| | Who Cites vcs singleton? |
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| vcs_singleton | Def < *v* > == < v > |
| | | Thm*  v:vc{i:l}(). < *v* >  VCs |
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| vc | Def vc{i:l}() == imp{i:l}()+qimp{i:l}() |
| | | Thm* vc{i:l}() Type{i'} |
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| col_singleton | Def < x > (y) == y = x T |
| | | Thm* T:Type, x:T. < x > Collection(T) |
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| qimp | Def qimp{i:l}() == Label FmlaFmla |
| | | Thm* qimp{i:l}() Type{i'} |
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| imp | Def imp{i:l}() == FmlaFmla |
| | | Thm* imp{i:l}() Type{i'} |
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| pred | Def Fmla == Collection(rel()) |
| | | Thm* Fmla{i} Type{i'} |
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| rel | Def rel() == relname()(Term List) |
| | | Thm* rel() Type |
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| term | Def Term == Tree(ts()) |
| | | Thm* Term Type |
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| relname | Def relname() == SimpleType+Label |
| | | Thm* relname() Type |
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| ts | Def ts() == Label+Label+Label+Label+Label |
| | | Thm* ts() Type |
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| st | Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
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| lbl | Def Label == {p:Pattern|  ground_ptn(p) } |
| | | Thm* Label Type |
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| col | Def Collection(T) == T  Prop |
| | | Thm* T:Type{i'}. Collection{i}(T) Type{i'} |
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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 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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| tree | Def Tree(E) == rec(T.tree_con(E;T)) |
| | | Thm* E:Type. Tree(E) 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)) |
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| tree_con | Def tree_con(E;T) == E+(TT) |
| | | Thm* E,T:Type. tree_con(E;T) Type |
