WhoCites Definitions mb event system 2 Sections EventSystems Doc
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Who Cites event system?
event_systemDef ES
Def == E:Type
Def == EqDecider(E)(T:IdIdType
Def == EqDecider(E)(V:IdIdType
Def == EqDecider(E)(M:IdLnkIdType
Def == EqDecider(E)(Top(loc:EId
Def == EqDecider(E)(Top(kind:EKnd
Def == EqDecider(E)(Top(val:(e:Eeventtype(kind;loc;V;M;e))
Def == EqDecider(E)(Top(when:(x:Ide:ET(loc(e),x))
Def == EqDecider(E)(Top(after:(x:Ide:ET(loc(e),x))
Def == EqDecider(E)(Top(sends:(l:IdLnkE(Msg_sub(lM) List))
Def == EqDecider(E)(Top(sender:{e:Eisrcv(kind(e)) }E
Def == EqDecider(E)(Top(index:(e:{e:Eisrcv(kind(e)) }||sends
Def == EqDecider(E)(Top(index:(e:{e:Eisrcv(kind(e)) }||(lnk(kind(e))
Def == EqDecider(E)(Top(index:(e:{e:Eisrcv(kind(e)) }||,sender(e))||)
Def == EqDecider(E)(Top(first:E
Def == EqDecider(E)(Top(pred:{e':E(first(e')) }E
Def == EqDecider(E)(Top(causl:EEProp
Def == EqDecider(E)(Top(ESAxioms{i:l}
Def == EqDecider(E)(Top(ESAxioms(E;
Def == EqDecider(E)(Top(ESAxioms(T;
Def == EqDecider(E)(Top(ESAxioms(M;
Def == EqDecider(E)(Top(ESAxioms(loc;
Def == EqDecider(E)(Top(ESAxioms(kind;
Def == EqDecider(E)(Top(ESAxioms(val;
Def == EqDecider(E)(Top(ESAxioms(when;
Def == EqDecider(E)(Top(ESAxioms(after;
Def == EqDecider(E)(Top(ESAxioms(sends;
Def == EqDecider(E)(Top(ESAxioms(sender;
Def == EqDecider(E)(Top(ESAxioms(index;
Def == EqDecider(E)(Top(ESAxioms(first;
Def == EqDecider(E)(Top(ESAxioms(pred;
Def == EqDecider(E)(Top(ESAxioms(causl)
Def == EqDecider(E)(Top(Top))
Thm* ES  Type{i'}
topDef Top == Void given Void
Thm* Top  Type
ESAxiomsDef ESAxioms{i:l}
Def ESAxioms(E;
Def ESAxioms(T;
Def ESAxioms(M;
Def ESAxioms(loc;
Def ESAxioms(kind;
Def ESAxioms(val;
Def ESAxioms(when;
Def ESAxioms(after;
Def ESAxioms(sends;
Def ESAxioms(sender;
Def ESAxioms(index;
Def ESAxioms(first;
Def ESAxioms(pred;
Def ESAxioms(causl)
Def == (e,e':Eloc(e) = loc(e' Id  causl(e,e' e = e'  causl(e',e))
Def == & (e:E(first(e))  (e':Eloc(e') = loc(e Id  causl(e',e)))
Def == & (e:E
Def == & ((first(e))
Def == & (
Def == & (loc(pred(e)) = loc(e Id & causl(pred(e),e)
Def == & (& (e':E
Def == & (& (loc(e') = loc(e Id  (causl(pred(e),e') & causl(e',e))))
Def == & (e:E
Def == & ((first(e))  (x:Id. when(x,e) = after(x,pred(e))  T(loc(e),x)))
Def == & (Trans e,e':Ecausl(e,e'))
Def == & SWellFounded(causl(e,e'))
Def == & (e:E
Def == & (isrcv(kind(e))
Def == & (
Def == & ((sends(lnk(kind(e)),sender(e)))[(index(e))]
Def == & (=
Def == & (msg(lnk(kind(e));tag(kind(e));val(e))
Def == & ( Msg(M))
Def == & (e:Eisrcv(kind(e))  causl(sender(e),e))
Def == & (e,e':E.
Def == & (causl(e,e')
Def == & (
Def == & ((first(e')) & causl(e,pred(e'))  e = pred(e')
Def == & ( isrcv(kind(e')) & causl(e,sender(e'))  e = sender(e'))
Def == & (e:Eisrcv(kind(e))  loc(e) = destination(lnk(kind(e))))
Def == & (e:El:IdLnk.
Def == & (loc(e) = source(l sends(l,e) = nil  Msg_sub(lM) List)
Def == & (e,e':E.
Def == & (isrcv(kind(e))
Def == & (
Def == & (isrcv(kind(e'))
Def == & (
Def == & (lnk(kind(e)) = lnk(kind(e'))
Def == & (
Def == & ((causl(e,e')
Def == & ((
Def == & ((causl(sender(e),sender(e'))
Def == & (( sender(e) = sender(e' E & index(e)<index(e')))
Def == & (e:El:IdLnk, n:||sends(l,e)||.
Def == & (e':E
Def == & (isrcv(kind(e')) & lnk(kind(e')) = l & sender(e') = e & index(e') = n)
Thm* E:Type{i}, T,V:(IdIdType{i}), M:(IdLnkIdType{i}), loc:(EId),
Thm* kind:(EKnd), val:(e:Eeventtype(kind;loc;V;M;e)),
Thm* when,after:(x:Ide:ET(loc(e),x)),
Thm* sends:(l:IdLnkE(Msg_sub(lM) List)),
Thm* sender:({e:E| isrcv(kind(e)) }E),
Thm* index:(e:{e:E| isrcv(kind(e)) }||sends(lnk(kind(e)),sender(e))||),
Thm* first:(E), pred:({e':Efirst(e') }E), causl:(EEProp{i}).
