Nuprl Lemma : hdf-sqequal7
∀[F,G,H,K,L,J,init:Top].
(fix((λmk-hdf,s0. (inl (λa.let X,s = s0
in case X
of inl(P) =>
let X',fs = P a
in let b ⟵ G[fs;s]
in let s' ⟵ J[b;s]
in <mk-hdf <X', K[s;s']>, L[s;s']>
| inr(z) =>
H[mk-hdf;s;z]))))
<fix((λmk-hdf.(inl (λa.let out ⟵ F[a] in <mk-hdf, out>)))), init> ~ fix((λmk-hdf,s. (inl (λa.let out ⟵ F[a]
in let b ⟵ G[out;s]
in let s' ⟵ J[b;s]
in <mk-hdf K[s;s'], L[s;s']>))))
init)
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
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,
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,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
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],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[F,G,H,K,L,J,init:Top].
(fix((\mlambda{}mk-hdf,s0. (inl (\mlambda{}a.let X,s = s0
in case X
of inl(P) =>
let X',fs = P a
in let b \mleftarrow{}{} G[fs;s]
in let s' \mleftarrow{}{} J[b;s]
in <mk-hdf <X', K[s;s']>, L[s;s']>
| inr(z) =>
H[mk-hdf;s;z]))))
<fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.let out \mleftarrow{}{} F[a] in <mk-hdf, out>)))), init> \msim{} fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.let\000C out \mleftarrow{}{} F[a]
in let b \mleftarrow{}{} G[out;s]
in let s' \mleftarrow{}{} J[b;s]
in <mk-hdf
K[s;s']
, L[s;s']
>))))
init)
Date html generated:
2016_05_16-AM-10_51_33
Last ObjectModification:
2016_01_17-AM-11_09_34
Theory : halting!dataflow
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