{ 
[A:Type]. [dfp:DataflowProgram(A)]. [s:df-program-statetype(dfp)]. [m:A].
(df-program-meaning(df-program-in-state(dfp;s))(m)
~ let s',x = df-program-in-state-ap(dfp;s;m)
in <case s'
of inl(s2) =>
df-program-meaning(df-program-in-state(dfp;s2))
| inr(z) =>
df-program-halt-meaning(dfp)
, x
>) }
{ Proof }
Definitions occuring in Statement :
df-program-in-state-ap: df-program-in-state-ap(dfp;s;m),
df-program-in-state: df-program-in-state(dfp;s),
df-program-halt-meaning: df-program-halt-meaning(dfp),
df-program-meaning: df-program-meaning(dfp),
df-program-statetype: df-program-statetype(dfp),
dataflow-program: DataflowProgram(A),
dataflow-ap: df(a),
uall: [x:A]. B[x],
spread: spread def,
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
universe: Type,
sqequal: s ~ t
Definitions :
implies: P 
Q,
unit: Unit,
union: left + right,
apply: f a,
df-program-halt-meaning: df-program-halt-meaning(dfp),
rec_dataflow_ap: rec_dataflow_ap_compseq_tag_def,
pi2: snd(t),
df-program-in-state-ap: df-program-in-state-ap(dfp;s;m),
set: {x:A| B[x]} ,
equal: s = t,
spread: spread def,
pi1: fst(t),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
quotient: x,y:A//B[x; y],
exists: 
x:A. B[x],
nat: 
,
top: Top,
lambda: 
x.A[x],
primrec: primrec(n;b;c),
corec: corec(T.F[T]),
so_lambda: 
x.t[x],
sq_type: SQType(T),
uimplies: b supposing a,
dataflow: dataflow(A;B),
product: x:A 
B[x],
df-program-type: df-program-type(dfp),
bag: bag(T),
df-program-in-state: df-program-in-state(dfp;s),
df-program-meaning: df-program-meaning(dfp),
dataflow-ap: df(a),
subtype_rel: A 
r B,
function: x:A 
B[x],
all: x:A. B[x],
universe: Type,
dataflow-program: DataflowProgram(A),
sqequal: s ~ t,
df-program-statetype: df-program-statetype(dfp),
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t 
T,
int: 
Lemmas :
df-program-meaning_wf,
dataflow-ap_wf,
subtype_base_sq,
product_subtype_base,
dataflow_wf,
df-program-in-state_wf,
df-program-type_wf,
top_wf,
primrec_wf,
nat_wf,
isect_subtype_base,
df-program-statetype_wf,
dataflow-program_wf,
unit_wf,
bag_wf
\mforall{}[A:Type]. \mforall{}[dfp:DataflowProgram(A)]. \mforall{}[s:df-program-statetype(dfp)]. \mforall{}[m:A].
(df-program-meaning(df-program-in-state(dfp;s))(m) \msim{} let s',x = df-program-in-state-ap(dfp;s;m)
in <case s'
of inl(s2) =>
df-program-meaning(
df-program-in-state(dfp;s2))
| inr(z) =>
df-program-halt-meaning(dfp)
, x
>)
Date html generated:
2011_08_16-AM-09_36_06
Last ObjectModification:
2011_06_02-PM-03_29_40
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