| Who Cites tla? |
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tla | Def (M |= x,x',tr,tr'.R(x;x';tr;tr')) == x,x':M.state, tr:M.action List, a:M.action. (M -tr- > x)  M.trans(x,a,x')  R(x;x';tr;tr @ [a]) |
| | Thm* M:sm{i:l}(), R:(M.state M.state (M.action List) (M.action List) Prop). (M |= x,x',tr,tr'.R(x,x',tr,tr')) Prop |
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append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | Thm* T:Type, as,bs:T List. (as @ bs) T List |
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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 |
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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 |
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sm_trans | Def t.trans == 2of(2of(2of(t))) |
| | Thm* M:sm{i:l}(). M.trans M.state M.action M.state Prop |
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sm_action | Def M.action == ( M.da) |
| | Thm* M:sm{i:l}(). M.action Type |
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sm_state | Def M.state == {M.ds} |
| | Thm* M:sm{i:l}(). M.state Type |
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sm_init | Def t.init == 1of(2of(2of(t))) |
| | Thm* M:sm{i:l}(). M.init M.state Prop |
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sm_ds | Def t.ds == 1of(2of(t)) |
| | Thm* t:sm{i:l}(). t.ds Decl |
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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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sm_da | Def t.da == 1of(t) |
| | Thm* t:sm{i:l}(). t.da Decl |
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sigma | Def ( d) == l:Label decl_type(d;l) |
| | Thm* d:Decl. ( d) Type |
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record | Def {d} == l:Label decl_type(d;l) |
| | Thm* d:Decl. {d} Type |
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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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decl_type | Def decl_type(d;x) == d(x) |
| | Thm* dec:Decl, x:Label. decl_type(dec;x) Type |
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lbl | Def Label == {p:Pattern| ground_ptn(p) } |
| | Thm* Label Type |
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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)  |
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assert | Def b == if b True else False fi |
| | Thm* b: . b Prop |
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ptn | Def Pattern == rec(T.ptn_con(T)) |
| | Thm* Pattern Type |
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case_default | Def Default = > body(value,value) == body |
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band | Def p q == if p q else false fi |
| | Thm* p,q: . (p q)  |
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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)))) |
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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]) |
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case | Def Case(value) body == body(value,value) |
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ptn_con | Def ptn_con(T) == Atom+ +Atom+(T T) |
| | Thm* T:Type. ptn_con(T) Type |
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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 |
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tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | Thm* A:Type, l:A List. tl(l) A List |
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case_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
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case_inr | Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |