| Some definitions of interest. |
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d-realizes | Def D
Def realizes es.P(es)
Def == D':Dsys.
Def == D D'  ( w:World, p:FairFifo. PossibleWorld(D';w)  P(ES(w))) |
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d-sub | Def D1 D2 == i:Id. M(i) M(i) |
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dsys | Def Dsys == Id MsgA |
| | Thm* Dsys Type{i'} |
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possible-world | Def PossibleWorld(D;w)
Def == FairFifo
Def == & ( i,x:Id. vartype(i;x) r M(i).ds(x))
Def == & & ( i:Id, a:Action(i).
Def == & & ( isnull(a)  (valtype(i;a) r M(i).da(kind(a))))
Def == & & ( l:IdLnk, tg:Id. (w.M(l,tg)) r M(source(l)).da(rcv(l; tg)))
Def == & & ( i,x:Id. M(i).init(x,s(i;0).x))
Def == & & ( i:Id, t: .
Def == & & ( isnull(a(i;t))
Def == & & (
Def == & & (( islocal(kind(a(i;t)))
Def == & & ((
Def == & & ((M(i).pre(act(kind(a(i;t))), x.s(i;t).x,val(a(i;t))))
Def == & & (& ( x:Id.
Def == & & (& (M(i).ef(kind(a(i;t)),x, x.s(i;t).x,val(a(i;t)),s(i;t+1).x))
Def == & & (& ( l:IdLnk.
Def == & & (& (M(i).send(kind(a(i;t));l; x.
Def == & & (& (s(i;t).x;val(a(i;t));withlnk(l;m(i;t));i))
Def == & & (& ( x:Id.
Def == & & (& ( M(i).frame(kind(a(i;t)) affects x)
Def == & & (& (
Def == & & (& (s(i;t).x = s(i;t+1).x M(i).ds(x))
Def == & & (& ( l:IdLnk, tg:Id.
Def == & & (& ( M(i).sframe(kind(a(i;t)) sends <l,tg>)
Def == & & (& (
Def == & & (& (w-tagged(tg; onlnk(l;m(i;t))) = nil Msg List))
Def == & & ( i,a:Id, t: .
Def == & & ( t': .
Def == & & (t t'
Def == & & (&  isnull(a(i;t')) & kind(a(i;t')) = locl(a)
Def == & & (& a declared in M(i)
Def == & & (& unsolvable M(i).pre(a, x.s(i;t').x)) |
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world | Def World
Def == T:Id Id Type
Def == TA:Id Id Type
Def == M:IdLnk Id Type
Def == (i:Id    (x:Id T(i,x))) (i:Id    action(w-action-dec(TA;M;i)))
Def == (i:Id    ({m:Msg(M)| source(mlnk(m)) = i } List)) Top |
| | Thm* World Type{i'} |
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Knd | Def Knd == (IdLnk Id)+Id |
| | Thm* Knd Type |
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fair-fifo | Def FairFifo
Def == ( i:Id, t: , l:IdLnk. source(l) = i  onlnk(l;m(i;t)) = nil Msg List)
Def == & ( i:Id, t: .
Def == & ( isnull(a(i;t))
Def == & (
Def == & (( x:Id. s(i;t+1).x = s(i;t).x vartype(i;x))
Def == & (& m(i;t) = nil Msg List)
Def == & ( i:Id, t: , l:IdLnk.
Def == & ( isrcv(l;a(i;t))
Def == & (
Def == & (destination(l) = i
Def == & (& ||queue(l;t)|| 1 & hd(queue(l;t)) = msg(a(i;t)) Msg)
Def == & ( l:IdLnk, t: .
Def == & ( t': .
Def == & (t t' & isrcv(l;a(destination(l);t')) queue(l;t') = nil Msg List) |
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ma-single-sends1 | Def ma-single-sends1(A; B; T; x; a; l; tg; f)
Def == ma-single-sends(x : A;
Def == ma-single-sends(a : B rcv(l; tg) : T;
Def == ma-single-sends(a;
Def == ma-single-sends(l;
Def == ma-single-sends([<tg, s,v. f(s(x),v)>]) |
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IdLnk | Def IdLnk == Id Id  |
| | Thm* IdLnk Type |
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es-locl | Def (e <loc e') == loc(e) = loc(e') Id & (e < e') |
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w-es | Def ES(the_w;p)
Def == <E
Def == ,product-deq(Id; ;IdDeq;NatDeq)
Def == ,( i,x. vartype(i;x))
Def == ,( i,a. V(i;locl(a)))
Def == ,the_w.M
Def == ,
Def == ,( e.loc(e))
Def == ,( e.kind(e))
Def == ,( e.val(e))
Def == ,( x,e. (x when e))
Def == ,( x,e. (x after e))
Def == ,( l,e. sends(l;e))
Def == ,( e.sender(e))
Def == ,( e.index(e))
Def == ,( e.first(e))
Def == ,( e.pred(e))
Def == ,( e,e'. e <c e')
Def == ,world_DASH_event_DASH_system{1:l, i:l}(the_w,p)
Def == , > |
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Id | Def Id == Atom  |
| | Thm* Id Type |
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es-E | Def E == 1of(es) |
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es-valtype | Def valtype(e) == if isrcv(e) rcvtype(e) else acttype(e) fi |
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es-kind | Def kind(e) == 1of(2of(2of(2of(2of(2of(2of(2of(es))))))))(e) |
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es-loc | Def loc(e) == 1of(2of(2of(2of(2of(2of(2of(es)))))))(e) |
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es-sender | Def sender(e)
Def == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(2of(es)))))))))))))(e) |
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es-val | Def val(e) == 1of(2of(2of(2of(2of(2of(2of(2of(2of(es)))))))))(e) |
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es-vartype | Def vartype(i;x) == 1of(2of(2of(es)))(i,x) |
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es-when | Def (x when e) == 1of(2of(2of(2of(2of(2of(2of(2of(2of(2of(es))))))))))(x,e) |
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iff | Def P  Q == (P  Q) & (P  Q) |
| | Thm* A,B:Prop. (A  B) Prop |
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l_before | Def x before y l == [x; y] l |
| | Thm* T:Type, l:T List, x,y:T. x before y l 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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lsrc | Def source(l) == 1of(l) |
| | Thm* l:IdLnk. source(l) Id |
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m-sys-at | Def @i: A(j) == if j = i A else fi |
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map | Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')]
Def (recursive) |
| | Thm* A,B:Type, f:(A B), l:A List. map(f;l) B List |
| | Thm* A,B:Type, f:(A B), l:A List . map(f;l) B List |
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rcv | Def rcv(l; tg) == inl(<l,tg>) |
| | Thm* l:IdLnk, tg:Id. rcv(l; tg) Knd |