Nuprl Lemma : hdf-transformation-test1
hdf-buffer((λn,m. {n + m}) o hdf-base(m.{m});{0}) ~ fix((λR,z. (inl (λa.let x ⟵ a + z in <R x, {x}>)))) 0
Proof
Definitions occuring in Statement :
hdf-buffer: hdf-buffer(X;bs),
hdf-compose1: f o X,
hdf-base: hdf-base(m.F[m]),
callbyvalueall: callbyvalueall,
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
add: n + m,
natural_number: $n,
sqequal: s ~ t,
single-bag: {x}
Definitions unfolded in proof :
top: Top,
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtract: n - m,
single-bag: {x},
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
eq_int: (i =z j),
bag-map: bag-map(f;bs),
bottom: ⊥,
bag-null: bag-null(bs),
btrue: tt,
bfalse: ff,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
uimplies: b supposing a,
strict4: strict4(F),
all: ∀x:A. B[x],
has-value: (a)↓,
ifthenelse: if b then t else f fi ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
select_fun_last: select_fun_last(g;m),
select_fun_ap: select_fun_ap(g;n;m),
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,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
cons: [a / b],
nil: [],
it: ⋅,
empty-bag: {},
bag-append: as + bs
Latex:
hdf-buffer((\mlambda{}n,m. \{n + m\}) o hdf-base(m.\{m\});\{0\}) \msim{} fix((\mlambda{}R,z. (inl (\mlambda{}a.let x \mleftarrow{}{} a + z in <R x, \{x\}>\000C)))) 0
Date html generated:
2016_05_16-AM-10_51_47
Last ObjectModification:
2016_01_18-PM-06_18_48
Theory : halting!dataflow
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