| Who Cites rel eq? |
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rel_eq | Def rel_eq(a;b) == eq_relname(a.name;b.name)![](FONT/and.png) termlist_eq(a.args;b.args) |
| | Thm* a,b:rel(). rel_eq(a;b) ![](FONT/bool.png) |
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rel_args | Def t.args == 2of(t) |
| | Thm* t:rel(). t.args Term List |
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termlist_eq | Def termlist_eq(a;b) == Case of a; nil Case of b; nil true ; x.xs false ; x.xs Case of b; nil false ; x'.xs' term_eq(x;x')![](FONT/and.png) termlist_eq(xs;xs') (recursive) |
| | Thm* a,b:Term List. termlist_eq(a;b) ![](FONT/bool.png) |
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rel_name | Def t.name == 1of(t) |
| | Thm* t:rel(). t.name relname() |
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eq_relname | Def eq_relname(a;b) == Case(a) Case eq(x) = > Case(b) Case eq(x') = > st_eq(x;x') Case x' = > false Default = > false Case x = > Case(b) Case eq(x') = > false Case x' = > x = x' Default = > false Default = > false![](FONT/2.png) |
| | Thm* a,b:relname(). eq_relname(a;b) ![](FONT/bool.png) |
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term_eq | Def term_eq(a;b) == Case(a) Case x;y = > Case(b) Case x';y' = > term_eq(x;x')![](FONT/and.png) term_eq(y;y') Case tree_leaf(x) = > false Default = > True Case tree_leaf(x) = > Case(b) Case x';y' = > false Case tree_leaf(x') = > (x=x') Default = > True Default = > True (recursive) |
| | Thm* a,b:Term. term_eq(a;b) ![](FONT/bool.png) |
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st_eq | Def st_eq(s1;s2) == Case(s1) Case a;b = > Case(s2) Case a';b' = > st_eq(a;a')![](FONT/and.png) st_eq(b;b') Default = > false Case tree_leaf(x) = > Case(s2) Case a';b' = > false Case tree_leaf(y) = > InjCase(x; x'. InjCase(y; y'. x' = y'; b. false ); a. InjCase(y; y'. false ; b. true )) Default = > false Default = > false (recursive) |
| | Thm* s1,s2:SimpleType. st_eq(s1;s2) ![](FONT/bool.png) |
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ts_eq | Def (a=b) == ts_case(a)var(v)= > ts_case(b)var(v')= > v = v'var'(x)= > false opr(x)= > false fvar(x)= > false trace(x)= > false end_ts_case var'(p)= > ts_case(b)var(x)= > false var'(p')= > p = p'opr(x)= > false fvar(x)= > false trace(x)= > false end_ts_case opr(op)= > ts_case(b)var(x)= > false var'(x)= > false opr(op')= > op = op'fvar(x)= > false trace(x)= > false end_ts_case fvar(f)= > ts_case(b)var(x)= > false var'(x)= > false opr(x)= > false fvar(f')= > f = f'trace(x)= > false end_ts_case trace(P)= > ts_case(b)var(x)= > false var'(x)= > false opr(x)= > false fvar(x)= > false trace(P')= > P = P'end_ts_case end_ts_case |
| | Thm* a,b:ts(). (a=b) ![](FONT/bool.png) |
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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![](FONT/and.png) y = v Default = > false Default = > false (recursive) |
| | Thm* l1,l2:Pattern. l1 = l2 ![](FONT/bool.png) |
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band | Def p![](FONT/and.png) q == if p q else false fi |
| | Thm* p,q: . (p![](FONT/and.png) q) ![](FONT/bool.png) |
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pi2 | Def 2of(t) == t.2 |
| | Thm* A:Type, B:(A![](FONT/dash.png) Type), p:(a:A B(a)). 2of(p) B(1of(p)) |
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pi1 | Def 1of(t) == t.1 |
| | Thm* A:Type, B:(A![](FONT/dash.png) Type), p:(a:A B(a)). 1of(p) A |
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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 = > ![](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 |
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case_default | Def Default = > body(value,value) == body |
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case_relname_other | Def Case x = > body(x) cont(x1,z) == ( x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x1]) |
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case_relname_eq | Def Case eq(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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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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eq_atom | Def x= y Atom == if x=y Atom true ; false fi |
| | Thm* x,y:Atom. x= y Atom ![](FONT/bool.png) |
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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) ![](FONT/bool.png) |
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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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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 ![](FONT/eq.png) 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)) |
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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)) |