a) Knd Thm* & (realizes es.& & ((& (v:T. P((x after e),v)))))	[s-pre-init-rule1]
Thm* i:Id, T:Type, v:T, x:Id. Thm* @i: x : T initially x = v Dsys Thm* & (D:Dsys. Thm* & (@i: x : T initially x = v D Thm* & ( Thm* & (D Thm* & (realizes es.(vartype(i;x) r T) Thm* & (realizes es.& (e:E. loc(e) = i Id first(e) (x when e) = v T))	[s-init-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]
Def spanner-root(f;T;to;from;i) == l:Edge(T). (l to(i)) (f(l))	[spanner-root]
Def spanner(f;T;to;from) Def == (l:Edge(T). f(l) = f(inverse(l))) Def == & (i:\|T\|, l1,l2:Edge(T). Def == & ((l1 to(i)) Def == & ( Def == & ((l2 to(i)) l1 = l2 IdLnk (f(l1)) (f(l2)))	[spanner]
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 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 \|R\| == {i:Id\| (R(i)) }	[rset]
Def trigger1(loc;T;A;P;i;k;a;x) Def == [(recognizer1(loc;T;A;P;k;i;"trigger";x)); Def == [if loc = i ma-single-pre1("trigger";;a;Unit;x,v.x) else fi]	[trigger1]
Def once(loc;a;i) Def == if loc = i Def == if [ma-single-pre-init1("done";;false;a;Unit;x,v.x); Def == if [only members of [locl(a)] affect "done" :; Def == if [ma-single-effect0("done";;locl(a);Unit;x,v. true)] Def == else nil fi	[once]