Nuprl Lemma : hdf-sqequal8-3
∀[mk-hdf,a,s,X,x:Top].
(let b ⟵ a
in case null(b) of inl(x1) => let s' ⟵ s in <mk-hdf <X, s'>, x> | inr(y1) => <mk-hdf <X, b>, x> ~ let b ⟵ a
in let s' ⟵ if null(b) then s else b fi
in <mk-hdf <X, s'>, x>)
Proof
Definitions occuring in Statement :
null: null(as),
callbyvalueall: callbyvalueall,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
null: null(as),
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
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,
bfalse: ff,
btrue: tt,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
ifthenelse: if b then t else f fi ,
has-valueall: has-valueall(a)
Latex:
\mforall{}[mk-hdf,a,s,X,x:Top].
(let b \mleftarrow{}{} a
in case null(b) of inl(x1) => let s' \mleftarrow{}{} s in <mk-hdf <X, s'>, x> | inr(y1) => <mk-hdf <X, b>, x> \000C\msim{} let b \mleftarrow{}{} a
in let s' \mleftarrow{}{} if null(b)
then s
else b
fi
in <mk-hdf <X, s'>, x>)
Date html generated:
2016_05_16-AM-10_45_11
Last ObjectModification:
2016_01_17-AM-11_13_02
Theory : halting!dataflow
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