Nuprl Lemma : hdf-sqequal2-cbva
∀[F,G,H:Top].
(fix((λmk-hdf,s0. case s0 of inl(y) => inl (λa.let X',bs = y a in let out ⟵ G[bs] in <mk-hdf X', out>) | inr(z) => H[\000Cz]))
fix((λmk-hdf.(inl (λm.let out ⟵ F[m]
in <mk-hdf, out>)))) ~ fix((λmk-hdf.(inl (λa.let out1 ⟵ F[a]
in let out2 ⟵ G[out1]
in <mk-hdf, out2>)))))
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
spread: spread def,
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
inl: inl x,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
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{}[F,G,H:Top].
(fix((\mlambda{}mk-hdf,s0. case s0
of inl(y) =>
inl (\mlambda{}a.let X',bs = y a
in let out \mleftarrow{}{} G[bs]
in <mk-hdf X', out>)
| inr(z) =>
H[z]))
fix((\mlambda{}mk-hdf.(inl (\mlambda{}m.let out \mleftarrow{}{} F[m]
in <mk-hdf, out>)))) \msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out1 \mleftarrow{}{} F[a]
in let out2 \mleftarrow{}{} G[out1]
in <mk-hdf, out2>)))))
Date html generated:
2016_05_16-AM-10_45_01
Last ObjectModification:
2016_01_17-AM-11_13_10
Theory : halting!dataflow
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