| | Who Cites closed rel? |
|
| closed_rel |
Def closed_rel(r) == rel_free_vars(r) = nil |
| | | Thm*  r:rel(). closed_rel(r)  Prop |
|
| closed_term |
Def closed_term(t) == term_free_vars(t) = nil |
| | | Thm* t:Term. closed_term(t) Prop |
|
| rel_free_vars |
Def rel_free_vars(r) == reduce( t,vs. term_free_vars(t) @ vs;nil;r.args) |
| | | Thm* r:rel(). rel_free_vars(r) Label List |
|
| term_free_vars |
Def term_free_vars(t)
== term_iterate(f.nil;
f.nil;
f.nil;
v.[v];
P.nil;
x,y. x @ y;
t) |
| | | Thm* t:Term. term_free_vars(t) Label List |
|
| append |
Def as @ bs == Case of as; nil  bs ; a.as' [a / (as' @ bs)] (recursive) |
| | |
Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
| rel |
Def rel() == relname() (Term List) |
| | | Thm* rel() Type |
|
| term |
Def Term == Tree(ts()) |
| | | Thm* Term Type |
|
| relname |
Def relname() == SimpleType+Label |
| | | Thm* relname() Type |
|
| ts |
Def ts() == Label+Label+Label+Label+Label |
| | | Thm* ts() Type |
|
| st |
Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
|
| lbl |
Def Label == {p:Pattern|  ground_ptn(p) } |
| | | Thm* Label Type |
|
| length |
Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | |
Thm* A:Type, l:A List. ||l||  |
| | |
Thm* ||nil|| |
|
| nat |
Def  == {i:| 0 i } |
| | | Thm* Type |
|
| reduce |
Def reduce(f;k;as) == Case of as; nil k ; a.as' f(a,reduce(f;k;as')) (recursive) |
| | |
Thm* A,B:Type, f:(A  BB), k:B, as:A List. reduce(f;k;as) B |
|
| rel_args |
Def t.args == 2of(t) |
| | |
Thm* t:rel(). t.args Term List |
|
| select |
Def l[i] == hd(nth_tl(i;l)) |
| | |
Thm* A:Type, l:A List, n:. 0n   n < ||l|| l[n] A |
|
| 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)  |
|
| assert |
Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| ptn |
Def Pattern == rec(T.ptn_con(T)) |
| | |
Thm* Pattern Type |
|
| le |
Def AB ==  B < A |
| | | Thm* i,j:. (ij) Prop |
|
| pi2 |
Def 2of(t) == t.2 |
| | |
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
|
| nth_tl |
Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | |
Thm* A:Type, as:A List, i:. nth_tl(i;as) A List |
|
| 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 |
|
| 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]) |
|
| 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 |
|
| 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]) |
|
| 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 |
|
| tree |
Def Tree(E) == rec(T.tree_con(E;T)) |
| | |
Thm* E:Type. Tree(E) Type |
|
| 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) |
|
| ptn_con |
Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
|
| not |
Def A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| tl |
Def tl(l) == Case of l; nil nil ; h.t t |
| | |
Thm* A:Type, l:A List. tl(l) A List |
|
| le_int |
Def ij == j < i |
| | | Thm* i,j:. (ij) |
|
| tree_con |
Def tree_con(E;T) == E+(TT) |
| | | Thm* E,T:Type. tree_con(E;T) Type |
|
| 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)) |
|
| lt_int |
Def i < j == if i < j true ; false fi |
| | | Thm* i,j:. (i < j) |
|
| bnot |
Def b == if b false else true fi |
| | | Thm* b:. b |
|
| case_ts_var |
Def Case ts_var(x) = > body(x) cont(x1,z)
== InjCase(x1; x2. body(x2); _. cont(z,z)) |
|
| 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)) |
