Nuprl Lemma : iterate-base-process-class-program
∀[f:Name ─→ Type]. ∀[Info,T:Type]. ∀[loc:Id]. ∀[hdr:Name].
∀[P:Id ─→ hdataflow(Info;T)]. ∀[L:Message(f) List]. ∀[m:Message(f)]. ∀[i:Top].
(snd(base-process-class-program(P;loc;hdr) i*(L)(m)) ~ if test-msg-header-and-loc(m;hdr;loc)
then snd(P loc*(mapfilter(λmsg.(snd(msg-body(msg)));λmsg.test-msg-header-and-loc(msg;hdr;loc);L))(snd(msg-body(m))))
else {}
fi )
supposing hdr encodes Id × Info
Proof
Definitions occuring in Statement :
base-process-class-program: base-process-class-program(X;loc;hdr),
test-msg-header-and-loc: test-msg-header-and-loc(msg;hdr;loc),
encodes-msg-type: hdr encodes T,
msg-body: msg-body(msg),
Message: Message(f),
Id: Id,
name: Name,
mapfilter: mapfilter(f;P;L),
list: T List,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pi2: snd(t),
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
sqequal: s ~ t,
empty-bag: {},
iterate-hdataflow: P*(inputs),
hdf-ap: X(a),
hdataflow: hdataflow(A;B)
Lemmas :
base-process-class-program-ap,
subtype_rel_product,
Id_wf,
top_wf,
subtype_rel_transitivity,
Message_wf,
list_wf,
hdataflow_wf,
encodes-msg-type_wf,
name_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
iter_hdf_nil_lemma,
mapfilter_nil_lemma,
hdf-halted_wf,
bool_wf,
eqtt_to_assert,
hdf-halted-is-inr,
hdf_ap_halt_lemma,
test-msg-header-and-loc_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
set_subtype_base,
int_subtype_base,
iter_hdf_cons_lemma,
iterate-hdf-halt,
subtype_rel_list,
mapfilter_wf,
cons_wf,
assert_wf,
assert-test-msg-header-and-loc,
msg-body_wf2,
subtype_rel-equal,
msg-type_wf,
iff_weakening_equal,
hdf-ap_wf,
bag_wf,
mapfilter-cons,
mapfilter-singleton,
map_cons_lemma,
map_nil_lemma,
list_ind_cons_lemma,
list_ind_nil_lemma
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[Info,T:Type]. \mforall{}[loc:Id]. \mforall{}[hdr:Name].
\mforall{}[P:Id {}\mrightarrow{} hdataflow(Info;T)]. \mforall{}[L:Message(f) List]. \mforall{}[m:Message(f)]. \mforall{}[i:Top].
(snd(base-process-class-program(P;loc;hdr) i*(L)(m)) \msim{} if test-msg-header-and-loc(m;hdr;loc)
then snd(P loc*(mapfilter(\mlambda{}msg.(snd(msg-body(msg)));
\mlambda{}msg.test-msg-header-and-loc(msg;hdr;loc);
L))(snd(msg-body(m))))
else \{\}
fi )
supposing hdr encodes Id \mtimes{} Info
Date html generated:
2015_07_22-PM-00_03_44
Last ObjectModification:
2015_02_04-PM-05_10_41
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