Who Cites decl? | |
decl | Def Decl == LabelType |
Thm* Decl{i} Type{i'} | |
ioa_mng | Def [[A]] rho de e == mk_sm([[A.da]] rho, [[A.ds]] rho, s.[[A.init]] rho A.ds < > de e s niltrace(), s1,a,s2. (p:pre(). p A.pre p.kind = kind(a) [[p.rel]] rho A.ds dec_lookup(A.da;kind(a)) de e s1 value(a) niltrace()) & (ef:eff(). ef A.eff ef.kind = kind(a) s2.ef.smt.lbl = [[ef.smt.term]] 1of(e) s1 value(a) niltrace() [[ef.smt.typ]] rho) & (fr:frame(). fr A.frame (kind(a) fr.acts) s2.fr.var = s1.fr.var [[fr.typ]] rho)) |
Thm* A:ioa{i:l}(), de:sig(), rho:Decl, e:{[[de]] rho}. tc_ioa(A;de) ioa_mentions_trace(A) [[A]] rho de e sm{i:l}() | |
decls_mng | Def [[ds]] rho == [[d]] rho for d {d:dec()| d ds } |
Thm* ds:Collection(dec()), rho:Decl. [[ds]] rho Decl | |
ioa | Def ioa{i:l}() == Collection(dec())Collection(dec())Collection(rel())Collection(pre())Collection(eff())Collection(frame()) |
Thm* ioa{i:l}() Type{i'} | |
ioa_all | Def ioa_all(I; i.A(i)) == mk_ioa(i:I. A(i).ds, i:I. A(i).da, i:I. A(i).init, i:I. A(i).pre, i:I. A(i).eff, i:I. A(i).frame) |
Thm* I:Type, A:(Iioa{i:l}()). ioa_all(I; i.A(i)) ioa{i:l}() | |
ioa_ds | Def t.ds == 1of(t) |
Thm* t:ioa{i:l}(). t.ds Collection(dec()) | |
record_pair | Def {p} == {1of(p)}{2of(p)} |
Thm* p:(DeclDecl). {p} Type | |
sm_state | Def M.state == {M.ds} |
Thm* M:sm{i:l}(). M.state Type | |
record | Def {d} == l:Labeldecl_type(d;l) |
Thm* d:Decl. {d} Type | |
sig | Def sig() == (LabelSimpleType)(Label(SimpleType List)) |
Thm* sig() Type | |
sig_mng | Def [[s]] rho == < op.[[s.fun(op)]] rho,R.[[s.rel(R)]] rho > |
Thm* s:sig(), rho:Decl{i}. sig_mng{i:l}(s; rho) Decl{i}Decl{i'} | |
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) | |
dec | Def dec() == LabelSimpleType |
Thm* dec() Type | |
frame | Def frame() == LabelSimpleType(Label List) |
Thm* frame() Type | |
eff | Def eff() == LabelLabelSimpleTypesmt() |
Thm* eff() Type | |
pre | Def pre() == LabelLabelrel() |
Thm* pre() Type | |
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 | |
rel | Def rel() == relname()(Term List) |
Thm* rel() Type | |
smt | Def smt() == LabelTermSimpleType |
Thm* smt() Type | |
relname | Def relname() == SimpleType+Label |
Thm* relname() 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 | |
dec_mng | Def [[d]] rho == Case(d) Case x : s = > x:[[s]] rho |
Thm* rho:Decl, d:dec(). [[d]] rho Decl | |
col_union | Def (i:I. C(i))(x) == i:I. x C(i) |
Thm* T,I:Type, C:(ICollection(T)). (i:I. C(i)) Collection(T) | |
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') | |
col_member | Def x c == c(x) |
Thm* T:Type, x:T, c:Collection(T). x c Prop | |
dall | Def D(i) for i I(x) == i:I. D(i)(x) |
Thm* I:Type, D:(IDecl). D(i) for i I Decl | |
col | Def Collection(T) == TProp |
Thm* T:Type{i'}. Collection{i}(T) Type{i'} | |
ioa_frame | Def t.frame == 2of(2of(2of(2of(2of(t))))) |
Thm* t:ioa{i:l}(). t.frame Collection(frame()) | |
ioa_eff | Def t.eff == 1of(2of(2of(2of(2of(t))))) |
Thm* t:ioa{i:l}(). t.eff Collection(eff()) | |
ioa_pre | Def t.pre == 1of(2of(2of(2of(t)))) |
Thm* t:ioa{i:l}(). t.pre Collection(pre()) | |
ioa_init | Def t.init == 1of(2of(2of(t))) |
Thm* t:ioa{i:l}(). t.init Collection(rel()) | |
Thm* t:ioa{i:l}(). t.init Fmla | |
ioa_da | Def t.da == 1of(2of(t)) |
Thm* t:ioa{i:l}(). t.da Collection(dec()) | |
mk_ioa | Def mk_ioa(ds, da, init, pre, eff, frame) == < ds,da,init,pre,eff,frame > |
Thm* ds,da:Collection(dec()), init:Collection(rel()), pre:Collection(pre()), eff:Collection(eff()), frame:Collection(frame()). mk_ioa(ds, da, init, pre, eff, frame) ioa{i:l}() | |
frame_var | Def t.var == 1of(t) |
Thm* t:frame(). t.var Label | |
frame_typ | Def t.typ == 1of(2of(t)) |
Thm* t:frame(). t.typ SimpleType | |
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 | |
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_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 | |
smt_term | Def t.term == 1of(2of(t)) |
Thm* t:smt(). t.term Term | |
smt_lbl | Def t.lbl == 1of(t) |
Thm* t:smt(). t.lbl Label | |
