Who Cites switch decomposable? | |
switch_decomposable | Def 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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