Nuprl Lemma : datastream-dataflow-to-Process
∀[A,B:Type]. ∀[g:B ⟶ LabeledDAG(Id × (Com(P.A) Process(P.A)))]. ∀[L:A List]. ∀[F:dataflow(A;B)].
(data-stream(dataflow-to-Process(
F;
g);L) ~ map(g;data-stream(F;L)))
Proof
Definitions occuring in Statement :
dataflow-to-Process: dataflow-to-Process,
Process: Process(P.M[P]),
Com: Com(P.M[P]),
data-stream: data-stream(P;L),
dataflow: dataflow(A;B),
ldag: LabeledDAG(T),
Id: Id,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
dataflow-to-Process: dataflow-to-Process,
rec-process: RecProcess(s0;s,m.next[s; m]),
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
pi2: snd(t),
pi1: fst(t)
Latex:
\mforall{}[A,B:Type]. \mforall{}[g:B {}\mrightarrow{} LabeledDAG(Id \mtimes{} (Com(P.A) Process(P.A)))]. \mforall{}[L:A List]. \mforall{}[F:dataflow(A;B)].
(data-stream(dataflow-to-Process(
F;
g);L) \msim{} map(g;data-stream(F;L)))
Date html generated:
2016_05_17-AM-10_24_19
Last ObjectModification:
2016_01_18-AM-00_18_39
Theory : process-model
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