WhoCites Definitions mb automata 4 Sections GenAutomata Doc

Who Cites covers rel?
covers_relDef covers_rel(A;r) == x:Label. rel_mentions(r;x) covers_var(A;x)
Thm* A:ioa{i:l}(), r:rel(). covers_rel(A;r) Prop
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 > ))
Thm* A:ioa{i:l}(), x:Label. covers_var(A;x) Prop
rel_mentions Def rel_mentions(r;x) == i:. i < ||r.args|| & (x term_vars(r.args[i]))
Thm* r:rel(), x:Label. rel_mentions(r;x) Prop
eff Def eff() == LabelLabelSimpleTypesmt()
Thm* eff() Type
frame Def frame() == LabelSimpleType(Label List)
Thm* frame() Type
smt Def smt() == LabelTermSimpleType
Thm* smt() Type
st Def SimpleType == Tree(Label+Unit)
Thm* SimpleType Type
term Def Term == Tree(ts())
Thm* Term Type
ts Def ts() == Label+Label+Label+Label+Label
Thm* ts() Type
lbl Def Label == {p:Pattern| ground_ptn(p) }
Thm* Label Type
ioa_eff Def t.eff == 1of(2of(2of(2of(2of(t)))))
Thm* t:ioa{i:l}(). t.eff Collection(eff())
eff_smt Def t.smt == 2of(2of(2of(t)))
Thm* t:eff(). t.smt smt()
smt_lbl Def t.lbl == 1of(t)
Thm* t:smt(). t.lbl Label
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 = uy = v Default = > false Default = > false (recursive)
Thm* l1,l2:Pattern. l1 = l2
assert Def b == if b True else False fi
Thm* b:. b Prop
eff_kind Def t.kind == 1of(t)
Thm* t:eff(). t.kind Label
col_filter Def < x c | P(x) > (x) == x c & P(x)
Thm* T:Type, c:Collection(T), Q:(TProp). < i c | Q(i) > Collection(T)
col_member Def x c == c(x)
Thm* T:Type, x:T, c:Collection(T). x c Prop
frame_acts Def t.acts == 2of(2of(t))
Thm* t:frame(). t.acts Label List
l_member Def (x l) == i:. i < ||l|| & x = l[i] T
Thm* T:Type, x:T, l:T List. (x l) Prop
ioa_frame Def t.frame == 2of(2of(2of(2of(2of(t)))))
Thm* t:ioa{i:l}(). t.frame Collection(frame())
frame_var Def t.var == 1of(t)
Thm* t:frame(). t.var Label
rel_args Def t.args == 2of(t)
Thm* t:rel(). t.args Term List
select Def l[i] == hd(nth_tl(i;l))
Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
term_vars Def term_vars(t) == iterate(statevar v- > [v] statevar v'- > [v] funsymbol f- > nil freevar f- > nil trace(P)- > nil x(y)- > x @ y over t)
Thm* t:Term. term_vars(t) Label List
length Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
Thm* A:Type, l:A List. ||l||
Thm* ||nil||
nat Def == {i:| 0i }
Thm* Type
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)
ptn Def Pattern == rec(T.ptn_con(T))
Thm* Pattern Type
pi2 Def 2of(t) == t.2
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
pi1 Def 1of(t) == t.1
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
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:(LabelA), comb:(AAA), 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
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
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
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
case_default Def Default = > body(value,value) == body
band Def pq == if p q else false fi
Thm* p,q:. (pq)
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))))
case Def Case(value) body == body(value,value)
eq_atom Def x=yAtom == if x=yAtomtrue; false fi
Thm* x,y:Atom. x=yAtom
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])
eq_int Def i=j == if i=j true ; false fi
Thm* i,j:. (i=j)
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])
case_ptn_atom Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
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
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])
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])
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])
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])
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
append Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive)
Thm* T:Type, as,bs:T List. (as @ bs) T List
le Def AB == B < A
Thm* i,j:. (ij) Prop
ptn_con Def ptn_con(T) == Atom++Atom+(TT)
Thm* T:Type. ptn_con(T) Type
tl Def tl(l) == Case of l; nil nil ; h.t t
Thm* A:Type, l:A List. tl(l) A List
case_inl Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))
case_inr Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
tree Def Tree(E) == rec(T.tree_con(E;T))
Thm* E:Type. Tree(E) Type
le_int Def ij == j < i
Thm* i,j:. (ij)
not Def A == A False
Thm* A:Prop. (A) Prop
tree_con Def tree_con(E;T) == E+(TT)
Thm* E,T:Type. tree_con(E;T) Type
lt_int Def i < j == if i < j true ; false fi
Thm* i,j:. (i < j)
bnot Def b == if b false else true fi
Thm* b:. b
case_ts_var Def Case ts_var(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case_tree_leaf Def Case tree_leaf(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
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))

Syntax:covers_rel(A;r) has structure: covers_rel(A; r)

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WhoCites Definitions mb automata 4 Sections GenAutomata Doc