| | Who Cites covers var? |
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| covers_var | Def covers_var(A;x) ==  fr:frame(). fr  < fr A.frame |  fr.var = x > & ( a:Label. (a fr.acts)   (ef:eff(). ef < ef A.eff | ef.kind = a & ef.smt.lbl = x > )) |
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| ioa_eff | Def t.eff == 1of(2of(2of(2of(2of(t))))) |
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| eff_smt | Def t.smt == 2of(2of(2of(t))) |
| | | Thm* t:eff(). t.smt smt() |
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| smt_lbl | Def t.lbl == 1of(t) |
| | | Thm* t:smt(). t.lbl Label |
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| eq_lbl | Def l1 = l2 == Case(l1) Case ptn_atom(x) = > Case(l2) Case ptn_atom(y) = > x= yAtom 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=yAtom 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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| eff | Def eff() == Label LabelSimpleTypesmt() |
| | | Thm* eff() Type |
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| frame | Def frame() == LabelSimpleType(Label List) |
| | | Thm* frame() Type |
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| smt | Def smt() == LabelTermSimpleType |
| | | Thm* smt() Type |
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| st | Def SimpleType == Tree(Label+Unit) |
| | | Thm* SimpleType Type |
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| term | Def Term == Tree(ts()) |
| | | Thm* Term Type |
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| ts | Def ts() == Label+Label+Label+Label+Label |
| | | Thm* ts() Type |
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| lbl | Def Label == {p:Pattern| ground_ptn(p) } |
| | | Thm* Label Type |
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| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
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| eff_kind | Def t.kind == 1of(t) |
| | | Thm* t:eff(). t.kind Label |
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| col_filter | Def < x c | P(x) > (x) == x c & P(x) |
| | | Thm* T:Type, c:Collection(T), Q:(T  Prop). < i c | Q(i) > Collection(T) |
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| col_member | Def x c == c(x) |
| | | Thm* T:Type, x:T, c:Collection(T). x c Prop |
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| frame_acts | Def t.acts == 2of(2of(t)) |
| | | Thm* t:frame(). t.acts Label List |
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| l_member | Def (x l) == i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
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| ioa_frame | Def t.frame == 2of(2of(2of(2of(2of(t))))) |
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| frame_var | Def t.var == 1of(t) |
| | | Thm* t:frame(). t.var Label |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
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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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| ground_ptn | Def ground_ptn(p) == Case(p) Case ptn_var(v) = > false Case ptn_pr( < x, y > ) = > ground_ptn(x)ground_ptn(y) Default = > true (recursive) |
| | | Thm* p:Pattern. ground_ptn(p) |
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| case_default | Def Default = > body(value,value) == body |
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| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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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=yAtom == if x=yAtomtrue; false fi |
| | | Thm* x,y:Atom. x=yAtom |
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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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| ptn | Def Pattern == rec(T.ptn_con(T)) |
| | | Thm* Pattern Type |
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| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0 n n < ||l|| l[n] A |
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| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
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| nat | Def == {i:| 0i } |
| | | Thm* Type |
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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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| nth_tl | Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | | Thm* A:Type, as:A List, i:. nth_tl(i;as) A List |
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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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| tree | Def Tree(E) == rec(T.tree_con(E;T)) |
| | | Thm* E:Type. Tree(E) Type |
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| ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
| | | Thm* T:Type. ptn_con(T) Type |
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| le | Def AB ==  B < A |
| | | Thm* i,j:. (ij) Prop |
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| tree_con | Def tree_con(E;T) == E+(TT) |
| | | Thm* E,T:Type. tree_con(E;T) Type |
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| le_int | Def ij == j < i |
| | | Thm* i,j:. (ij) |
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| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
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| lt_int | Def i < j == if i < j true ; false fi |
| | | Thm* i,j:. (i < j) |
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| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
