Nuprl Lemma : hdf-sqequal4
∀[F1,F2:Top].
(fix((λmk-hdf.(inl (λa.let out ⟵ F1[a]
in <mk-hdf, out>)))) || fix((λmk-hdf.(inl (λa.let out ⟵ F2[a]
in <mk-hdf, out>))))
~ fix((λmk-hdf.(inl (λa.let out1 ⟵ F1[a]
in let out2 ⟵ F2[a]
in let out ⟵ out1 + out2
in <mk-hdf, out>)))))
Proof
Definitions occuring in Statement :
hdf-parallel: X || Y,
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
sqequal: s ~ t,
bag-append: as + bs
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hdf-parallel: X || Y,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
ifthenelse: if b then t else f fi ,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
band: p ∧b q,
hdf-halted: hdf-halted(P),
isr: isr(x),
bfalse: ff,
hdf-run: hdf-run(P),
hdf-ap: X(a),
empty-bag: {},
nil: [],
it: ⋅,
btrue: tt,
hdf-halt: hdf-halt(),
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
decidable: Dec(P),
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
callbyvalueall: callbyvalueall,
ge: i ≥ j ,
sq_type: SQType(T)
Latex:
\mforall{}[F1,F2:Top].
(fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out \mleftarrow{}{} F1[a]
in <mk-hdf, out>)))) || fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out \mleftarrow{}{} F2[a]
in <mk-hdf, out>))))
\msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out1 \mleftarrow{}{} F1[a]
in let out2 \mleftarrow{}{} F2[a]
in let out \mleftarrow{}{} out1 + out2
in <mk-hdf, out>)))))
Date html generated:
2016_05_16-AM-10_51_00
Last ObjectModification:
2016_01_17-AM-11_09_38
Theory : halting!dataflow
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