Nuprl Lemma : hdf-parallel-bag-iterate
∀[A,B:Type]. ∀[Xs:bag(hdataflow(A;B))]. ∀[inputs:A List].
hdf-parallel-bag(Xs)*(inputs) = hdf-parallel-bag(bag-map(λx.x*(inputs);Xs)) ∈ hdataflow(A;B)
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
hdf-parallel-bag: hdf-parallel-bag(Xs),
iterate-hdataflow: P*(inputs),
hdataflow: hdataflow(A;B),
list: T List,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T,
bag-map: bag-map(f;bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
hdf-parallel-bag: hdf-parallel-bag(Xs),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
pi1: fst(t),
subtype_rel: A ⊆r B,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
compose: f o g,
true: True,
has-value: (a)↓,
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a)
Latex:
\mforall{}[A,B:Type]. \mforall{}[Xs:bag(hdataflow(A;B))]. \mforall{}[inputs:A List].
hdf-parallel-bag(Xs)*(inputs) = hdf-parallel-bag(bag-map(\mlambda{}x.x*(inputs);Xs))
supposing valueall-type(B)
Date html generated:
2016_05_16-AM-10_41_58
Last ObjectModification:
2016_01_17-AM-11_12_07
Theory : halting!dataflow
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