Nuprl Lemma : last-stream-parallel-df-program-meaning
[A:
']. [dfps:DataflowProgram(A) List].
[B:{B:Type| valueall-type(B)} ]. [F:k:
||dfps|| 
bag(df-program-type(dfps[k])) bag(B)]. [L:A List].
last(data-stream(df-program-meaning(parallel-df-program(B;F;dfps));L))
= (F (
k.last(data-stream(df-program-meaning(dfps[k]);L))))
supposing (0 < ||L||) 
((F (i.{})) = {})
supposing 0 < ||dfps||
Proof not projected
Definitions occuring in Statement :
parallel-df-program: parallel-df-program(B;F;dfps),
df-program-meaning: df-program-meaning(dfp),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
data-stream: data-stream(P;L),
select: l[i],
length: ||as||,
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
and: P Q,
less_than: a < b,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
last: last(L),
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
false: False,
implies: P 
Q,
not: 
A,
le: A 
B,
member: t 
T,
and: P Q,
uimplies: b supposing a,
uall: [x:A]. B[x],
iff: P 
Q,
rev_implies: P Q,
lelt: i j < k,
last: last(L),
int_seg: {i..j},
subtype: S 
T,
all: x:A. B[x],
top: Top,
prop: 
,
so_lambda: 
x.t[x],
true: True,
squash: 
T,
uiff: uiff(P;Q),
so_apply: x[s]
Lemmas :
valueall-type_wf,
int_seg_wf,
dataflow-program_wf,
select_wf,
df-program-type_wf,
empty-bag_wf,
bag_wf,
equal_wf,
length_wf,
less_than_wf,
and_wf,
parallel-df-program-meaning,
select_upto,
lelt_wf,
length_wf_nat,
length_upto,
df-program-meaning_wf,
pos_length2,
top_wf,
null-data-stream,
data-stream_wf,
last_wf,
better-parallel-data-stream,
null_wf3,
assert_wf,
not_wf,
squash_wf,
select-map,
upto_wf,
last-map,
non_null_iff_length,
length-data-stream,
le_wf,
dataflow_wf,
true_wf
\mforall{}[A:\mBbbU{}']. \mforall{}[dfps:DataflowProgram(A) List].
\mforall{}[B:\{B:Type| valueall-type(B)\} ]. \mforall{}[F:k:\mBbbN{}||dfps|| {}\mrightarrow{} bag(df-program-type(dfps[k])) {}\mrightarrow{} bag(B)].
\mforall{}[L:A List].
last(data-stream(df-program-meaning(parallel-df-program(B;F;dfps));L))
= (F (\mlambda{}k.last(data-stream(df-program-meaning(dfps[k]);L))))
supposing (0 < ||L||) \mwedge{} ((F (\mlambda{}i.\{\})) = \{\})
supposing 0 < ||dfps||
Date html generated:
2012_01_23-PM-12_00_36
Last ObjectModification:
2011_12_18-AM-09_15_12
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