source: src/joint/BEMem.ma @ 2497

(* Memory model used in the dynamic semantics of the back-end intermediate
   languages. Inspired by common/Mem.ma, adapted from Compcert *)

(* * This file develops the memory model that is used in the dynamic
  semantics of all the languages used in the compiler.
  It defines a type [mem] of memory states, the following 4 basic
  operations over memory states, and their properties:
- [load]: read a memory chunk at a given address;
- [store]: store a memory chunk at a given address;
- [alloc]: allocate a fresh memory block;
- [free]: invalidate a memory block.
*)

include "common/ByteValues.ma".
include "common/GenMem.ma".

definition bemem ≝ mem.

definition is_addressable : region → bool ≝ λr.match r with
  [ XData ⇒ true | Code ⇒ true | _ ⇒ false ].

(* CSC: only pointers to XRAM or code memory ATM *)
definition address ≝ beval × beval.

definition pointer_of_address: address → res pointer ≝
 λp. let 〈v1,v2〉 ≝ p in pointer_of_bevals [v1;v2].

definition is_address : (beval × beval) → Prop ≝ λa.
  ∃ptr.pointer_of_address a = OK … ptr.

lemma bevals_of_pointer_is_address :
  ∀p.is_address (list_to_pair … (bevals_of_pointer p) (refl …)).
* #bl #o
whd in ⊢ (?%); whd %
[2: whd in ⊢ (??%?);
  >eq_block_b_b
  change with (eq_bv ???) in match (eq_bv_suffix ?????);
  >eq_bv_refl normalize %]
qed.

(* For full 8051 memory spaces 
definition pointer_compat' ≝ λb,r.
  match b with
  [ mk_block r' z ⇒
    if eq_region r' r then True
    else
      match r with
      [ Any ⇒ True
      | XData ⇒ match r' with
        [ PData ⇒ True
        | _ ⇒ False
        ]
      | _ ⇒ False
      ]
   ].

lemma pointer_compat_to_ind : ∀b,r.pointer_compat' b r → pointer_compat b r.
** #z ** //
qed.

lemma pointer_compat_from_ind : ∀b,r.pointer_compat b r → pointer_compat' b r.
#b #r #H inversion H
[ #s #id #EQ1 #EQ2 #EQ3 whd >reflexive_eq_region %
| #id #EQ1 #EQ2 #EQ3 %
| #r #id #EQ1 #EQ2 #EQ3 whd @eq_region_elim #EQ4 destruct(EQ4) %
]
qed.
*)
(*lemma pointer_of_address_is_safe : ∀a : safe_address.pointer_of_address a = OK … (pointer_of_address_safe a).
** #a0 #a1 ***** #z #o
#Hr
(*
** #a0 #a1 ***** #r #z #Hr #o * lapply (pointer_compat_from_ind ?? Hr)
cases r in Hr ⊢ %; #Hr *
*)
** #part0 #H0 ** #part1 #H1 *** #EQa0 #EQpart0 #EQa1 #EQpart1
destruct normalize
@eqZb_elim [2,4,6: * #ABS elim (ABS (refl …))]
change with (eq_bv ???) in match (eq_v ?????);
@eq_bv_elim [2,4,6: * #ABS elim (ABS (refl …))]
#_ #_ normalize %
qed.*)
    
(*definition safe_address_of_pointer: pointer → res safe_address ≝ λp.
  do a as EQ ← address_of_pointer p ; return «a ,address_of_pointer_OK_to_safe ?? EQ».

lemma address_of_pointer_is_safe :
  ∀p.address_of_pointer p = ! a ← safe_address_of_pointer p ; return (a : address).
#p normalize % qed.
(*
****#z #H
lapply (pointer_compat_from_ind ?? H) * #o
normalize %
qed.*)

definition code_pointer_of_address: address → res (Σp:pointer. ptype p = Code) ≝
code_pointer_of_beval_pair.

definition address_of_code_pointer: (Σp:pointer. ptype p = Code) → address ≝ beval_pair_of_code_pointer.

definition safe_address_of_code_pointer: (Σp:pointer. ptype p = Code) → safe_address ≝ address_of_code_pointer.
cases H -H * #b #o normalize cases b * #z #EQ destruct
%{«mk_pointer  (mk_block Code z)  o,I»}
% [2: % [2: % [ % [ % ]]]] %
qed.
(*
cases H -H * #r #b #H #o #EQ destruct(EQ) normalize lapply H
lapply (pointer_compat_from_ind … H) -H cases b * #z * #H
%{«mk_pointer ? (mk_block Code z) H o,I»}
% [2: % [2: % [ % [ % ]] % |]|]
qed.*)
*)

(* Paolo: why only code pointers and not XRAM too? *)
(*definition addr_add: address → nat → res address ≝
 λaddr,n.
  do ptr ← code_pointer_of_address addr ;
  OK … (address_of_code_pointer (shift_pointer 16 ptr (bitvector_of_nat … n))).
normalize cases ptr #p #E @E
qed.

definition safe_addr_add: safe_address → nat → res safe_address ≝
 λaddr,n.
  do ptr ← code_pointer_of_address addr ;
  OK … (safe_address_of_code_pointer (shift_pointer 16 ptr (bitvector_of_nat … n))).
normalize cases ptr #p #E @E
qed.

definition addr_sub: address → nat → res address ≝
 λaddr,n.
  do ptr ← code_pointer_of_address addr ;
  OK … (address_of_code_pointer (neg_shift_pointer 16 ptr (bitvector_of_nat … n))).
normalize cases ptr #p #E @E
qed.

definition safe_addr_sub: safe_address → nat → res safe_address ≝
 λaddr,n.
  do ptr ← code_pointer_of_address addr ;
  OK … (safe_address_of_code_pointer (neg_shift_pointer 16 ptr (bitvector_of_nat … n))).
normalize cases ptr #p #E @E
qed.
*)