| | Some definitions of interest. |
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| w-Msg | Def Msg == Msg(w.M) |
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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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| Msg | Def Msg(M) == l:IdLnk t:Id M(l,t) |
| | | Thm* M:(IdLnk Id Type). Msg(M) Type |
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| IdLnk | Def IdLnk == Id Id  |
| | | Thm* IdLnk Type |
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| w-causl | Def e <c e' == e e,e'. e <loc e' isrcv(kind(e')) & e = sender(e') E^+ e' |
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| w-E | Def E == {p:(Id )|  isnull(a(1of(p);2of(p))) } |
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| w-index | Def index(e)
Def == ||rcvs(lnk(kind(e));time(e))||-||snds(lnk(kind(e));time(sender(e)))|| |
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| w-queue | Def queue(l;t) == nth_tl(||rcvs(l;t)||;snds(l;t)) |
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| w-sender | Def sender(e) == <source(lnk(kind(e))),mu( t.match(lnk(kind(e));t;time(e)))> |
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| w-isrcvl | Def isrcv(l;a) ==  isnull(a) isrcv(kind(a)) lnk(kind(a)) = l |
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| w-sends | Def sends(l;e) == onlnk(l;m(loc(e);time(e))) |
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| w-onlnk | Def onlnk(l;mss) == filter( ms.mlnk(ms) = l;mss) |
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| Id | Def Id == Atom  |
| | | Thm* Id Type |
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| assert | Def b == if b True else False fi |
| | | Thm* b: . b Prop |
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| ge | Def i j == j i |
| | | Thm* i,j: . (i j) Prop |
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| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n: . 0 n  n<||l||  l[n] A |
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| hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | | Thm* A:Type, l:A List. ||l|| 1  hd(l) A |
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| iff | Def P  Q == (P  Q) & (P  Q) |
| | | Thm* A,B:Prop. (A  B) Prop |
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| isrcv | Def isrcv(k) == isl(k) |
| | | Thm* k:Knd. isrcv(k)  |
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| ldst | Def destination(l) == 1of(2of(l)) |
| | | Thm* l:IdLnk. destination(l) Id |
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| strongwellfounded | Def SWellFounded(R(x;y)) == f:(T  ). x,y:T. R(x;y)  f(x)<f(y) |
| | | Thm* T:Type, R:(T T Type). SWellFounded(R(x,y)) Prop |
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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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| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l||  |
| | | Thm* ||nil||  |
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| w-msg | Def msg(a) == msg(lnk(kind(a));tag(kind(a));val(a)) |
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| lnk | Def lnk(k) == 1of(outl(k)) |
| | | Thm* k:Knd. isrcv(k)  lnk(k) IdLnk |
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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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| w-M | Def w.M == 1of(2of(2of(w))) |
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| w-eval | Def val(e) == val(act(e)) |
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| w-first | Def first(e)
Def == if time(e)= 0 true
Def == i; isnull(a(loc(e);time(e)-1)) first(<loc(e),time(e)-1>)
Def == else false fi
Def (recursive) |
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| w-pred | Def pred(e)
Def == if isnull(a(loc(e);time(e)-1)) pred(<loc(e),time(e)-1>)
Def == else <loc(e),time(e)-1> fi
Def (recursive) |
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| w-a | Def a(i;t) == 1of(2of(2of(2of(2of(w)))))(i,t) |
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| w-after | Def (x after e) == s(1of(e);2of(e)+1).x |
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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-when | Def (x when e) == s(1of(e);2of(e)).x |
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| w-s | Def s(i;t).x == 1of(2of(2of(2of(w))))(i,t,x) |
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| w-vartype | Def vartype(i;x) == w.T(i,x) |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(A Type), p:(a:A B(a)). 1of(p) A |
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| tagof | Def tag(k) == 2of(outl(k)) |
| | | Thm* k:Knd. isrcv(k)  tag(k) Id |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(A Type), p:(a:A B(a)). 2of(p) B(1of(p)) |
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| trans | Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b)  E(b;c)  E(a;c) |
| | | Thm* T:Type, E:(T T Prop). (Trans x,y:T. E(x,y)) Prop |
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| w-isnull | Def isnull(a) == isl(a) |