Nuprl Lemma : base-process-class-program-ap
∀[f:Name ⟶ Type]. ∀[Info,T:Type]. ∀[loc:Id]. ∀[hdr:Name].
∀[P:Id ⟶ hdataflow(Info;T)]. ∀[a:Message(f)]. ∀[i:Top].
(base-process-class-program(P;loc;hdr) i(a) ~ if hdf-halted(P loc) then <hdf-halt(), {}>
if test-msg-header-and-loc(a;hdr;loc)
then let P',b = P loc(snd(msg-body(a)))
in <base-process-class-program(λi.P';loc;hdr) i, b>
else <base-process-class-program(P;loc;hdr) i, {}>
fi )
supposing hdr encodes Id × Top
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),
hdf-halt: hdf-halt(),
hdf-halted: hdf-halted(P),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
Id: Id,
name: Name,
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],
spread: spread def,
pair: <a, b>,
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,
base-process-class-program: base-process-class-program(X;loc;hdr),
hdf-ap: X(a),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-halt: hdf-halt(),
hdf-run: hdf-run(P),
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[Info,T:Type]. \mforall{}[loc:Id]. \mforall{}[hdr:Name].
\mforall{}[P:Id {}\mrightarrow{} hdataflow(Info;T)]. \mforall{}[a:Message(f)]. \mforall{}[i:Top].
(base-process-class-program(P;loc;hdr) i(a) \msim{} if hdf-halted(P loc) then <hdf-halt(), \{\}>
if test-msg-header-and-loc(a;hdr;loc)
then let P',b = P loc(snd(msg-body(a)))
in <base-process-class-program(\mlambda{}i.P';loc;hdr) i, b>
else <base-process-class-program(P;loc;hdr) i, \{\}>
fi )
supposing hdr encodes Id \mtimes{} Top
Date html generated:
2016_05_17-AM-09_08_18
Last ObjectModification:
2015_12_29-PM-03_36_22
Theory : local!classes
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