Nuprl Lemma : hdf-parallel-transformation1
∀[L1,L2:Base]. ∀[m1,m2:ℕ+].
(fix((λmk-hdf.(inl (λa.simple-cbva-seq(L1[a];λout.<mk-hdf, out>;m1)))))
|| fix((λmk-hdf.(inl (λa.simple-cbva-seq(L2[a];λout.<mk-hdf, out>;m2)))))
~ fix((λmk-hdf.(inl (λa.simple-cbva-seq(λn.if n <z m1 then L1[a] n
if n <z m1 + m2 then mk_lambdas(L2[a] (n - m1);m1)
else mk_lambdas(λout1.mk_lambdas(λout2.(out1 + out2);m2 - 1);m1 - 1)
fi ;λout.<mk-hdf, out>;(m1 + m2) + 1))))))
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
nat_plus: ℕ+,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
subtract: n - m,
add: n + m,
natural_number: $n,
base: Base,
sqequal: s ~ t,
bag-append: as + bs,
simple-cbva-seq: simple-cbva-seq(L;F;m),
mk_lambdas: mk_lambdas(F;m)
Lemmas :
lifting-strict-spread,
top_wf,
has-value_wf_base,
base_wf,
base_sq,
pair-eta,
lifting-strict-decide,
decide_bfalse_lemma,
empty_bag_append_lemma,
strict4-spread,
lifting-strict-callbyvalueall,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
lifting-strict-less,
simple-cbva-seq-spread,
simple-cbva-seq-extend-2,
simple-cbva-seq-combine,
decidable__lt,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
less_than_wf,
lifting-strict-int_eq,
general_add_assoc,
simple-cbva-seq-list-case1,
nat_plus_subtype_nat,
simple-cbva-seq-sqequal-n,
set_subtype_base,
int_subtype_base,
zero-le-nat,
decidable__le,
not-le-2,
minus-zero,
add-swap,
minus-minus,
le-add-cancel-alt,
subtype_base_sq,
le-add-cancel2,
lelt_wf,
not-equal-2,
nat_wf,
nat_plus_wf,
all_wf,
sqequal_n_wf,
int_seg_subtype-nat,
set_wf,
primrec-wf2,
sq_stable__le,
add-mul-special,
zero-mul
\mforall{}[L1,L2:Base]. \mforall{}[m1,m2:\mBbbN{}\msupplus{}].
(fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.simple-cbva-seq(L1[a];\mlambda{}out.<mk-hdf, out>m1)))))
|| fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.simple-cbva-seq(L2[a];\mlambda{}out.<mk-hdf, out>m2)))))
\msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.simple-cbva-seq(\mlambda{}n.if n <z m1 then L1[a] n
if n <z m1 + m2 then mk\_lambdas(L2[a] (n - m1);m1)
else mk\_lambdas(\mlambda{}out1.mk\_lambdas(\mlambda{}out2.(out1
+ out2);m2
- 1);m1 - 1)
fi ;\mlambda{}out.<mk-hdf, out>(m1 + m2) + 1))))))
Date html generated:
2015_07_17-AM-08_09_15
Last ObjectModification:
2015_04_23-PM-10_57_35
Home
Index