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),
iterate-hdataflow: P*(inputs),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
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: {}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
encodes-msg-type: hdr encodes T,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
top: Top,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
prop: ℙ,
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
pi2: snd(t),
hdf-halt: hdf-halt(),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
pi1: fst(t),
msg-type: msg-type(msg;f),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
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:
2016_05_17-AM-09_08_23
Last ObjectModification:
2016_01_17-PM-09_14_25
Theory : local!classes
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