Who Cites vc mng? | |
vc_mng | Def vc_mng(v;rho;ds;da;de;e;s;tr) == Case(v) Case vc_imp(hc) = > [[hc.hyp]] rho ds < > de e s mk_trace_env(nil, tr.proj) [[hc.concl]] rho ds < > de e s mk_trace_env(nil, tr.proj) Case vc_qimp(qhc) = > v:[[dec_lookup(da;qhc.lbl)]] rho. [[qhc.hyp]] rho ds dec_lookup(da;qhc.lbl) de e s v tr [[qhc.concl]] rho ds dec_lookup(da;qhc.lbl) de e s v tappend(tr; < qhc.lbl,v > ) Default = > False |
Thm* v:vc{i:l}(), ds,da:Collection(dec()), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds]] rho}, tr:trace_env([[da]] rho). tc_vc(v;ds;da;de) trace_consistent_vc(rho;da;tr.proj;v) vc_mng(v;rho;ds;da;de;e;s;tr) Prop | |
dec_lookup | Def dec_lookup(ds;x) == < d.typ | d < d ds | d.lbl = x > > |
Thm* ds:Collection(dec()), x:Label. dec_lookup(ds;x) Collection(SimpleType) | |
pred_mng | Def [[p]] rho ds da de e s a tr == r:rel(). r p [[r]] rho ds da de e s a tr |
Thm* p:Fmla, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s:{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p) tc_pred(p;ds;da;de) [[p]] rho ds da de e s a tr Prop | |
sts_mng | Def [[sts]] rho == x:{x:SimpleType| x sts }. [[x]] rho |
Thm* sts:Collection(SimpleType), rho:Decl. [[sts]] rho Type | |
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 | |
dec | Def dec() == LabelSimpleType |
Thm* dec() Type | |
rel | Def rel() == relname()(Term List) |
Thm* rel() Type | |
relname | Def relname() == SimpleType+Label |
Thm* relname() Type | |
st | Def SimpleType == Tree(Label+Unit) |
Thm* SimpleType Type | |
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) |
Thm* r:rel(), ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType), e:{[[de]] rho}, s:{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) [[r]] rho ds st1 de e s a tr Prop | |
Thm* rho:Decl, ds,daa:Collection(dec()), da1:Collection(SimpleType), de:sig(), s:{[[ds]] rho}, e:{[[de]] rho}, tr:trace_env([[daa]] rho), r:rel(). closed_rel(r) tc(r;ds;da1;de) trace_consistent_rel(rho;daa;tr.proj;r) [[r]] rho ds da1 de e s tr Prop | |
relname_mng | Def [[rn]] rho e == Case(rn) Case eq(Q) = > x,y. x = y [[Q]] rho Case R = > e.R Default = > True |
st_mng | Def [[s]] rho == t_iterate(st_lift(rho);x,y. xy;s) |
Thm* rho:Decl, s:SimpleType. [[s]] rho 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 | |
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) |
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 | |
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 |
qimp_lbl | Def t.lbl == 1of(t) |
Thm* t:qimp{i:l}(). t.lbl Label | |
tappend | Def tappend(tr;a) == mk_trace_env(tr.trace @ [a], tr.proj) |
Thm* d:Decl, tr:trace_env(d), a:(d). tappend(tr;a) trace_env(d) | |
qimp_concl | Def t.concl == 2of(2of(t)) |
Thm* t:qimp{i:l}(). t.concl Fmla | |
qimp_hyp | Def t.hyp == 1of(2of(t)) |
Thm* t:qimp{i:l}(). t.hyp Fmla | |
case_vc_qimp | Def Case vc_qimp(x) = > body(x) cont(x1,z) == (x1.inr(x2) = > body(hd([x2 / tl(x1)])) cont(hd(x1),z))([x1]) |
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 | |
mk_trace_env | Def mk_trace_env(trace, proj) == < trace,proj > |
Thm* d:Decl, trace:(d) List, proj:(LabelLabel). mk_trace_env(trace, proj) trace_env(d) | |
col_none | Def < > (x) == False |
Thm* T:Type. < > Collection(T) | |
imp_concl | Def t.concl == 2of(t) |
Thm* t:imp{i:l}(). t.concl Fmla | |
imp_hyp | Def t.hyp == 1of(t) |
Thm* t:imp{i:l}(). t.hyp Fmla | |
case_vc_imp | Def Case vc_imp(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
case | Def Case(value) body == body(value,value) |
trace_env_trace | Def t.trace == 1of(t) |
Thm* d:Decl, t:trace_env(d). t.trace (d) List | |
dec_lbl | Def t.lbl == 1of(t) |
Thm* t:dec(). t.lbl Label | |
rel_name | Def t.name == 1of(t) |
Thm* t:rel(). t.name relname() | |
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 | |
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 | |
dec_typ | Def t.typ == 2of(t) |
Thm* t:dec(). t.typ SimpleType | |
assert | Def b == if b True else False fi |
Thm* b:. b Prop | |
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_map | Def < f(x) | x c > (y) == x:T. x c & y = f(x) T' |
Thm* T,T':Type, f:(TT'), c:Collection(T). < f(x) | x c > Collection(T') | |
rel_args | Def t.args == 2of(t) |
Thm* t:rel(). t.args Term List | |
pi2 | Def 2of(t) == t.2 |
Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) | |
col_member | Def x c == c(x) |
Thm* T:Type, x:T, c:Collection(T). x c Prop | |
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_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_relname_other | Def Case x = > body(x) cont(x1,z) == (x1.inr(x2) = > body(hd([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)) |
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)))) |
eq_atom | Def x=yAtom == if x=yAtomtrue; false fi |
Thm* x,y:Atom. x=yAtom | |
eq_int | Def i=j == if i=j true ; false fi |
Thm* i,j:. (i=j) | |
case_ptn_atom | Def Case ptn_atom(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
tree | Def Tree(E) == rec(T.tree_con(E;T)) |
Thm* E:Type. Tree(E) Type | |
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) |
st_lift | Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) |
Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type | |
case_inl | Def inl(x) = > body(x) cont(value,contvalue) == InjCase(value; x. body(x); _. cont(contvalue,contvalue)) |
ptn | Def Pattern == rec(T.ptn_con(T)) |
Thm* Pattern Type | |
tree_con | Def tree_con(E;T) == E+(TT) |
Thm* E,T:Type. tree_con(E;T) Type | |
r_select | Def r.l == r(l) |
Thm* d:Decl, r:{d}, l:Label. r.l d(l) | |
case_relname_eq | Def Case eq(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
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)) |
ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
Thm* T:Type. ptn_con(T) Type | |
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 | |
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)) |
Syntax: | vc_mng(v;rho;ds;da;de;e;s;tr) | has structure: | vc_mng(v; rho; ds; da; de; e; s; tr) |
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