| Who Cites term subst? |
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term_subst | Def term_subst(as;t)
== iterate(statevar v- > apply_alist(as;v;v)
statevar v'- > apply_alist(as;v;v')
funsymbol f- > f
freevar f- > f
trace(P)- > trace(P)
x(y)- > x y
over t) |
| | Thm* t:Term, as:(Label Term) List. term_subst(as;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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apply_alist | Def apply_alist(as;l;d) == 2of((first p as s.t. 1of(p) = l else < l,d > )) |
| | Thm* T:Type, as:(Label T) List, l:Label, d:T. apply_alist(as;l;d) T |
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tvar | Def l == tree_leaf(ts_var(l)) |
| | Thm* l:Label. l Term |
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term_iter | Def iterate(statevar x- > v(x)
statevar x''- > v'(x')
funsymbol op- > opr(op)
freevar f- > fvar(f)
trace(tr)- > trace(tr)
a(b)- > comb(a;b)
over t)
== term_iterate( x.v(x);
x'.v'(x');
op.opr(op);
f.fvar(f);
tr.trace(tr);
a,b. comb(a;b);
t) |
| | Thm* A:Type, v,v',opr,fvar,trace:(Label A), comb:(A A A), t:Term.
iterate(statevar x- > v(x)
statevar x''- > v'(x')
funsymbol op- > opr(op)
freevar f- > fvar(f)
trace(tr)- > trace(tr)
a(b)- > comb(a,b)
over t)
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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pi1 | Def 1of(t) == t.1 |
| | Thm* A:Type, B:(A Type), p:(a:A B(a)). 1of(p) A |
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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  |
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find | Def (first x as s.t. P(x) else d) == Case of filter( x.P(x);as); nil d ; a.b a |
| | Thm* T:Type, P:(T  ), as:T List, d:T. (first a as s.t. P(a) else d) T |
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pi2 | Def 2of(t) == t.2 |
| | Thm* A:Type, B:(A Type), p:(a:A B(a)). 2of(p) B(1of(p)) |
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ts_var | Def ts_var(x) == inl(x) |
| | Thm* x:Label. ts_var(x) ts() |
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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:(Label A), a:(A A A), t:Term. term_iterate(v;p;op;f;tr;a;t) A |
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tree_node | Def tree_node(x) == inr(x) |
| | Thm* E,T:Type, x:(T T). tree_node(x) tree_con(E;T) |
| | Thm* E:Type, x,y:Tree(E). tree_node( < x,y > ) Tree(E) |
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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:(Label 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 |
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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:(E A), n:(A A A), t:Tree(E). t_iterate(l;n;t) A |
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case_default | Def Default = > body(value,value) == body |
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band | Def p q == if p q else false fi |
| | Thm* p,q: . (p q)  |
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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)))) |
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case | Def Case(value) body == body(value,value) |
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eq_atom | Def x= y Atom == if x=y Atom true ; false fi |
| | Thm* x,y:Atom. x= y Atom  |
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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]) |
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eq_int | Def i= j == if i=j true ; false fi |
| | Thm* i,j: . (i= j)  |
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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]) |
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case_ptn_atom | Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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filter | Def filter(P;l) == reduce( a,v. if P(a) [a / v] else v fi;nil;l) |
| | Thm* T:Type, P:(T  ), l:T List. filter(P;l) T List |
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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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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_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
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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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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 B B), k:B, as:A List. reduce(f;k;as) B |
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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_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)) |