eff_kind | Def t.kind == 1of(t) |
Thm* t:eff(). t.kind Label | |
pre_kind | Def t.kind == 1of(t) |
Thm* t:pre(). t.kind Label | |
sig_fun | Def t.fun == 1of(t) |
Thm* t:sig(). t.fun LabelSimpleType | |
sm_ds | Def t.ds == 1of(2of(t)) |
Thm* t:sm{i:l}(). t.ds Decl | |
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_env_trace | Def t.trace == 1of(t) |
Thm* d:Decl, t:trace_env(d). t.trace (d) List | |
pi1 | Def 1of(t) == t.1 |
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A | |
relname_mng | Def [[rn]] rho e == Case(rn) Case eq(Q) = > x,y. x = y [[Q]] rho Case R = > e.R Default = > True |
r_select | Def r.l == r(l) |
Thm* d:Decl, r:{d}, l:Label. r.l d(l) | |
st_list_mng | Def [[l]] rho == reduce(s,m. [[s]] rhom;Prop;l) |
Thm* l:SimpleType List, rho:Decl{i}. [[l]] rho{i} Type{i'} | |
st_mng | Def [[s]] rho == t_iterate(st_lift(rho);x,y. xy;s) |
Thm* rho:Decl, s:SimpleType. [[s]] rho Type | |
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 | |
nat | Def == {i:| 0i } |
Thm* Type | |
le | Def AB == B < A |
Thm* i,j:. (ij) Prop | |
not | Def A == A False |
Thm* A:Prop. (A) Prop | |
niltrace | Def niltrace() == mk_trace_env(nil, P,k. false) |
Thm* d:Decl. niltrace() trace_env(d) | |
value | Def value(a) == 2of(a) |
Thm* d:Decl, a:(d). value(a) d(kind(a)) | |
eff_smt | Def t.smt == 2of(2of(2of(t))) |
Thm* t:eff(). t.smt smt() | |
smt_typ | Def t.typ == 2of(2of(t)) |
Thm* t:smt(). t.typ SimpleType | |
pre_rel | Def t.rel == 2of(2of(t)) |
Thm* t:pre(). t.rel rel() | |
col_none | Def < > (x) == False |
Thm* T:Type. < > Collection(T) | |
mk_sm | Def mk_sm(da, ds, init, trans) == < da,ds,init,trans > |
Thm* da,ds:Decl, init:({ds}Prop), trans:({ds}(da){ds}Prop). mk_sm(da, ds, init, trans) sm{i:l}() | |
decl_type | Def decl_type(d;x) == d(x) |
Thm* dec:Decl, x:Label. decl_type(dec;x) Type | |
sig_rel | Def t.rel == 2of(t) |
Thm* t:sig(). t.rel Label(SimpleType List) | |
dec_typ | Def t.typ == 2of(t) |
Thm* t:dec(). t.typ SimpleType | |
rel_args | Def t.args == 2of(t) |
Thm* t:rel(). t.args Term 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)) | |
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) | |
assert | Def b == if b True else False fi |
Thm* b:. b Prop | |
ptn | Def Pattern == rec(T.ptn_con(T)) |
Thm* Pattern Type | |
dbase | Def x:y(a) == if a = x y else Top fi |
Thm* x:Label, y:Type. x:y Decl | |
case_mk_dec | Def Case lbl : typ = > body(lbl;typ)(x,z) == x/x2,x1. body(x2;x1) |
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 | |
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 | |
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 | Def Case(value) body == body(value,value) |
st_lift | Def st_lift(rho)(x) == InjCase(x; x'. rho(x'); a. Top) |
Thm* rho:(LabelType). st_lift(rho) (Label+Unit)Type | |
select | Def l[i] == hd(nth_tl(i;l)) |
Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A | |
length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
Thm* A:Type, l:A List. ||l|| | |
Thm* ||nil|| | |
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) | |
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) |
tree | Def Tree(E) == rec(T.tree_con(E;T)) |
Thm* E:Type. Tree(E) 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_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_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]) |
ptn_con | Def ptn_con(T) == Atom++Atom+(TT) |
Thm* T:Type. ptn_con(T) 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)) |
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_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 | |
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)) |
case_relname_eq | Def Case eq(x) = > body(x) cont(x1,z) == InjCase(x1; x2. body(x2); _. cont(z,z)) |
tree_con | Def tree_con(E;T) == E+(TT) |
Thm* E,T:Type. tree_con(E;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)) |
le_int | Def ij == j < i |
Thm* i,j:. (ij) | |
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)) |
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