| Who Cites st? |
|
st |
Def SimpleType == Tree(Label+Unit) |
| | Thm* SimpleType Type |
|
lbl |
Def Label == {p:Pattern| ground_ptn(p) } |
| | Thm* Label Type |
|
assert |
Def b == if b True else False fi |
| | Thm* b: . b Prop |
|
iff |
Def P  Q == (P  Q) & (P  Q) |
| | Thm* A,B:Prop. (A  B) Prop |
|
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)  |
|
rev_implies |
Def P  Q == Q  P |
| | Thm* A,B:Prop. (A  B) Prop |
|
tree |
Def Tree(E) == rec(T.tree_con(E;T)) |
| |
Thm* E:Type. Tree(E) Type |
|
eq_lbl |
Def l1 = l2
== Case(l1)
Case ptn_atom(x) = >
Case(l2)
Case ptn_atom(y) = >
x= y Atom
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= y Atom
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  |
|
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 |
|
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)) |
|
case |
Def Case(value) body == body(value,value) |
|
band |
Def p q == if p q else false fi |
| | Thm* p,q: . (p q)  |
|
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= y Atom == if x=y Atom true ; false fi |
| | Thm* x,y:Atom. x= y Atom  |
|
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+(T T) |
| | 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)) |