| Some definitions of interest. |
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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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ma-da | Def M.da(a) == 1of(2of(M))(a)?Top |
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ma-sub | Def M1 M2
Def == 1of(M1) 1of(M2) & 1of(2of(M1)) 1of(2of(M2))
Def == & 1of(2of(2of(M1))) 1of(2of(2of(M2)))
Def == & & 1of(2of(2of(2of(M1)))) 1of(2of(2of(2of(M2))))
Def == & & 1of(2of(2of(2of(2of(M1))))) 1of(2of(2of(2of(2of(M2)))))
Def == & & 1of(2of(2of(2of(2of(2of(M1)))))) 1of(2of(2of(2of(2of(2of(M2))))))
Def == & & 1of(2of(2of(2of(2of(2of(2of(M1))))))) 1of(2of(2of(2of(2of(2of(2of(
Def == & & 1of(2of(2of(2of(2of(2of(2of(M1))))))) 1of(M2)))))))
Def == & & 1of(2of(2of(2of(2of(2of(2of(2of(
Def == & & 1of(M1)))))))) 1of(2of(2of(2of(2of(2of(2of(2of(M2)))))))) |
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msga | Def MsgA
Def == ds:x:Id fp-> Type
Def == da:a:Knd fp-> Type
Def == x:Id fp-> ds(x)?Void a:Id fp-> State(ds) ma-valtype(da; locl(a)) Prop
Def == kx:Knd Id fp-> State(ds) ma-valtype(da; 1of(kx)) ds(2of(kx))?Void
Def == kl:Knd IdLnk fp-> (tg:Id
Def == kl:Knd IdLnk fp-> ( State(ds) ma-valtype(da; 1of(kl))
Def == kl:Knd IdLnk fp-> ((da(rcv(2of(kl); tg))?Void List)) List
Def == x:Id fp-> Knd List ltg:IdLnk Id fp-> Knd List Top |
| | Thm* MsgA Type{i'} |
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Kind-deq | Def KindDeq == union-deq(IdLnk Id;Id;product-deq(IdLnk;Id;IdLnkDeq;IdDeq);IdDeq) |
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Knd | Def Knd == (IdLnk Id)+Id |
| | Thm* Knd Type |
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IdLnk | Def IdLnk == Id Id  |
| | Thm* IdLnk Type |
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idlnk-deq | Def IdLnkDeq == product-deq(Id;Id ;IdDeq;product-deq(Id; ;IdDeq;NatDeq)) |
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ma-st | Def M.state == State(1of(M)) |
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ma-state | Def State(ds) == x:Id ds(x)?Top |
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Id | Def Id == Atom  |
| | Thm* Id Type |
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eq_id | Def a = b == eqof(IdDeq)(a,b) |
| | Thm* a,b:Id. a = b  |
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fpf-sub | Def f g == x:A. x dom(f)  x dom(g) & f(x) = g(x) B(x) |
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id-deq | Def IdDeq == product-deq(Atom; ;AtomDeq;NatDeq) |
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product-deq | Def product-deq(A;B;a;b) == <proddeq(a;b),prod-deq(A;B;a;b)> |
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assert | Def b == if b True else False fi |
| | Thm* b: . b Prop |
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concat | Def concat(ll) == reduce( l,l'. l @ l';nil;ll) |
| | Thm* T:Type, ll:(T List) List. concat(ll) T List |
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fpf | Def a:A fp-> B(a) == d:A List a:{a:A| (a d) } B(a) |
| | Thm* A:Type, B:(A Type). a:A fp-> B(a) Type |
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fpf-cap | Def f(x)?z == if x dom(f) f(x) else z fi |
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fpf-ap | Def f(x) == 2of(f)(x) |
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fpf-dom | Def x dom(f) == deq-member(eq;x;1of(f)) |
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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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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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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |
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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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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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rcv | Def rcv(l; tg) == inl(<l,tg>) |
| | Thm* l:IdLnk, tg:Id. rcv(l; tg) Knd |
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top | Def Top == Void given Void |
| | Thm* Top Type |