{ 
A:{A:Type| 
A} . B:{B:Type| valueall-type(B)} . df:dataflow(A;bag(B)).
dfp:DataflowProgram(A)
((df-program-type(dfp) = B) 
(df-program-meaning(dfp) = df)) }
{ Proof }
Definitions occuring in Statement :
df-program-meaning: df-program-meaning(dfp),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
dataflow: dataflow(A;B),
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
and: P Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t,
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
dataflow: dataflow(A;B),
bag: bag(T),
lambda: 
x.A[x],
spread: spread def,
dataflow-ap: df(a),
pair: <a, b>,
inl: inl x ,
Try: Error :Try,
Complete: Error :Complete,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
MaAuto: Error :MaAuto,
equal: s = t,
product: x:A 
B[x],
and: P Q,
exists: x:A. B[x],
set: {x:A| B[x]} ,
universe: Type,
function: x:A 
B[x],
all: x:A. B[x],
valueall-type: valueall-type(T),
prop: 
,
squash: T,
dataflow-program: DataflowProgram(A),
uall: [x:A]. B[x],
isect: 
x:A. B[x],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
uimplies: b supposing a,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
corec: corec(T.F[T]),
member: t 
T,
primrec: primrec(n;b;c),
union: left + right,
subtype: S T,
l_member: (x l),
unit: Unit,
fpf: a:A fp-> B[a],
fpf-cap: f(x)?z,
sq_stable: SqStable(P),
implies: P 
Q,
fpf-sub: f g,
true: True,
select: l[i],
list: type List,
ma-state: State(ds),
deq: EqDecider(T),
top: Top,
b-union: A 
B,
isect2: T1 T2,
stream: stream(A),
tuple-type: tuple-type(L),
fset: FSet{T},
record: record(x.T[x]),
record+: record+,
iff: P 
Q,
or: P 
Q,
rev_implies: P Q,
tag-by: zT,
so_lambda: 
x.t[x],
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
bag-member: bag-member(T;x;bs),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
assert: 
b,
value-type: value-type(T),
no_repeats: no_repeats(T;l),
prime_ideal_p: IsPrimeIdeal(R;P),
integ_dom_p: IsIntegDom(r),
grp_leq: a b,
monoid_hom_p: IsMonHom{M1,M2}(f),
group_p: IsGroup(T;op;id;inv),
monoid_p: IsMonoid(T;op;id),
monot: monot(T;x,y.R[x; y];f),
cancel: Cancel(T;S;op),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
action_p: IsAction(A;x;e;S;f),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
bilinear: BiLinear(T;pl;tm),
inverse: Inverse(T;op;id;inv),
comm: Comm(T;op),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
coprime: CoPrime(a,b),
uconnex: uconnex(T; x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
eqfun_p: IsEqFun(T;eq),
inject: Inj(A;B;f),
inv_funs: InvFuns(A;B;f;g),
uni_sat: a = !x:T. Q[x],
tunion: x:A.B[x],
quotient: x,y:A//B[x; y],
rec: rec(x.A[x]),
atom: Atom,
int: 
,
atom: Atom$n,
guard: {T},
false: False,
fpf-dom: x dom(f),
apply: f a,
nat: 
,
sqequal: s ~ t,
df-program-type: df-program-type(dfp),
df-program-meaning: df-program-meaning(dfp),
cand: A c B,
bool: 
,
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
empty-bag: {},
so_lambda: x y.t[x; y],
sq_type: SQType(T),
intensional-universe: IType,
limited-type: LimitedType,
tactic: Error :tactic,
AssertBY: Error :AssertBY,
let: let,
pi2: snd(t),
iterate-dataflow: P*(inputs),
axiom: Ax,
rec_dataflow_ap: rec_dataflow_ap_compseq_tag_def,
iter_df_nil: iter_df_nil{iter_df_nil_compseq_tag_def:o}(P),
iter_df_cons: iter_df_cons{iter_df_cons_compseq_tag_def:o}(as; a; P),
pi1: fst(t)
Lemmas :
dataflow-equal,
rec-dataflow_wf,
empty-bag_wf,
true_wf,
intensional-universe_wf,
df-program-meaning_wf,
df-program-type_wf,
sq_stable__equal,
sq_stable__and,
dataflow-valueall-type,
sq_stable__valueall-type,
nat_wf,
primrec_wf,
top_wf,
corec_wf,
subtype_rel_simple_product,
sq_stable__all,
subtype_rel_self,
subtype_rel_product,
sq_stable__subtype_rel,
dataflow-ap_wf,
subtype_rel_wf,
squash_wf,
dataflow-program_wf,
member_wf,
unit_wf,
valueall-type_wf,
bag_wf,
dataflow_wf
\mforall{}A:\{A:Type| \mdownarrow{}A\} . \mforall{}B:\{B:Type| valueall-type(B)\} . \mforall{}df:dataflow(A;bag(B)).
\mexists{}dfp:DataflowProgram(A). ((df-program-type(dfp) = B) \mwedge{} (df-program-meaning(dfp) = df))
Date html generated:
2011_08_16-AM-09_35_18
Last ObjectModification:
2011_06_13-PM-03_23_20
Home
Index