Nuprl Lemma : hdataflow-equal
∀[A,B:Type]. ∀[P,Q:hdataflow(A;B)].
uiff(P = Q ∈ hdataflow(A;B);∀[inputs:A List]
(hdf-halted(P*(inputs)) = hdf-halted(Q*(inputs))
∧ (∀[a:A]. (hdf-out(P*(inputs);a) = hdf-out(Q*(inputs);a) ∈ bag(B)))))
Proof
Definitions occuring in Statement :
iterate-hdataflow: P*(inputs),
hdf-out: hdf-out(P;x),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
list: T List,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
prop: ℙ,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
rev_implies: P ⇐ Q,
hdataflow: hdataflow(A;B),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
F-bisimulation: x,y.R[x; y] is an T.F[T]-bisimulation,
subtype_rel: A ⊆r B,
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
cand: A c∧ B,
type-monotone: Monotone(T.F[T]),
top: Top,
hdf-halted: hdf-halted(P),
isr: isr(x),
not: ¬A,
false: False,
hdf-ap: X(a),
hdf-out: hdf-out(P;x)
Latex:
\mforall{}[A,B:Type]. \mforall{}[P,Q:hdataflow(A;B)].
uiff(P = Q;\mforall{}[inputs:A List]
(hdf-halted(P*(inputs)) = hdf-halted(Q*(inputs))
\mwedge{} (\mforall{}[a:A]. (hdf-out(P*(inputs);a) = hdf-out(Q*(inputs);a)))))
Date html generated:
2016_05_16-AM-10_38_41
Last ObjectModification:
2015_12_28-PM-07_45_54
Theory : halting!dataflow
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