Nuprl Lemma : C_DVALUEp-ext
C_DVALUEp() ≡ lbl:Atom × if lbl =a "Null" then Unit
if lbl =a "Int" then ℤ
if lbl =a "Pointer" then C_LVALUE()?
if lbl =a "Array" then lower:ℤ × upper:ℤ × ({lower..upper-} ─→ C_DVALUEp())
if lbl =a "Struct" then lbls:Atom List × ({a:Atom| (a ∈ lbls)} ─→ C_DVALUEp())
else Void
fi
Proof
Definitions occuring in Statement :
C_DVALUEp: C_DVALUEp(),
C_LVALUE: C_LVALUE(),
l_member: (x ∈ l),
list: T List,
int_seg: {i..j-},
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
ext-eq: A ≡ B,
unit: Unit,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
product: x:A × B[x],
union: left + right,
int: ℤ,
token: "$token",
atom: Atom,
void: Void
Lemmas :
C_DVALUEpco-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
C_LVALUE_wf,
value-type-has-value,
int-value-type,
sum-partial-has-value,
assert_of_le_int,
subtract_wf,
zero-le-nat,
le_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
sq_stable__le,
less-iff-le,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
C_DVALUEpco_size_wf,
bool_cases,
iff_transitivity,
assert_wf,
bnot_wf,
not_wf,
iff_weakening_uiff,
assert_of_bnot,
less_than_transitivity1,
less_than_irreflexivity,
lelt_wf,
int_seg_wf,
trivial-int-eq1,
has-value_wf-partial,
nat_wf,
set-value-type,
C_DVALUEp_wf,
less_than_wf,
length_wf,
equal-wf-base-T,
select_wf,
l_member_wf,
length_wf_nat,
list-subtype,
list_wf,
subtype_rel_dep_function,
C_DVALUEpco_wf,
set_wf,
add-nat,
false_wf,
sum-nat,
le_int_wf,
C_DVALUEp_size_wf,
nat_properties,
and_wf,
squash_wf,
value-type_wf,
partial_wf
C\_DVALUEp() \mequiv{} lbl:Atom \mtimes{} if lbl =a "Null" then Unit
if lbl =a "Int" then \mBbbZ{}
if lbl =a "Pointer" then C\_LVALUE()?
if lbl =a "Array" then lower:\mBbbZ{} \mtimes{} upper:\mBbbZ{} \mtimes{} (\{lower..upper\msupminus{}\} {}\mrightarrow{} C\_DVALUEp())
if lbl =a "Struct"
then lbls:Atom List \mtimes{} (\{a:Atom| (a \mmember{} lbls)\} {}\mrightarrow{} C\_DVALUEp())
else Void
fi
Date html generated:
2015_07_17-AM-07_44_06
Last ObjectModification:
2015_01_29-PM-04_39_27
Home
Index