Nuprl Lemma : hdf-sqequal6
∀[s,F,G:Top].
(fix((λmk-hdf,s0. (inl (λa.let bs' ⟵ reduce(λl,l'. (l @ l');[];map(λb.[G[a;b]];s0))
in <mk-hdf case null(bs') of inl() => s0 | inr() => bs', F[s0;bs']>))))
[s] ~ fix((λmk-hdf,s0. (inl (λa.let bs' ⟵ G[a;s0] in <mk-hdf bs', F[[s0];[bs']]>)))) s)
Proof
Definitions occuring in Statement :
null: null(as),
map: map(f;as),
append: as @ bs,
reduce: reduce(f;k;as),
cons: [a / b],
nil: [],
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
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,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
fun_exp: f^n,
primrec: primrec(n;b;c),
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
null: null(as),
cons: [a / b],
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[s,F,G:Top].
(fix((\mlambda{}mk-hdf,s0. (inl (\mlambda{}a.let bs' \mleftarrow{}{} reduce(\mlambda{}l,l'. (l @ l');[];map(\mlambda{}b.[G[a;b]];s0))
in <mk-hdf case null(bs') of inl() => s0 | inr() => bs', F[s0;bs']>))))\000C
[s] \msim{} fix((\mlambda{}mk-hdf,s0. (inl (\mlambda{}a.let bs' \mleftarrow{}{} G[a;s0] in <mk-hdf bs', F[[s0];[bs']]>)))) s)
Date html generated:
2016_05_16-AM-10_51_19
Last ObjectModification:
2016_01_17-AM-11_09_12
Theory : halting!dataflow
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