| | Who Cites col? |
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| col | Def Collection(T) == T  Prop |
| | | Thm*  T:Type{i'}. Collection{i}(T)  Type{i'} |
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| col_equal | Def c1 = c2 == x:T. x c1   x c2 |
| | | Thm* T:Type, c1,c2:Collection(T). c1 = c2 Prop |
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| sts_mng | Def [[sts]] rho ==  x:{x:SimpleType| x sts }. [[x]] rho |
| | | Thm* sts:Collection(SimpleType), rho:Decl. [[sts]] rho Type |
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| col_member | Def x c == c(x) |
| | | Thm* T:Type, x:T, c:Collection(T). x c Prop |
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| decl | Def Decl == LabelType |
| | | Thm* Decl{i} Type{i'} |
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| st | Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
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| iff | Def P Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
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| lbl | Def Label == {p:Pattern|  ground_ptn(p) } |
| | | Thm* Label Type |
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| tree | Def Tree(E) == rec(T.tree_con(E;T)) |
| | | Thm* E:Type. Tree(E) Type |
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| st_mng | Def [[s]] rho == t_iterate(st_lift(rho); x,y. xy;s) |
| | | Thm* rho:Decl, s:SimpleType. [[s]] rho Type |
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| rev_implies | Def P Q == Q P |
| | | Thm* A,B:Prop. (A B) Prop |
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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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| tree_con | Def tree_con(E;T) == E+(T T) |
| | | Thm* E,T:Type. tree_con(E;T) Type |
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| st_lift | Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) |
| | | Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type |
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| t_iterate | Def t_iterate(l;n;t) == Case(t) Case x;y = > n(t_iterate(l;n;x),t_iterate(l;n;y)) Case tree_leaf(x) = > l(x) Default = > True (recursive) |
| | | Thm* E,A:Type, l:(EA), n:(AAA), t:Tree(E). t_iterate(l;n;t) A |
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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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| top | Def Top == Void given Void |
| | | Thm* Top Type |
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| case_tree_leaf | Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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| case_node | Def Case x;y = > body(x;y) cont(x1,z) == InjCase(x1; _. cont(z,z); x2. x2/x3,x2@0. body(x3;x2@0)) |
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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)) |
