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Arthur Azevedo de Amorim
Tutorial POPL20
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a155e29a
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a155e29a
authored
Jan 19, 2020
by
Robbert Krebbers
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theories/language.v
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a155e29a
...
...
@@ -423,7 +423,16 @@ Lemma wp_add_two_fancy `{!heapG Σ} (x : Z) :
auto
with
f_equal
lia
.
Qed
.
(** * Reasoning about unsafe functions *)
(** * Reasoning about "unsafe" functions *)
(** Since HeapLang is an untyped language, we can write down arbitrary
programs, i.e. that are not typeable by any reasonable type system, and prove
logical specifications of them. We will show this on two small examples that
will use at other places in this tutorial. *)
(** The program below containts the expression [#13 #37] in the else-branch
of the conditional. The expression [#13 #37], which will get stuck in the
operational semantics, i.e. it is unsafe. However, the else-branch is never
executed, so we can still prove a specification of this function. *)
Definition
unsafe_pure
:
val
:
=
λ
:
<>,
if
:
#
true
then
#
13
else
#
13
#
37
.
...
...
@@ -436,6 +445,7 @@ Proof.
Qed
.
(** Exercise (unsafe_ref, easy) *)
(** The function below reuses a reference using values of different types. *)
Definition
unsafe_ref
:
val
:
=
λ
:
<>,
let
:
"l"
:
=
ref
#
0
in
"l"
<-
#
true
;;
!
"l"
.
...
...
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