| | Who Cites rel addprime? |
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| rel_addprime | Def (r)' == mk_rel(r.name, map( t.(t)';r.args)) |
| | | Thm*  r:rel(). (r)'  rel() |
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| rel_args | Def t.args == 2of(t) |
| | | Thm* t:rel(). t.args Term List |
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| 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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| map | Def map(f;as) == Case of as; nil  nil ; a.as' [(f(a)) / map(f;as')] (recursive) |
| | | Thm* A,B:Type, f:(A  B), l:A List. map(f;l) B List |
| | | Thm* A,B:Type, f:(AB), l:A List . map(f;l) B List |
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| rel_name | Def t.name == 1of(t) |
| | | Thm* t:rel(). t.name relname() |
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| mk_rel | Def mk_rel(name, args) == < name,args > |
| | | Thm* name:relname(), args:Term List. mk_rel(name, args) rel() |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:A B(a)). 2of(p) B(1of(p)) |
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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 |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
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| 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]) |
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| 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]) |
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| 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]) |
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| 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]) |
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| case_ts_var | Def Case ts_var(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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| 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)) |
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| 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)) |
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| 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)) |
