| Who Cites term mentions guard? |
|
term_mentions_guard | Def term_mentions_guard(g;t) == term_iterate( x.false ; x.false ; x.false ; x.false ; x.x = g; x,y. x ![](FONT/or.png) y;t) |
| | Thm* t:Term, g:Label. term_mentions_guard(g;t) ![](FONT/bool.png) |
|
bor | Def p ![](FONT/or.png) q == if p true else q fi |
| | Thm* p,q: . (p ![](FONT/or.png) q) ![](FONT/bool.png) |
|
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![](FONT/and.png) y = v Default = > false Default = > false (recursive) |
| | Thm* l1,l2:Pattern. l1 = l2 ![](FONT/bool.png) |
|
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:(Label![](FONT/dash.png) A), a:(A![](FONT/dash.png) A![](FONT/dash.png) A), t:Term. term_iterate(v;p;op;f;tr;a;t) A |
|
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 = > ![](FONT/dot.png) |
| | Thm* A:Type, v,op,f,p,t:(Label![](FONT/dash.png) A), 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 |
|
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:(E![](FONT/dash.png) A), n:(A![](FONT/dash.png) A![](FONT/dash.png) A), t:Tree(E). t_iterate(l;n;t) A |
|
case_default | Def Default = > body(value,value) == body |
|
band | Def p![](FONT/and.png) q == if p q else false fi |
| | Thm* p,q: . (p![](FONT/and.png) q) ![](FONT/bool.png) |
|
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= y Atom == if x=y Atom true ; false fi |
| | Thm* x,y:Atom. x= y Atom ![](FONT/bool.png) |
|
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) ![](FONT/bool.png) |
|
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_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 ![](FONT/eq.png) 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)) |
|
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)) |