| | Who Cites st app? |
|
| st_app | Def st_app(c1;c2) == ( s2 c2.(s1c1.st_app1(s1;s2))) |
| | | Thm*  c1,c2:Collection(SimpleType). st_app(c1;c2) Collection(SimpleType) |
|
| st_app1 | Def st_app1(s1;s2) == Case(s1) Case a;b = > if st_eq(a;s2) < b > else < > fi Default = > < > |
| | | Thm* s1,s2:SimpleType. st_app1(s1;s2) Collection(SimpleType) |
|
| st | Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
|
| col_accum | Def (xc.f(x))(y) ==  x:T. x c & y f(x) |
| | | Thm* T,T':Type, f:(T  Collection(T')), c:Collection(T). (xc.f(x)) Collection(T') |
|
| col_none | Def < > (x) == False |
| | | Thm* T:Type. < > Collection(T) |
|
| st_eq | Def st_eq(s1;s2) == Case(s1) Case a;b = > Case(s2) Case a';b' = > st_eq(a;a')  st_eq(b;b') Default = > false Case tree_leaf(x) = > Case(s2) Case a';b' = > false Case tree_leaf(y) = > InjCase(x; x'. InjCase(y; y'. x' = y'; b. false); a. InjCase(y; y'. false; b. true)) Default = > false Default = > false (recursive) |
| | | Thm* s1,s2:SimpleType. st_eq(s1;s2)  |
|
| lbl | Def Label == {p:Pattern|  ground_ptn(p) } |
| | | Thm* Label Type |
|
| 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 |
|
| 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) |
|
| case_default | Def Default = > body(value,value) == body |
|
| col_singleton | Def < x > (y) == y = x T |
| | | Thm* T:Type, x:T. < x > Collection(T) |
|
| 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)) |
|
| case | Def Case(value) body == body(value,value) |
|
| tree | Def Tree(E) == rec(T.tree_con(E;T)) |
| | | Thm* E:Type. Tree(E) Type |
|
| col_member | Def x c == c(x) |
| | | Thm* T:Type, x:T, c:Collection(T). x c Prop |
|
| case_tree_leaf | Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| ptn | Def Pattern == rec(T.ptn_con(T)) |
| | | Thm* Pattern Type |
|
| tree_con | Def tree_con(E;T) == E+(T T) |
| | | Thm* E,T:Type. tree_con(E;T) Type |
|
| 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)))) |
|
| eq_atom | Def x=yAtom == if x=yAtomtrue; false fi |
| | | Thm* x,y:Atom. x=yAtom |
|
| 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]) |
|
| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j: . (i=j) |
|
| 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]) |
|
| case_ptn_atom | Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
|
| 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 |
|
| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
|
| case_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
|
| case_inr | Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |
