bedrock.lang.cpp.logic.core_string

(*
* Copyright (C) BedRock Systems Inc. 2023

* This software is distributed under the terms of the BedRock Open-Source License.
* See the LICENSE-BedRock file in the repository root for details.
*)
Require Import elpi.apps.locker.locker.
Require Import bedrock.lang.proofmode.proofmode.

Require Import bedrock.lang.bi.prelude.
Require Import bedrock.lang.bi.observe.
Require Import bedrock.lang.cpp.semantics.values.
Require Import bedrock.lang.cpp.logic.arr.
Require Import bedrock.lang.cpp.logic.heap_pred.

Import ChargeNotation.
#[local] Open Scope Z_scope.

Core C++ string theory: part of the semantics.

strings_bytesR ct q chars is q (const) fractional ownership of chars with a trailing 0.

Unlike zstring.t, does not assume the contents avoid `0` elements, since that property might not be guaranteed in all character types/encodings.
Used for string literals of arbitrary character types.

NOTE that chars is in units of *characters* using the standard character encoding (see syntax/expr.v). This is *not* the same as bytes, and will not be for multi-byte characters.

mlock
Definition string_bytesR `{Σ : cpp_logic } {σ : genv } (cty : char_type ) (q : cQp.t ) (ls : list N ) : Rep :=
  let ty := Tchar_ cty in
  arrayR ty (λ c , primR ty q (N_to_char cty c )) (ls ++ [0%N ]).
#[global] Arguments string_bytesR {_ _ _ _} _ _ _ : assert.

(* Arguments char_type.bitsN !_ /.
Arguments char_type.bytesN !_ /. *)
Lemma N_to_char_Cchar_eq (c : N) :
  (c < 2 ^ 8)%N ->
  N_to_char char_type.Cchar c = Vchar c.
Proof.
  intros.
  rewrite /N_to_char /operator.trimN/=. f_equiv.
  exact: N.mod_small.
Qed.

Section with_Σ.
  Context `{Σ : cpp_logic} {σ : genv}.

  #[global] Instance string_bytesR_timeless : Timeless3 string_bytesR.
  Proof. rewrite string_bytesR.unlock /=. apply _. Qed.

  #[global] Instance string_bytesR_cfrac cty : CFractional1 (string_bytesR cty).
  Proof. rewrite string_bytesR.unlock /=. apply _. Qed.
End with_Σ.