Thm* ESAxioms{i:l}
Thm* ESAxioms(E;
Thm* ESAxioms(T;
Thm* ESAxioms(M;
Thm* ESAxioms(loc;
Thm* ESAxioms(kind;
Thm* ESAxioms(val;
Thm* ESAxioms(when;
Thm* ESAxioms(after;
Thm* ESAxioms(sends;
Thm* ESAxioms(sender;
Thm* ESAxioms(index;
Thm* ESAxioms(first;
Thm* ESAxioms(pred;
Thm* ESAxioms(causl)
Thm*  Prop{i'}
deqDef EqDecider(T) == eq:TTx,y:Tx = y  (eq(x,y))
Thm* T:Type. EqDecider(T Type
assertDef b == if b True else False fi
Thm* b:b  Prop
int_segDef {i..j} == {k:i  k < j }
Thm* m,n:. {m..n Type
Msg_subDef Msg_sub(lM) == {m:Msg(M)| haslink(lm) }
Thm* M:(IdLnkIdType), l:IdLnk. Msg_sub(lM Type
KndDef Knd == (IdLnkId)+Id
Thm* Knd  Type
MsgDef Msg(M) == l:IdLnkt:IdM(l,t)
Thm* M:(IdLnkIdType). Msg(M Type
haslinkDef haslink(lm) == mlnk(m) = l
Thm* M:(IdLnkIdType), l:IdLnk, m:Msg(M). haslink(lm Prop
IdLnkDef IdLnk == IdId
Thm* IdLnk  Type
IdDef Id == Atom
Thm* Id  Type
strongwellfoundedDef SWellFounded(R(x;y)) == f:(T). x,y:TR(x;y f(x)<f(y)
Thm* T:Type, R:(TTType). SWellFounded(R(x,y))  Prop
leltDef i  j < k == ij & j<k
natDef  == {i:| 0i }
Thm*   Type
leDef AB == B<A
Thm* i,j:. (ij Prop
notDef A == A  False
Thm* A:Prop. (A Prop
eventtypeDef eventtype(k;loc;V;M;e) == kindcase(k(e);a.V(loc(e),a);l,t.M(l,t))
Thm* E:Type, V:(IdIdType), M:(IdLnkIdType), loc:(EId), k:(EKnd),
Thm* e:E. eventtype(k;loc;V;M;e Type
kindcaseDef kindcase(k;a.f(a);l,t.g(l;t))
Def == if islocal(k) f(act(k)) else g(lnk(k);tag(k)) fi
Thm* B:Type, k:Knd, f:(IdB), g:(IdLnkIdB).
Thm* kindcase(k;a.f(a);l,t.g(l,t))  B
lnkDef lnk(k) == 1of(outl(k))
Thm* k:Knd. isrcv(k lnk(k IdLnk
lengthDef ||as|| == Case of as; nil  0 ; a.as'  ||as'||+1  (recursive)
Thm* A:Type, l:A List. ||l||  
Thm* ||nil||  
isrcvDef isrcv(k) == isl(k)
Thm* k:Knd. isrcv(k 
iffDef P  Q == (P  Q) & (P  Q)
Thm* A,B:Prop. (A  B Prop
lsrcDef source(l) == 1of(l)
Thm* l:IdLnk. source(l Id
ldstDef destination(l) == 1of(2of(l))
Thm* l:IdLnk. destination(l Id
tagofDef tag(k) == 2of(outl(k))
Thm* k:Knd. isrcv(k tag(k Id
selectDef l[i] == hd(nth_tl(i;l))
Thm* A:Type, l:A List, n:. 0n  n<||l||  l[n A
transDef Trans x,y:TE(x;y) == a,b,c:TE(a;b E(b;c E(a;c)
Thm* T:Type, E:(TTProp). (Trans x,y:TE(x,y))  Prop
outlDef outl(x) == InjCase(xyyz. "???")
Thm* A,B:Type, x:A+B. isl(x outl(x A
mlnkDef mlnk(m) == 1of(m)
Thm* M:(IdLnkIdType), m:Msg(M). mlnk(m IdLnk
pi1Def 1of(t) == t.1
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p A
islocalDef islocal(k) == isl(k)
Thm* k:Knd. islocal(k 
islDef isl(x) == InjCase(xy. truez. false)
Thm* A,B:Type, x:A+B. isl(x 
rev_impliesDef P  Q == Q  P
Thm* A,B:Prop. (A  B Prop
pi2Def 2of(t) == t.2
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p B(1of(p))
nth_tlDef nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi  (recursive)
Thm* A:Type, as:A List, i:. nth_tl(i;as A List
hdDef hd(l) == Case of l; nil  "?" ; h.t  h
Thm* A:Type, l:A List. ||l|| hd(l A
actofDef act(k) == outr(k)
Thm* k:Knd. islocal(k act(k Id
tlDef tl(l) == Case of l; nil  nil ; h.t  t
Thm* A:Type, l:A List. tl(l A List
le_intDef ij == j<i
Thm* i,j:. (ij 
outrDef outr(x) == InjCase(xy. "???"; zz)
Thm* A,B:Type, x:A+Bisl(x outr(x B
bnotDef b == if b false else true fi
Thm* b:b  
lt_intDef i<j == if i<j true ; false fi
Thm* i,j:. (i<j 

Syntax:ES has structure: event_system{i:l}

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WhoCites Definitions mb event system 2 Sections EventSystems Doc