| | Who Cites sm a rename? |
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| sm_a_rename | Def (f o M) == mk_sm(M.da o f, M.ds, M.init,  s1,a,s2.  l:Label. kind(a) = f(l) & M.trans(s1, < l,value(a) > ,s2)) |
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| value | Def value(a) == 2of(a) |
| | | Thm*  d:Decl, a:( d). value(a)  d(kind(a)) |
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| sm_trans | Def t.trans == 2of(2of(2of(t))) |
| | | Thm* M:sm{i:l}(). M.trans M.state  M.actionM.stateProp |
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| kind | Def kind(a) == 1of(a) |
| | | Thm* d:Decl, a:(d). kind(a) Label |
| | | Thm* M:sm{i:l}(), a:M.action. kind(a) Label & kind(a) Pattern |
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| rename_decl | Def d o f(x) ==  y:Label. if x = f(y) d(y) else Top fi |
| | | Thm* d:Decl, f:(LabelLabel). d o f Decl |
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| lbl | Def Label == {p:Pattern|  ground_ptn(p) } |
| | | Thm* Label Type |
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| sm_init | Def t.init == 1of(2of(2of(t))) |
| | | Thm* M:sm{i:l}(). M.init M.stateProp |
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| sm_ds | Def t.ds == 1of(2of(t)) |
| | | Thm* t:sm{i:l}(). t.ds Decl |
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| sm_da | Def t.da == 1of(t) |
| | | Thm* t:sm{i:l}(). t.da Decl |
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| mk_sm | Def mk_sm(da, ds, init, trans) == < da,ds,init,trans > |
| | | Thm* da,ds:Decl, init:({ds}Prop), trans:({ds}(da){ds}Prop). mk_sm(da, ds, init, trans) sm{i:l}() |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:A B(a)). 2of(p) B(1of(p)) |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
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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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| top | Def Top == Void given Void |
| | | Thm* Top Type |
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| 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 |
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| case_default | Def Default = > body(value,value) == body |
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| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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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+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
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| eq_atom | Def x=yAtom == if x=yAtomtrue; false fi |
| | | Thm* x,y:Atom. x=yAtom |
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| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j) |
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| 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]) |
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| case_ptn_atom | Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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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)) |
