{ 
[A,B,C,S:Type]. [F:S 
A (S 
C)]. [G:C B]. [s1:S].
(better-parallel-dataflow(
1;
k.[rec-dataflow(s1;s,a.F[s;a])][k];
g.G[g 0])
= rec-dataflow(s1;s,a.let s',out = F[s;a]
in <s', G[out]>)) }
{ Proof }
Definitions occuring in Statement :
better-parallel-dataflow: better-parallel-dataflow,
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
dataflow: dataflow(A;B),
select: l[i],
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
apply: f a,
lambda: x.A[x],
function: x:A B[x],
spread: spread def,
pair: <a, b>,
product: x:A B[x],
cons: [car / cdr],
nil: [],
natural_number: $n,
universe: Type,
equal: s = t
Definitions :
top: Top,
tl: tl(l),
hd: hd(l),
length: ||as||,
lelt: i 
j < k,
let: let,
int_seg: {i..j
},
p-outcome: Outcome,
prop: 
,
void: Void,
implies: P 
Q,
false: False,
set: {x:A| B[x]} ,
real: 
,
rationals: 
,
subtype: S 
T,
nat: 
,
int: 
,
sqequal: s ~ t,
so_lambda: 
x y.t[x; y],
data-stream: data-stream(P;L),
list: type List,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
axiom: Ax,
pair: <a, b>,
spread: spread def,
so_apply: x[s],
nil: [],
apply: f a,
so_apply: x[s1;s2],
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
cons: [car / cdr],
select: l[i],
lambda: x.A[x],
natural_number: $n,
better-parallel-dataflow: better-parallel-dataflow,
dataflow: dataflow(A;B),
equal: s = t,
universe: Type,
product: x:A B[x],
uall: [x:A]. B[x],
function: x:A B[x],
member: t 
T,
isect: 
x:A. B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
so_lambda: x.t[x],
CollapseTHENA: Error :CollapseTHENA,
THENM: Error :THENM,
D: Error :D
Lemmas :
le_wf,
false_wf,
not_wf,
int_seg_wf,
member_wf,
nat_wf,
dataflow_wf,
rec-dataflow_wf,
select_wf,
better-parallel-dataflow_wf,
parallel-1-rec-dataflow,
dataflow-extensionality,
top_wf,
data-stream_wf
\mforall{}[A,B,C,S:Type]. \mforall{}[F:S {}\mrightarrow{} A {}\mrightarrow{} (S \mtimes{} C)]. \mforall{}[G:C {}\mrightarrow{} B]. \mforall{}[s1:S].
(better-parallel-dataflow(
1;\mlambda{}k.[rec-dataflow(s1;s,a.F[s;a])][k];
\mlambda{}g.G[g 0])
= rec-dataflow(s1;s,a.let s',out = F[s;a]
in <s', G[out]>))
Date html generated:
2011_08_10-AM-08_21_02
Last ObjectModification:
2011_06_18-AM-08_32_12
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