WhoCites Definitions mb automata 3 Sections GenAutomata Doc

Who Cites pred mng?
pred_mngDef [[p]] rho ds da de e s a tr == r:rel(). r p [[r]] rho ds da de e s a tr
rel_mng Def [[r]] rho ds da de e s a tr == list_accum(x,t.x([[t]] 1of(e) s a tr);[[r.name]] rho 2of(e) ;r.args)
col_member Def x c == c(x)
Thm* T:Type, x:T, c:Collection(T). x c Prop
rel Def rel() == relname()(Term List)
Thm* rel() Type
rel_args Def t.args == 2of(t)
Thm* t:rel(). t.args Term List
term_mng Def [[t]] e s a tr == iterate(statevar x- > s.x statevar x'- > s.x funsymbol f- > e.f freevar x- > a trace(P)- > tr.P x(y)- > x(y) over t)
tproj Def tre.P == tre.trace | tre.proj(P)
Thm* d:Decl, tre:trace_env(d), P:Label. tre.P (d) List
trace_env_proj Def t.proj == 2of(t)
Thm* d:Decl, t:trace_env(d). t.proj LabelLabel
pi2 Def 2of(t) == t.2
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
rel_name Def t.name == 1of(t)
Thm* t:rel(). t.name relname()
relname_mng Def [[rn]] rho e == Case(rn) Case eq(Q) = > x,y. x = y [[Q]] rho Case R = > e.R Default = > True
trace_env_trace Def t.trace == 1of(t)
Thm* d:Decl, t:trace_env(d). t.trace (d) List
trace_projection Def tr | P == filter(x.P(kind(x));tr)
Thm* d:Decl, tr:(d) List, P:(Label). tr | P (d) List
kind Def kind(a) == 1of(a)
Thm* d:Decl, a:(d). kind(a) Label
Thm* M:sm{i:l}(), a:M.action. kind(a) Label & kind(a) Pattern
pi1 Def 1of(t) == t.1
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
list_accum Def list_accum(x,a.f(x;a);y;l) == Case of l; nil y ; b.l' list_accum(x,a.f(x;a);f(y;b);l') (recursive)
term Def Term == Tree(ts())
Thm* Term Type
relname Def relname() == SimpleType+Label
Thm* relname() Type
st_mng Def [[s]] rho == t_iterate(st_lift(rho);x,y. xy;s)
Thm* rho:Decl, s:SimpleType. [[s]] rho Type
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
ts Def ts() == Label+Label+Label+Label+Label
Thm* ts() Type
st Def SimpleType == Tree(Label+Unit)
Thm* SimpleType Type
lbl Def Label == {p:Pattern| ground_ptn(p) }
Thm* Label Type
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
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
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)
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
case_default Def Default = > body(value,value) == body
r_select Def r.l == r(l)
Thm* d:Decl, r:{d}, l:Label. r.l d(l)
case_relname_other Def Case x = > body(x) cont(x1,z) == (x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x1])
case_relname_eq Def Case eq(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case Def Case(value) body == body(value,value)
tree Def Tree(E) == rec(T.tree_con(E;T))
Thm* E:Type. Tree(E) Type
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])
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
tl Def tl(l) == Case of l; nil nil ; h.t t
Thm* A:Type, l:A List. tl(l) A List
case_inr Def inr(x) = > body(x) cont(value,contvalue) == InjCase(value; _. cont(contvalue,contvalue); x. body(x))
st_lift Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top)
Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type
tree_con Def tree_con(E;T) == E+(TT)
Thm* E,T:Type. tree_con(E;T) Type
assert Def b == if b True else False fi
Thm* b:. b Prop
ptn Def Pattern == rec(T.ptn_con(T))
Thm* Pattern Type
top Def Top == Void given Void
Thm* Top Type
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))
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
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))))
ptn_con Def ptn_con(T) == Atom++Atom+(TT)
Thm* T:Type. ptn_con(T) Type
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:(ABB), k:B, as:A List. reduce(f;k;as) B
case_ts_var Def Case ts_var(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z))
case_inl Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue))

Syntax:[[p]] rho ds da de e s a tr has structure: pred_mng(p; rho; ds; da; de; e; s; a; tr)

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WhoCites Definitions mb automata 3 Sections GenAutomata Doc