2. a : Id
3. T : Type
4. ds : x:Id fp-> Type
5. P : State(ds)
TProp
6. w : World
7. p1 :
i:Id, t:
, l:IdLnk. 
source(l) = i 
onlnk(l;m(i;t)) = nil
8. p3 :
8.
i:Id, t:. isnull(a(i;t)) (x:Id. s(i;t+1).x = s(i;t).x) & m(i;t) = nil
9. p5 :
9.
i:Id, t:, l:IdLnk.
9. isrcv(l;a(i;t))
9.
9. destination(l) = i & ||queue(l;t)||
1 & hd(queue(l;t)) = msg(a(i;t))
10. p6 :
10.
l:IdLnk, t:.
10.
t':. t
t' & isrcv(l;a(destination(l);t')) 
queue(l;t') = nil
11.
i:Id, t:, l:IdLnk. source(l) = i onlnk(l;m(i;t)) = nil
12.
i:Id, t:. isnull(a(i;t)) (x:Id. s(i;t+1).x = s(i;t).x) & m(i;t) = nil
13.
i:Id, t:, l:IdLnk.
13. isrcv(l;a(i;t))
13.
13. destination(l) = i & ||queue(l;t)||
1 & hd(queue(l;t)) = msg(a(i;t))
14.
l:IdLnk, t:.
14.
t':. tt' & isrcv(l;a(destination(l);t')) queue(l;t') = nil
15.
l:IdLnk, tg:Id.
15. (w.M(l,tg))
r if eqof(IdDeq)(source(l),i)
15. (w.M(l,tg))
r if <ds,<[locl(a)],
x.T>,,<[a],x.P>,,,,,
>
15. (w.M(l,tg))
r else fi.da(rcv(l; tg))
16. (eqof(IdDeq)(i,i)) ~ true
17.
a@0:Id, t:.
17.
t':.
17. t
t'
17. &
isnull(a(i;t')) & kind(a(i;t')) = locl(a@0)
17. &
locl(a@0) 
dom(<[locl(a)],x.T>)
17. &
P@0 != <[a],x.P>(a@0) ==> v:<[locl(a)],x.T>(locl(a@0))?Top.
17. &
P@0((x.s(i;t').x),v)
18.
t:.
18.
isnull(a(i;t))
18.
18. (islocal(kind(a(i;t)))
18. (
18. ((eqof(IdDeq)(a,act(kind(a(i;t))))
false)
18. (
18. (P((
x.s(i;t).x),val(a(i;t))))
18. & (
x:Id.
18. & (deq-member(product-deq(Knd;Id;KindDeq;IdDeq);<kind(a(i;t)),x>;1of())
18. & (
18. & (s(i;t+1).x = 2of()(<kind(a(i;t)),x>,
x.s(i;t).x,val(a(i;t))))
18. & (
l:IdLnk.
18. & (deq-member(product-deq(Knd;IdLnk;KindDeq;IdLnkDeq);<kind(a(i;t)),l>;1of(
18. & (deq-member(product-deq(Knd;IdLnk;KindDeq;IdLnkDeq);<kind(a(i;t)),l>;))
18. & (
18. & (withlnk(l;m(i;t))
18. & (=
18. & (if source(l) = i
18. & (if concat(map(
tgf.map(x.<1of(tgf)
18. & (if concat(map(
tgf.map(x.,x>;2of(tgf)
18. & (if concat(map(
tgf.map(x.,x>;((x.s(i;t).x)
18. & (if concat(map(
tgf.map(x.,x>;,val(a(i;t))));2of()(<kind(a(i;t)),l>)))
18. & (else nil fi)
18. & (
x:Id.
18. & (
(deq-member(IdDeq;x;1of()) deq-member(KindDeq;kind(a(i;t));2of()(x)))
18. & (
18. & (s(i;t).x = s(i;t+1).x)
18. & (
l:IdLnk, tg:Id.
18. & (
(deq-member(product-deq(IdLnk;Id;IdLnkDeq;IdDeq);<l,tg>;1of())
18. & (
(
18. & (
(deq-member(KindDeq;kind(a(i;t));2of()(<l,tg>)))
18. & (
18. & (w-tagged(tg; onlnk(l;m(i;t))) = nil)
19.
x:Id. deq-member(IdDeq;x;1of()) s(i;0).x = 2of()(x)
20.
a@0:Action(i).
20.
isnull(a@0) (valtype(i;a@0) r <[locl(a)],x.T>(kind(a@0))?Top)
21.
x:Id.
21. vartype(i;x)
r if deq-member(IdDeq;x;1of(ds)) 2of(ds)(x) else Top fi
22. IdDeq
EqDecider(Id)
23.
x:Id. vartype(i;x) r ds(x)?Top
24. j : Id
25. t :
26. j = i
27.
isnull(a(j;t))
28.
isnull(a(i;t))
29. (
x.s(i;t).x) State(ds)
30. t' :
31. t+1
t'
32.
v:T. P((x.s(i;t').x),v)
33. t2 :
34. t2<t'
35.
isnull(a(i;t2))
36.
t3:. t2<t3 & t3<t' isnull(a(i;t3))
37. t
t2
38. loc(<j,t>) = loc(<i,t2>) & (<j,t> < <i,t2>)
<j,t> = <i,t2>
39. v : T
40.
P((x.s(i;t').x),v)
41. z : Id
42. t3 :
43. 0<t3
44. t2+1
t3
45. t3
t'
46. t2+1
t3-1
47. s(i;t2+1).z = s(i;t3-1).z
48. isnull(a(i;t3-1))
49.
x:Id. s(i;t3-1+1).x = s(i;t3-1).x
50. m(i;t3-1) = nil
51. s(i;t3-1+1).z = s(i;t3-1).z
52.
x:Id. s(i;t3-1+1).x = s(i;t3-1).x
53. m(i;t3-1) = nil
54. s(i;t3).z = s(i;t3-1).z
55. vartype(i;z)
vartype(i;z) r ds(z)?Top
