| | Some definitions of interest. |
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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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| ma-ef | Def M.ef(k,x,s,v,w)
Def == E != 1of(2of(2of(2of(2of(M)))))(<k,x>) ==> w = E(s,v) M.ds(x) |
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| ma-send | Def M.send(k;l;s;v;ms;i)
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> ms
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> =
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> if source(l) = i
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> if concat(map( tgf.
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> if map( x.
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> if <1of(tgf),x>;2of(tgf)
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> if <1of(tgf),x>;(s
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> if <1of(tgf),x>;,v));L))
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> else nil fi
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> (tg:Id
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> ( if source(l) = i
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> ( if M.da(rcv(l; tg))
Def == L != 1of(2of(2of(2of(2of(2of(M))))))(<k,l>) ==> ( else Top fi) List |
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| w-action | Def Action(i) == action(w-action-dec(w.TA;w.M;i)) |
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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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| ma-npre | Def unsolvable M.pre(a,s)
Def == P != 1of(2of(2of(2of(M))))(a) ==> v:M.da(locl(a)). P(s,v) |
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| ma-da | Def M.da(a) == 1of(2of(M))(a)?Top |
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| ma-decla | Def a declared in M == locl(a) dom(1of(2of(M))) |
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| ma-frame | Def M.frame(k affects x)
Def == L != 1of(2of(2of(2of(2of(2of(2of(M)))))))(x) ==> deq-member(KindDeq;k;L) |
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| ma-sframe | Def M.sframe(k sends <l,tg>)
Def == L != 1of(2of(2of(2of(2of(2of(2of(2of(
Def == L != 1of(M))))))))(<l,tg>) ==> deq-member(KindDeq;k;L) |
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| w-Msg | Def Msg == Msg(w.M) |
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| IdLnk | Def IdLnk == Id Id  |
| | | Thm* IdLnk Type |
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| ma-st | Def M.state == State(1of(M)) |
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| w-onlnk | Def onlnk(l;mss) == filter( ms.mlnk(ms) = l;mss) |
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| w-withlnk | Def withlnk(l;mss) == mapfilter( ms.2of(ms); ms.mlnk(ms) = l;mss) |
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| Id | Def Id == Atom  |
| | | Thm* Id Type |
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| w-valtype | Def valtype(i;a) == kindcase(kind(a);a.w.TA(i,a);l,tg.w.M(l,tg)) |
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| actof | Def act(k) == outr(k) |
| | | Thm* k:Knd. islocal(k)  act(k) Id |
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| ma-ds | Def M.ds(x) == 1of(M)(x)?Top |
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| ma-init | Def M.init(x,v) == x0 != 1of(2of(2of(M)))(x) ==> v = x0 1of(M)(x)?Void |
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| ma-pre | Def M.pre(a,s,v) == P != 1of(2of(2of(2of(M))))(a) ==> P(s,v) |
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| w-tagged | Def w-tagged(tg; mss) == filter( ms.mtag(ms) = tg;mss) |
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| assert | Def b == if b True else False fi |
| | | Thm* b: . b Prop |
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| d-m | Def M(i) == D(i) |
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| islocal | Def islocal(k) ==  isl(k) |
| | | Thm* k:Knd. islocal(k)  |
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| nat | Def == {i: | 0 i } |
| | | Thm* Type |
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| le | Def A B == B<A |
| | | Thm* i,j: . (i j) Prop |
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| locl | Def locl(a) == inr(a) |
| | | Thm* a:Id. locl(a) Knd |
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| lsrc | Def source(l) == 1of(l) |
| | | Thm* l:IdLnk. source(l) Id |
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| not | Def A == A  False |
| | | Thm* A:Prop. ( A) Prop |
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| rcv | Def rcv(l; tg) == inl(<l,tg>) |
| | | Thm* l:IdLnk, tg:Id. rcv(l; tg) Knd |
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| w-M | Def w.M == 1of(2of(2of(w))) |
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| w-a | Def a(i;t) == 1of(2of(2of(2of(2of(w)))))(i,t) |
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| w-isnull | Def isnull(a) == isl(a) |
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| w-kind | Def kind(a) == 1of(outr(a)) |
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| w-m | Def m(i;t) == 1of(2of(2of(2of(2of(2of(w))))))(i,t) |
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| w-s | Def s(i;t).x == 1of(2of(2of(2of(w))))(i,t,x) |
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| w-val | Def val(a) == 2of(outr(a)) |
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| w-vartype | Def vartype(i;x) == w.T(i,x) |