| | Who Cites col? |
|
| col |
Def Collection(T) == T  Prop |
| | | Thm*  T:Type{i'}. Collection{i}(T)  Type{i'} |
|
| 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) |
|
| decls_mng |
Def [[ds]] rho == [[d]] rho for d {d:dec()| d ds } |
| | | Thm* ds:Collection(dec()), rho:Decl. [[ds]] rho Decl |
|
| dec |
Def dec() == Label SimpleType |
| | | Thm* dec() Type |
|
| decl |
Def Decl == LabelType |
| | | Thm* Decl{i} Type{i'} |
|
| sigma |
Def ( d) == l:Labeldecl_type(d;l) |
| | | Thm* d:Decl. (d) Type |
|
| sts_mng |
Def [[sts]] rho ==  x:{x:SimpleType| x sts }. [[x]] rho |
| | | Thm* sts:Collection(SimpleType), rho:Decl. [[sts]] rho Type |
|
| st |
Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
|
| lbl |
Def Label == {p:Pattern| ground_ptn(p) } |
| | | Thm* Label Type |
|
| dec_typ |
Def t.typ == 2of(t) |
| | |
Thm* t:dec(). t.typ SimpleType |
|
| dec_lbl |
Def t.lbl == 1of(t) |
| | |
Thm* t:dec(). t.lbl Label |
|
| dec_mng |
Def [[d]] rho == Case(d) Case x : s = > x:[[s]] rho |
| | |
Thm* rho:Decl, d:dec(). [[d]] rho Decl |
|
| dbase |
Def x:y(a) == if a = x y else Top fi |
| | | Thm* x:Label, y:Type. x:y Decl |
|
| 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  |
|
| assert |
Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| 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) |
|
| 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') |
|
| col_member |
Def x c == c(x) |
| | | Thm* T:Type, x:T, c:Collection(T). x c Prop |
|
| dall |
Def D(i) for i I(x) == i:I. D(i)(x) |
| | | Thm* I:Type, D:(IDecl). D(i) for i I Decl |
|
| 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) |
|
| ptn |
Def Pattern == rec(T.ptn_con(T)) |
| | |
Thm* Pattern Type |
|
| decl_type |
Def decl_type(d;x) == d(x) |
| | | Thm* dec:Decl, x:Label. decl_type(dec;x) Type |
|
| st_mng |
Def [[s]] rho == t_iterate(st_lift(rho); x,y. xy;s) |
| | | Thm* rho:Decl, s:SimpleType. [[s]] rho Type |
|
| tree |
Def Tree(E) == rec(T.tree_con(E;T)) |
| | |
Thm* E:Type. Tree(E) Type |
|
| pi2 |
Def 2of(t) == t.2 |
| | |
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
|
| pi1 |
Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
|
| 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 |
|
| case_default |
Def Default = > body(value,value) == body |
|
| band |
Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
|
| 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)))) |
|
| case |
Def Case(value) body == body(value,value) |
|
| 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)) |
|
| case_mk_dec |
Def Case lbl : typ = > body(lbl;typ)(x,z) == x/x2,x1. body(x2;x1) |
|
| ptn_con |
Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
|
| st_lift |
Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) |
| | | Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type |
|
| tree_con |
Def tree_con(E;T) == E+(TT) |
| | | Thm* E,T:Type. tree_con(E;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)) |
|
| top |
Def Top == Void given Void |
| | |
Thm* Top Type |
|
| case_tree_leaf |
Def Case tree_leaf(x) = > body(x) cont(x1,z)
== InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| 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)) |
