Who Cites reachable via? | |
reachable_via | Def (M -tr- > s) == s0:M.state. M.init(s0) & trace_reachable(M;s0;tr;s) |
Thm* M:sm{i:l}(), s:M.state, tr:M.action List. (M -tr- > s) Prop | |
trace_reachable | Def trace_reachable(M;s;l;s') == Case of l; nil s = s' M.state ; a.l' x:M.state. M.trans(s,a,x) & trace_reachable(M;x;l';s') (recursive) |
Thm* M:sm{i:l}(), l:M.action List, s,s':M.state. trace_reachable(M;s;l;s') Prop | |
sm_init | Def t.init == 1of(2of(2of(t))) |
Thm* M:sm{i:l}(). M.init M.stateProp | |
sm_state | Def M.state == {M.ds} |
Thm* M:sm{i:l}(). M.state Type | |
sm_trans | Def t.trans == 2of(2of(2of(t))) |
Thm* M:sm{i:l}(). M.trans M.stateM.actionM.stateProp | |
sm_ds | Def t.ds == 1of(2of(t)) |
Thm* t:sm{i:l}(). t.ds Decl | |
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 | |
record | Def {d} == l:Labeldecl_type(d;l) |
Thm* d:Decl. {d} Type | |
decl_type | Def decl_type(d;x) == d(x) |
Thm* dec:Decl, x:Label. decl_type(dec;x) Type | |
lbl | Def Label == {p:Pattern| ground_ptn(p) } |
Thm* Label Type | |
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) | |
assert | Def b == if b True else False fi |
Thm* b:. b Prop | |
ptn | Def Pattern == rec(T.ptn_con(T)) |
Thm* Pattern Type | |
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_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 | Def Case(value) body == body(value,value) |
ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
Thm* T:Type. ptn_con(T) Type | |
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 | |
tl | Def tl(l) == Case of l; nil nil ; h.t t |
Thm* A:Type, l:A List. tl(l) A List | |
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)) |
Syntax: | (M -tr- > s) | has structure: | reachable_via(M; s; tr) |
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