Nuprl Lemma : hdf-bind-gen-left-halt
∀[A,B,C:Type]. ∀[Y:B ⟶ hdataflow(A;C)]. ∀[hdfs:bag(hdataflow(A;C))].
hdf-halt() (hdfs) >>= Y = hdf-halt() (hdfs) >>= λx.hdf-return({x}) ∈ hdataflow(A;C) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
hdf-bind-gen: X (hdfs) >>= Y,
hdf-return: hdf-return(x),
hdf-halt: hdf-halt(),
hdataflow: hdataflow(A;B),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
prop: ℙ,
hdf-bind-gen: X (hdfs) >>= Y,
bind-nxt: bind-nxt(Y;p;a),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
bool: 𝔹,
unit: Unit,
it: ⋅,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
subtype_rel: A ⊆r B,
pi1: fst(t),
pi2: snd(t),
squash: ↓T,
true: True,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[Y:B {}\mrightarrow{} hdataflow(A;C)]. \mforall{}[hdfs:bag(hdataflow(A;C))].
hdf-halt() (hdfs) >>= Y = hdf-halt() (hdfs) >>= \mlambda{}x.hdf-return(\{x\}) supposing valueall-type(C)
Date html generated:
2016_05_16-AM-10_43_21
Last ObjectModification:
2016_01_17-AM-11_12_19
Theory : halting!dataflow
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