{ 
[A,B,M:Type]. [ms:M List]. [P:dataflow(M;bag(A))].
[Q:A 
dataflow(M;bag(B))].
(bind-dataflow(P;a.Q[a])*(ms)
= bind-dataflow-aux(P*(ms);bag-map(
df.df*(ms);{})
+ 
n
upto(||ms||).bag-map(a.Q[a]*(nth_tl(n;ms));
snd(P*(firstn(n;ms))(ms[n])));a.Q[a])) }
{ Proof }
Definitions occuring in Statement :
bind-dataflow: bind-dataflow(P;a.Q[a]),
bind-dataflow-aux: bind-dataflow-aux(P;dfs;a.Q[a]),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
dataflow: dataflow(A;B),
select: l[i],
firstn: firstn(n;as),
nth_tl: nth_tl(n;as),
length: ||as||,
uall: [x:A]. B[x],
so_apply: x[s],
pi2: snd(t),
lambda: x.A[x],
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t,
bag-combine: xbs.f[x],
bag-append: as + bs,
bag-map: bag-map(f;bs),
empty-bag: {},
bag: bag(T),
upto: upto(n)
Definitions :
all: x:A. B[x],
axiom: Ax,
select: l[i],
firstn: firstn(n;as),
dataflow-ap: df(a),
pi2: snd(t),
nth_tl: nth_tl(n;as),
length: ||as||,
upto: upto(n),
bag-combine: xbs.f[x],
lambda: x.A[x],
bag-map: bag-map(f;bs),
bag-append: as + bs,
bind-dataflow-aux: bind-dataflow-aux(P;dfs;a.Q[a]),
apply: f a,
so_apply: x[s],
bind-dataflow: bind-dataflow(P;a.Q[a]),
iterate-dataflow: P*(inputs),
member: t T,
so_lambda: 
x.t[x],
equal: s = t,
function: x:A B[x],
dataflow: dataflow(A;B),
bag: bag(T),
list: type List,
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
RepeatFor: Error :RepeatFor,
RepUR: Error :RepUR,
empty-bag: {},
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic
Lemmas :
bag_wf,
dataflow_wf,
empty-bag_wf,
uall_wf,
iterate-bind-dataflow-aux
\mforall{}[A,B,M:Type]. \mforall{}[ms:M List]. \mforall{}[P:dataflow(M;bag(A))]. \mforall{}[Q:A {}\mrightarrow{} dataflow(M;bag(B))].
(bind-dataflow(P;a.Q[a])*(ms)
= bind-dataflow-aux(P*(ms);bag-map(\mlambda{}df.df*(ms);\{\})
+ \mcup{}n\mmember{}upto(||ms||).bag-map(\mlambda{}a.Q[a]*(nth\_tl(n;ms));snd(P*(firstn(n;ms))(ms[n])));a.Q[a]))
Date html generated:
2011_08_16-AM-09_49_44
Last ObjectModification:
2011_05_09-PM-06_26_08
Home
Index