| Who Cites dec mng? |
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dec_mng | Def [[d]] rho == Case(d) Case x : s = > x:[[s]] rho |
| | Thm* rho:Decl, d:dec(). [[d]] rho Decl |
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st_mng | Def [[s]] rho == t_iterate(st_lift(rho); x,y. x![](FONT/dash.png) y;s) |
| | Thm* rho:Decl, s:SimpleType. [[s]] rho Type |
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dbase | Def x:y(a) == if a = x y else Top fi |
| | Thm* x:Label, y:Type. x:y Decl |
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case_mk_dec | Def Case lbl : typ = > body(lbl;typ)(x,z) == x/x2,x1. body(x2;x1) |
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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![](FONT/dash.png) A), n:(A![](FONT/dash.png) A![](FONT/dash.png) A), t:Tree(E). t_iterate(l;n;t) 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![](FONT/and.png) y = v Default = > false Default = > false (recursive) |
| | Thm* l1,l2:Pattern. l1 = l2 ![](FONT/bool.png) |
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case | Def Case(value) body == body(value,value) |
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st_lift | Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) |
| | Thm* rho:(Label![](FONT/dash.png) Type). st_lift(rho) (Label+Unit)![](FONT/dash.png) Type |
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top | Def Top == Void given Void |
| | Thm* Top Type |
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case_default | Def Default = > body(value,value) == body |
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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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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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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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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_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)) |