Nuprl Lemma : hdf-compose1-transformation0-2
∀[f,F:Top].
(f o fix((λmk-hdf.(inl (λa.<mk-hdf, F[a]>)))) ~ fix((λmk-hdf.(inl (λa.cbva_seq(λn.bag-map(f;F[a]); λg.<mk-hdf
, g (λx.x)
>; 1))))))
Proof
Definitions occuring in Statement :
hdf-compose1: f o X,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
natural_number: $n,
sqequal: s ~ t,
bag-map: bag-map(f;bs),
cbva_seq: cbva_seq(L; F; m)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cbva_seq: cbva_seq(L; F; m),
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
hdf-compose1: f o X,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-halted: hdf-halted(P),
isr: isr(x),
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,
hdf-run: hdf-run(P),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
hdf-ap: X(a),
bag-map: bag-map(f;bs),
map: map(f;as),
list_ind: list_ind,
cons: [a / b],
nil: [],
it: ⋅,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
empty-bag: {},
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,
ge: i ≥ j ,
sq_type: SQType(T)
Latex:
\mforall{}[f,F:Top].
(f o fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.<mk-hdf, F[a]>)))) \msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}a.cbva\_seq(\mlambda{}n.bag-map(f;F[a]);
\mlambda{}g.<mk-hdf
, g (\mlambda{}x.x)
> 1))))))
Date html generated:
2016_05_16-AM-10_45_42
Last ObjectModification:
2016_01_17-AM-11_10_43
Theory : halting!dataflow
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