| Who Cites addprime? |
|
addprime | Def (t)' == term_iterate(x.x';x.x';op.op;f.f;P.trace(P);a,b. a b;t) |
| | Thm* t:Term. (t)' Term |
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tapp |
Def t1 t2 == tree_node( < t1, t2 > ) |
| | Thm* t1,t2:Term. t1 t2 Term |
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ttrace |
Def trace(l) == tree_leaf(ts_trace(l)) |
| | Thm* l:Label. trace(l) Term |
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tfvar |
Def l == tree_leaf(ts_fvar(l)) |
| | Thm* l:Label. l Term |
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topr |
Def f == tree_leaf(ts_op(f)) |
| | Thm* f:Label. f Term |
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tpvar |
Def l' == tree_leaf(ts_pvar(l)) |
| | Thm* l:Label. l' Term |
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term_iterate |
Def term_iterate(v;
p;
op;
f;
tr;
a;
t)
== t_iterate(x.ts_case(x)
var(a)= > v(a)
var'(b)= > p(b)
opr(c)= > op(c)
fvar(d)= > f(d)
trace(P)= > tr(P)
end_ts_case ;a;t) |
| | Thm* A:Type, v,op,f,p,tr:(LabelA), a:(AAA), t:Term. term_iterate(v;p;op;f;tr;a;t) A |
|
node |
Def tree_node( < x, y > ) == tree_node( < x,y > ) |
| | Thm* E:Type, x,y:Tree(E). tree_node( < x, y > ) Tree(E) |
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ts_trace |
Def ts_trace(x) == inr(inr(inr(inr(x)))) |
| | Thm* x:Label. ts_trace(x) ts() |
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tree_leaf |
Def tree_leaf(x) == inl(x) |
| | Thm* E,T:Type, x:E. tree_leaf(x) tree_con(E;T) |
| |
Thm* E:Type, x:E. tree_leaf(x) Tree(E) |
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ts_fvar |
Def ts_fvar(x) == inr(inr(inr(inl(x)))) |
| | Thm* x:Label. ts_fvar(x) ts() |
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ts_op |
Def ts_op(x) == inr(inr(inl(x))) |
| | Thm* x:Label. ts_op(x) ts() |
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ts_pvar |
Def ts_pvar(x) == inr(inl(x)) |
| | Thm* x:Label. ts_pvar(x) ts() |
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ts_case |
Def ts_case(x)
var(a)= > v(a)
var'(b)= > p(b)
opr(f)= > op(f)
fvar(x)= > f(x)
trace(P)= > t(P)
end_ts_case
== Case(x)
Case ts_var(a) = >
v(a)
Case ts_pvar(b) = >
p(b)
Case ts_op(f) = >
op(f)
Case ts_fvar(x) = >
f(x)
Case ts_trace(P) = >
t(P)
Default = > |
| |
Thm* A:Type, v,op,f,p,t:(LabelA), x:ts().
ts_case(x)var(a)= > v(a)var'(b)= > p(b)opr(f)= > op(f)fvar(y)= > f(y)trace(P)= > t(P)end_ts_case A |
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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 |
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tree_node |
Def tree_node(x) == inr(x) |
| | Thm* E,T:Type, x:(TT). tree_node(x) tree_con(E;T) |
| |
Thm* E:Type, x,y:Tree(E). tree_node( < x,y > ) Tree(E) |
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case_default |
Def Default = > body(value,value) == body |
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case_ts_trace |
Def Case ts_trace(x) = > body(x) cont(x1,z)
== (x1.inr(x2) = >
(x1.inr(x2) = >
(x1.inr(x2) = >
(x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x1]) |
|
case_ts_fvar |
Def Case ts_fvar(x) = > body(x) cont(x1,z)
== (x1.inr(x2) = >
(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))
([x2 / tl(x1)])
cont
(hd(x1)
,z))
([x1]) |
|
case_ts_op |
Def Case ts_op(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]) |
|
case_ts_pvar |
Def Case ts_pvar(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_ts_var |
Def Case ts_var(x) = > body(x) cont(x1,z)
== InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
case |
Def Case(value) body == body(value,value) |
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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)) |
|
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_inr |
Def inr(x) = > body(x) cont(value,contvalue)
== InjCase(value; _. cont(contvalue,contvalue); x. body(x)) |
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case_inl |
Def inl(x) = > body(x) cont(value,contvalue)
== InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |