WhoCites Definitions mb automata 2 Sections GenAutomata Doc

Who Cites col?
col Def Collection(T) == TProp
Thm* T:Type{i'}. Collection{i}(T) Type{i'}
col_le Def c1 c2 == x:T. x c1 x c2
Thm* T:Type, c1,c2:Collection(T). c1 c2 Prop
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)
dec Def dec() == LabelSimpleType
Thm* dec() Type
st Def SimpleType == Tree(Label+Unit)
Thm* SimpleType Type
lbl Def Label == {p:Pattern| ground_ptn(p) }
Thm* Label Type
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
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
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
assert Def b == if b True else False fi
Thm* b:. b Prop
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
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
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))
ptn_con Def ptn_con(T) == Atom++Atom+(TT)
Thm* T:Type. ptn_con(T) 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))

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WhoCites Definitions mb automata 2 Sections GenAutomata Doc