| | 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_le | Def c1  c2 == x:T. x c1   x c2 |
| | | Thm* T:Type, c1,c2:Collection(T). c1 c2 Prop |
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| dec_lookup | Def dec_lookup(ds;x) == < d.typ | d < d ds |  d.lbl = x > > |
| | | Thm* ds:Collection(dec()), x:Label. dec_lookup(ds;x) Collection(SimpleType) |
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| dec | Def dec() == Label SimpleType |
| | | Thm* dec() 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_filter | Def < x c | P(x) > (x) == x c & P(x) |
| | | Thm* T:Type, c:Collection(T), Q:(TProp). < i c | Q(i) > Collection(T) |
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| col_map | Def < f(x) | x c > (y) ==  x:T. x c & y = f(x) T' |
| | | Thm* T,T':Type, f:(TT'), c:Collection(T). < f(x) | x c > Collection(T') |
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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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| dec_typ | Def t.typ == 2of(t) |
| | | Thm* t:dec(). t.typ SimpleType |
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| dec_lbl | Def t.lbl == 1of(t) |
| | | Thm* t:dec(). t.lbl Label |
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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 = u y = v Default = > false Default = > false (recursive) |
| | | Thm* l1,l2:Pattern. l1 = l2  |
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| assert | Def b == if b True else False fi |
| | | Thm* b:. 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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| ptn | Def Pattern == rec(T.ptn_con(T)) |
| | | Thm* Pattern 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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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(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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| 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 | Def Case(value) body == body(value,value) |
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| eq_atom | Def x=yAtom == if x=yAtomtrue; false fi |
| | | Thm* x,y:Atom. x=yAtom |
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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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| 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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| ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
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| tree_con | Def tree_con(E;T) == E+(TT) |
| | | Thm* E,T:Type. tree_con(E;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)) |
