File size: 2,320 Bytes
bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | Require Import Coq.ZArith.ZArith.
Require Import Coq.Lists.List.
Require Import Coq.micromega.Lia.
From AUXLib Require Import ListLib.
From SimpleC.SL Require Import Mem SeparationLogic ArrayLib.
Require Import Logic.LogicGenerator.demo932.Interface.
Import ListNotations.
Local Open Scope Z_scope.
Local Open Scope list_scope.
Import naive_C_Rules.
Local Open Scope sac.
(**
[sll] is the abstract, singly-linked-list-shaped sequence used to describe
stack contents. It is deliberately independent of the concrete memory
representation: this case stores the sequence in a contiguous C array.
The head of an [sll] is the logical top of the stack.
*)
Definition sll : Type := list Z.
Definition sll_empty : sll := [].
Definition sll_cons (x : Z) (contents : sll) : sll :=
x :: contents.
Definition sll_from_array (concrete : list Z) : sll :=
rev concrete.
Definition stack_capacity : Z := 100000.
(**
Physical array index 0 is the bottom of the stack, so the concrete array is
the reverse of the abstract [sll]. Keeping the size in the relation makes
every public stack state carry the capacity and exact-length invariants.
*)
Definition stack_representation
(contents : sll) (concrete : list Z) (size : Z) : Prop :=
0 <= size /\
size <= stack_capacity /\
Zlength contents = size /\
Zlength concrete = size /\
concrete = rev contents.
Definition store_stack
(p : Z) (contents : sll) (size : Z) : Assertion :=
EX concrete : list Z,
“ stack_representation contents concrete size ” &&
IntArray.full p size concrete.
(**
Mathematical state shared by the incremental [build] annotations. The C
invariant owns the loop bounds and the array resources; this predicate owns
only the abstract meaning of the already processed input prefix.
*)
Definition BuildStackPrefix
(contents : sll) (input : list Z) (processed : Z) : Prop :=
contents = sll_from_array (sublist 0 processed input).
(**
Body-facing view of the frozen public representation relation. Keeping a
separate internal root preserves the frozen [store_stack] dependency
surface while allowing QCP assertions to open its concrete array facts.
*)
Definition StackConcreteView
(contents : sll) (concrete : list Z) (size : Z) : Prop :=
stack_representation contents concrete size.
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