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Who Cites switch decomposable?
switch_decomposableDef switch-decomposable(E)(L) == L = nil |E| List (Q:(||L||Prop). (i:||L||. Dec(Q(i))) & (i:||L||. Q(i)) & (i:||L||. Q(i) (is-send(E)(L[i]))) & (i,j:||L||. Q(i) Q(j) tag(E)(L[i]) = tag(E)(L[j])) & (i,j:||L||. Q(i) ij C(Q)(j)))
message_closure Def C(Q)(i) == k:||L||. Q(k) & (L[k] =msg=(E) L[i])
Thm* E:EventStruct, L:|E| List, Q:(||L||Prop). C(Q) ||L||Prop
int_seg Def {i..j} == {k:| i k < j }
Thm* m,n:. {m..n} Type
lelt Def i j < k == ij & j < k
le Def AB == B < A
Thm* i,j:. (ij) Prop
length Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
Thm* A:Type, l:A List. ||l||
Thm* ||nil||
select Def l[i] == hd(nth_tl(i;l))
Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
event_tag Def tag(E) == 1of(2of(2of(2of(2of(2of(E))))))
Thm* E:TaggedEventStruct. tag(E) |E|Label
lbl Def Label == {p:Pattern| ground_ptn(p) }
Thm* Label Type
event_is_snd Def is-send(E) == 1of(2of(2of(2of(2of(E)))))
Thm* E:EventStruct. is-send(E) |E|
assert Def b == if b True else False fi
Thm* b:. b Prop
decidable Def Dec(P) == P P
Thm* A:Prop. Dec(A) Prop
carrier Def |S| == 1of(S)
Thm* S:Structure. |S| Type
event_msg_eq Def =msg=(E)(e_1,e_2) == (msg(E)(e_1)) =(MS(E)) (msg(E)(e_2))
Thm* E:EventStruct. =msg=(E) |E||E|
not Def A == A False
Thm* A:Prop. (A) Prop
nth_tl Def 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
ground_ptn Def ground_ptn(p) == Case(p) Case ptn_var(v) = > false Case ptn_pr( < x, y > ) = > ground_ptn(x)ground_ptn(y) Default = > true (recursive)
Thm* p:Pattern. ground_ptn(p)
msg_eq Def =(M)(m_1,m_2) == ((content(M)(m_1)) =(cEQ(M)) (content(M)(m_2)))sender(M)(m_1) = sender(M)(m_2)(uid(M)(m_1)=uid(M)(m_2))
Thm* M:MessageStruct. =(M) |M||M|
eq_lbl Def l1 = l2 == Case(l1) Case ptn_atom(x) = > Case(l2) Case ptn_atom(y) = > x=yAtom Default = > false Case ptn_int(x) = > Case(l2) Case ptn_int(y) = > x=y Default = > false Case ptn_var(x) = > Case(l2) Case ptn_var(y) = > x=yAtom Default = > false Case ptn_pr( < x, y > ) = > Case(l2) Case ptn_pr( < u, v > ) = > x = uy = v Default = > false Default = > false (recursive)
Thm* l1,l2:Pattern. l1 = l2
case_ptn_var Def Case ptn_var(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
case_ptn_int Def Case ptn_int(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > (x1.inl(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)]) cont(hd(x1),z))([x1])
hd Def hd(l) == Case of l; nil "?" ; h.t h
Thm* A:Type, l:A List. ||l||1 hd(l) A
Thm* A:Type, l:A List. hd(l) A
event_msg Def msg(E) == 1of(2of(2of(E)))
Thm* E:EventStruct. msg(E) |E||MS(E)|
event_msg_str Def MS(E) == 1of(2of(E))
Thm* E:EventStruct. MS(E) MessageStruct
msg_id Def uid(MS) == 1of(2of(2of(2of(2of(MS)))))
Thm* M:MessageStruct. uid(M) |M|
msg_sender Def sender(MS) == 1of(2of(2of(2of(MS))))
Thm* M:MessageStruct. sender(M) |M|Label
msg_content Def content(MS) == 1of(2of(2of(MS)))
Thm* M:MessageStruct. content(M) |M||cEQ(M)|
msg_content_eq Def cEQ(MS) == 1of(2of(MS))
Thm* M:MessageStruct. cEQ(M) DecidableEquiv
eq_dequiv Def =(DE) == 1of(2of(DE))
Thm* E:DecidableEquiv. =(E) |E||E|
pi2 Def 2of(t) == t.2
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
pi1 Def 1of(t) == t.1
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
ptn Def Pattern == rec(T.ptn_con(T))
Thm* Pattern Type
tl Def tl(l) == Case of l; nil nil ; h.t t
Thm* A:Type, l:A List. tl(l) A List
le_int Def ij == j < i
Thm* i,j:. (ij)
case_default Def Default = > body(value,value) == body
band Def pq == if p q else false fi
Thm* p,q:. (pq)
case_lbl_pair Def Case ptn_pr( < x, y > ) = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. InjCase(x2; _. cont(z,z); x2@0. InjCase(x2@0; _. cont(z,z); x2@1. x2@1/x3,x2@2. body(x3;x2@2))))
case Def Case(value) body == body(value,value)
ptn_con Def ptn_con(T) == Atom++Atom+(TT)
Thm* T:Type. ptn_con(T) Type
eq_int Def i=j == if i=j true ; false fi
Thm* i,j:. (i=j)
lt_int Def i < j == if i < j true ; false fi
Thm* i,j:. (i < j)
bnot Def b == if b false else true fi
Thm* b:. b
case_inl Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))
case_inr Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
eq_atom Def x=yAtom == if x=yAtomtrue; false fi
Thm* x,y:Atom. x=yAtom
case_ptn_atom Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))

Syntax:switch-decomposable(E) has structure: switch_decomposable{i:l}(E)

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WhoCites Definitions GenAutomata Sections NuprlLIB Doc