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Why3
why3
Commits
d21fa51e
Commit
d21fa51e
authored
Dec 04, 2012
by
Guillaume Melquiond
Browse files
Introduce the concept of decidable equality into Coq realizations.
parent
86385555
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38 additions
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+38
3
lib/coq/BuiltIn.v
lib/coq/BuiltIn.v
+34
2
lib/coq/set/Set.v
lib/coq/set/Set.v
+4
1
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lib/coq/BuiltIn.v
View file @
d21fa51e
Require
Export
ZArith
.
Require
Export
Rbase
.
Class
WhyType
T
:=
why_inhabitant
:
T
.
Class
WhyType
T
:=
{
why_inhabitant
:
T
;
why_decidable_eq
:
forall
x
y
:
T
,
{
x
=
y
}
+
{
x
<>
y
}
}
.
Notation
int
:=
Z
.
Global
Instance
int_WhyType
:
WhyType
int
.
Proof
.
split
.
exact
Z0
.
exact
Z_eq_dec
.
Qed
.
Notation
real
:=
R
.
Global
Instance
real_WhyType
:
WhyType
real
.
Proof
.
split
.
exact
R0
.
intros
x
y
.
destruct
(
total_order_T
x
y
)
as
[[
H

H
]

H
]
;
try
(
left
;
exact
H
)
;
right
.
now
apply
Rlt_not_eq
.
now
apply
Rgt_not_eq
.
Qed
.
Global
Instance
tuple_WhyType
:
forall
T
{
T
'
:
WhyType
T
}
U
{
U
'
:
WhyType
U
}
,
WhyType
(
T
*
U
).
now
split
.
Proof
.
intros
T
WT
U
WU
.
split
.
split
;
apply
why_inhabitant
.
intros
(
x1
,
x2
)
(
y1
,
y2
).
destruct
(
why_decidable_eq
x1
y1
)
as
[
H1

H1
].
destruct
(
why_decidable_eq
x2
y2
)
as
[
H2

H2
].
left
.
now
apply
f_equal2
.
right
.
now
injection
.
right
.
now
injection
.
Qed
.
Global
Instance
unit_WhyType
:
WhyType
unit
.
Proof
.
split
.
exact
tt
.
intros
[]
[].
now
left
.
Qed
.
Global
Instance
bool_WhyType
:
WhyType
bool
.
Proof
.
split
.
exact
false
.
exact
Bool
.
bool_dec
.
Qed
.
lib/coq/set/Set.v
View file @
d21fa51e
...
...
@@ 20,7 +20,10 @@ Defined.
Global
Instance
set_WhyType
:
forall
(
a
:
Type
)
{
a_WT
:
WhyType
a
}
,
WhyType
(
set
a
).
Proof
.
intros
.
split
.
exact
(
fun
_
=>
False
).
intros
x
y
.
apply
excluded_middle_informative
.
Qed
.
(
*
Why3
goal
*
)
...
...
@@ 176,7 +179,7 @@ Qed.
(
*
Why3
goal
*
)
Definition
choose
:
forall
{
a
:
Type
}
{
a_WT
:
WhyType
a
}
,
(
set
a
)
>
a
.
intros
a
a_WT
s
.
assert
(
i
:
inhabited
a
)
by
(
apply
inhabits
;
assumption
).
assert
(
i
:
inhabited
a
)
by
(
apply
inhabits
,
why_inhabitant
).
exact
(
epsilon
i
(
fun
x
=>
mem
x
s
)).
Defined
.
...
...
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