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e5c727d8
Commit
e5c727d8
authored
Feb 18, 2019
by
Ralf Jung
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HeapLang.md
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e5c727d8
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...
@@ 9,10 +9,11 @@ language for simple examples.
HeapLang is a lambdacalculus with operations to allocate individual locations,
`load`
,
`store`
,
`CAS`
(compareandswap) and
`FAA`
(fetchandadd). Moreover,
it has a
`fork`
construct to spawn new threads. In terms of values, we have
integers, booleans, unit, heap locations as well as (binary) sums and products.
integers, booleans, unit, heap locations
,
as well as (binary) sums and products.
Functions are the only binders, so the sum elimination (
`Case`
) expects both
branches to be of function type and passes them the data component of the sum.
Recursive functions are the only binders, so the sum elimination (
`Case`
)
expects both branches to be of function type and passes them the data component
of the sum.
For technical reasons, the only terms that are considered values are those that
begin with the
`Val`
expression former. This means that, for example,
`Pair
...
...
@@ 20,8 +21,8 @@ begin with the `Val` expression former. This means that, for example, `Pair
This leads to some administrative redexes, and to a distinction between "value
pairs", "value sums", "value closures" and their "expression" counterparts.
However, this also makes values
very syntactically uniform, which we exploit in
the
definition of substitution which just skips over
`Val`
terms, because values
However, this also makes values
syntactically uniform, which we exploit in the
definition of substitution which just skips over
`Val`
terms, because values
should be closed and hence not affected by substitution. As a consequence, we
can entirely avoid even talking about "closed terms", that notion just does not
have to come up anywhere. We also exploit this when writing specifications,
...
...
@@ 47,7 +48,7 @@ eagerly.
## Tactics
HeapLang com
s with a bunch of tactics that facilitate stepping through Hea
Lang
HeapLang com
es with a bunch of tactics that facilitate stepping through Heap
Lang
programs as part of proving a weakest precondition. All of these tactics assume
that the current goal is of the shape
`WP e @ E {{ Q }}`
.
...
...
@@ 72,22 +73,22 @@ Tactics to take one or more pure program steps:
Tactics for the heap:

`wp_alloc l as "H"`
: Reduce an allocation instruction and call the new
location
`l`
(in the Coq context) and the
assertion that we own it
`H`
(in the
location
`l`
(in the Coq context) and the
pointsto assertion
`H`
(in the
spatial context). You can leave away the
`as "H"`
to introduce it as an
anonymous assertion, i.e., that is equivalent to
`as "?"`
.

`wp_load`
: Reduce a load operation. This automatically finds the
necessary
ownership
in the spatial context, and fails if it cannot be found.

`wp_store`
: Reduce a store operation. This automatically finds the
necessary
ownership
in the spatial context, and fails if it cannot be found.

`wp_load`
: Reduce a load operation. This automatically finds the
pointsto
assertion
in the spatial context, and fails if it cannot be found.

`wp_store`
: Reduce a store operation. This automatically finds the
pointsto
assertion
in the spatial context, and fails if it cannot be found.

`wp_cas_suc`
,
`wp_cas_fail`
: Reduce a succeeding/failing CAS. This
automatically finds the
necessary ownership
. It also automatically tries to
automatically finds the
pointsto assertion
. It also automatically tries to
solve the (in)equality to show that the CAS succeeds/fails, and opens a new
goal if it cannot prove this goal.

`wp_cas as H1  H2`
: Reduce a CAS, performing a case distinction over whether
it succeeds or fails. This automatically finds the
necessary ownership
. The
it succeeds or fails. This automatically finds the
pointsto assertion
. The
proof of equality in the first new subgoal will be called
`H1`
, and the proof
of the inequality in the second new subgoal will be called
`H2`
.

`wp_faa`
: Reduce a FAA. This automatically finds the
necessary ownership
.

`wp_faa`
: Reduce a FAA. This automatically finds the
pointsto assertion
.
Further tactics:
...
...
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