| Who Cites arrow? |
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arrow | Def a b == tree_node( < a, b > ) |
| | Thm* a,b:SimpleType. a b SimpleType |
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col | Def Collection(T) == T Prop |
| | Thm* T:Type{i'}. Collection{i}(T) Type{i'} |
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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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st | Def SimpleType == Tree(Label+Unit) |
| | Thm* SimpleType Type |
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node | Def tree_node( < x, y > ) == tree_node( < x,y > ) |
| | Thm* E:Type, x,y:Tree(E). tree_node( < x, y > ) Tree(E) |
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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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tree_node | Def tree_node(x) == inr(x) |
| | Thm* E,T:Type, x:(T T). tree_node(x) tree_con(E;T) |
| | Thm* E:Type, x,y:Tree(E). tree_node( < x,y > ) Tree(E) |
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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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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)) |