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cpdt
Commits
a38e22e5
Commit
a38e22e5
authored
Aug 23, 2012
by
Adam Chlipala
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9e88ea6a
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Large.v
src/Large.v
+1
-1
StackMachine.v
src/StackMachine.v
+1
-1
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src/Large.v
View file @
a38e22e5
...
@@ -49,7 +49,7 @@ Fixpoint times (k : nat) (e : exp) : exp :=
...
@@ -49,7 +49,7 @@ Fixpoint times (k : nat) (e : exp) : exp :=
|
Plus
e1
e2
=>
Plus
(
times
k
e1
)
(
times
k
e2
)
|
Plus
e1
e2
=>
Plus
(
times
k
e1
)
(
times
k
e2
)
end
.
end
.
(
**
We
can
write
a
very
manual
proof
that
[
double
]
really
doubles
an
expression
'
s
value
.
*
)
(
**
We
can
write
a
very
manual
proof
that
[
times
]
really
implements
multiplication
.
*
)
Theorem
eval_times
:
forall
k
e
,
Theorem
eval_times
:
forall
k
e
,
eval
(
times
k
e
)
=
k
*
eval
e
.
eval
(
times
k
e
)
=
k
*
eval
e
.
...
...
src/StackMachine.v
View file @
a38e22e5
...
@@ -550,7 +550,7 @@ Inductive tbinop : type -> type -> type -> Set :=
...
@@ -550,7 +550,7 @@ Inductive tbinop : type -> type -> type -> Set :=
(
**
The
definition
of
[
tbinop
]
is
different
from
[
binop
]
in
an
important
way
.
Where
we
declared
that
[
binop
]
has
type
[
Set
]
,
here
we
declare
that
[
tbinop
]
has
type
[
type
->
type
->
type
->
Set
]
.
We
define
[
tbinop
]
as
an
_
indexed
type
family_
.
Indexed
inductive
types
are
at
the
heart
of
Coq
'
s
expressive
power
;
almost
everything
else
of
interest
is
defined
in
terms
of
them
.
(
**
The
definition
of
[
tbinop
]
is
different
from
[
binop
]
in
an
important
way
.
Where
we
declared
that
[
binop
]
has
type
[
Set
]
,
here
we
declare
that
[
tbinop
]
has
type
[
type
->
type
->
type
->
Set
]
.
We
define
[
tbinop
]
as
an
_
indexed
type
family_
.
Indexed
inductive
types
are
at
the
heart
of
Coq
'
s
expressive
power
;
almost
everything
else
of
interest
is
defined
in
terms
of
them
.
The
inuitive
explanation
of
[
tbinop
]
is
that
a
[
tbinop
t1
t2
t
]
is
a
binary
operator
whose
operands
should
have
types
[
t1
]
and
[
t2
]
,
and
whose
result
has
type
[
t
]
.
For
instance
,
constructor
[
TLt
]
(
for
less
-
than
comparison
of
numbers
)
is
assigned
type
[
tbinop
Nat
Nat
Bool
]
,
meaning
the
operator
'
s
arguments
are
naturals
and
its
result
is
Boolean
.
The
type
of
[
TEq
]
introduces
a
small
bit
of
additional
complication
via
polymorphism
:
we
want
to
allow
equality
comparison
of
any
two
values
of
any
type
,
as
long
as
they
have
the
_
same_
type
.
The
in
t
uitive
explanation
of
[
tbinop
]
is
that
a
[
tbinop
t1
t2
t
]
is
a
binary
operator
whose
operands
should
have
types
[
t1
]
and
[
t2
]
,
and
whose
result
has
type
[
t
]
.
For
instance
,
constructor
[
TLt
]
(
for
less
-
than
comparison
of
numbers
)
is
assigned
type
[
tbinop
Nat
Nat
Bool
]
,
meaning
the
operator
'
s
arguments
are
naturals
and
its
result
is
Boolean
.
The
type
of
[
TEq
]
introduces
a
small
bit
of
additional
complication
via
polymorphism
:
we
want
to
allow
equality
comparison
of
any
two
values
of
any
type
,
as
long
as
they
have
the
_
same_
type
.
ML
and
Haskell
have
indexed
algebraic
datatypes
.
For
instance
,
their
list
types
are
indexed
by
the
type
of
data
that
the
list
carries
.
However
,
compared
to
Coq
,
ML
and
Haskell
98
place
two
important
restrictions
on
datatype
definitions
.
ML
and
Haskell
have
indexed
algebraic
datatypes
.
For
instance
,
their
list
types
are
indexed
by
the
type
of
data
that
the
list
carries
.
However
,
compared
to
Coq
,
ML
and
Haskell
98
place
two
important
restrictions
on
datatype
definitions
.
...
...
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