Port partial atomic integer specs to libstdc++

rocq-brick-libstdcpp/proof/atomic/inc_int.cpp

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+#include <atomic>
+template<> class std::atomic<int>;

rocq-brick-libstdcpp/proof/atomic/pred.v

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+(**
+ * Copyright (C) 2025 SkyLabs AI, Inc.
+ * All rights reserved.
+ *
+ * SPDX-License-Identifier: LGPL-2.1 WITH BlueRock Exception for use over network, see repository root for details.
+ *)
+Require Import skylabs.auto.cpp.spec.
+Require Import skylabs.cpp.spec.concepts.
+Require skylabs.brick.libstdcpp.atomic.inc_int_cpp.
+
+Require Import skylabs.cpp.spec.concepts.
+
+(** * Interface to Atomic<T> *)
+(**
+These specifications assume that all memory order parameters (template,
+function arguments) are _SEQ_CST. In the C++ code, redefine the other
+memory order macros to __ATOMIC_SEQ_CST.
+*)
+
+cpp.enum "std::memory_order" from (inc_int_cpp.source) variant.
+#[global] Abbreviation Tmemory_order := {%cpp_type[inc_int_cpp.source] "std::memory_order"} (only parsing).
+
+NES.Begin std.atomic.
+Module Type ATOMIC_PREDS.
+
+  (** Type [t] indexing our spec models the type name T in Atomic<T>. *)
+
+  (** The base class used by libstdc++ integral specializations (excluding bool).
+  Pointer, bool, and primary-template atomics have different layouts and are
+  not covered by these partial specs. *)
+  #[global] Abbreviation base_name ty :=
+    (Ninst "std::__atomic_base" [Atype ty]).
+  (** The type <<std::atomic<T>>> *)
+  #[global] Abbreviation class_name ty := (Ninst "std::atomic" [Atype ty]).
+  #[global] Abbreviation T ty := (Tnamed (class_name ty)).
+
+  (** Abstract predicates *)
+
+  (** Fraction [q] ownership of atomically accessible value [v]. *)
+  Parameter R : ∀ `{Σ : cpp_logic} {σ : genv} (ty : type) `{PV : @PrimVal ty A} (q : cQp.t) (x : A), Rep.
+
+  Section R_props.
+    Context `{Σ : cpp_logic} {σ : genv} `{PV : @PrimVal ty A}.
+    Abbreviation R := (R ty (PV:=PV)).
+
+    #[global] Declare Instance R_frac : CFractional1 R.
+    #[global] Declare Instance R_timeless : Timeless2 R.
+    #[global] Declare Instance R_frac_valid : CFracValid1 R.
+    #[global] Declare Instance R_agree : Cbn (Learn (any ==> learn_eq ==> learn_hints.fin) R).
+    #[global] Declare Instance R_type : Typed2 (class_name ty) R.
+  End R_props.
+
+End ATOMIC_PREDS.
+
+Declare Module atomic : ATOMIC_PREDS.
+
+NES.End std.atomic.