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+// SPDX-License-Identifier: GPL-2.0+
+(*
+ * Copyright (C) 2015 Jade Alglave <j.alglave@ucl.ac.uk>,
+ * Copyright (C) 2016 Luc Maranget <luc.maranget@inria.fr> for Inria
+ * Copyright (C) 2017 Alan Stern <stern@rowland.harvard.edu>,
+ *                    Andrea Parri <parri.andrea@gmail.com>
+ *
+ * An earlier version of this file appeared in the companion webpage for
+ * "Frightening small children and disconcerting grown-ups: Concurrency
+ * in the Linux kernel" by Alglave, Maranget, McKenney, Parri, and Stern,
+ * which appeared in ASPLOS 2018.
+ *)
+
+"Linux-kernel memory consistency model"
+
+(*
+ * File "lock.cat" handles locks and is experimental.
+ * It can be replaced by include "cos.cat" for tests that do not use locks.
+ *)
+
+include "lock.cat"
+
+(*******************)
+(* Basic relations *)
+(*******************)
+
+(* Release Acquire *)
+let acq-po = [Acquire] ; po ; [M]
+let po-rel = [M] ; po ; [Release]
+let po-unlock-lock-po = po ; [UL] ; (po|rf) ; [LKR] ; po
+
+(* Fences *)
+let R4rmb = R \ Noreturn	(* Reads for which rmb works *)
+let rmb = [R4rmb] ; fencerel(Rmb) ; [R4rmb]
+let wmb = [W] ; fencerel(Wmb) ; [W]
+let mb = ([M] ; fencerel(Mb) ; [M]) |
+	([M] ; fencerel(Before-atomic) ; [RMW] ; po? ; [M]) |
+	([M] ; po? ; [RMW] ; fencerel(After-atomic) ; [M]) |
+	([M] ; po? ; [LKW] ; fencerel(After-spinlock) ; [M]) |
+(*
+ * Note: The po-unlock-lock-po relation only passes the lock to the direct
+ * successor, perhaps giving the impression that the ordering of the
+ * smp_mb__after_unlock_lock() fence only affects a single lock handover.
+ * However, in a longer sequence of lock handovers, the implicit
+ * A-cumulative release fences of lock-release ensure that any stores that
+ * propagate to one of the involved CPUs before it hands over the lock to
+ * the next CPU will also propagate to the final CPU handing over the lock
+ * to the CPU that executes the fence.  Therefore, all those stores are
+ * also affected by the fence.
+ *)
+	([M] ; po-unlock-lock-po ;
+		[After-unlock-lock] ; po ; [M]) |
+	([M] ; po? ; [Srcu-unlock] ; fencerel(After-srcu-read-unlock) ; [M])
+let gp = po ; [Sync-rcu | Sync-srcu] ; po?
+let strong-fence = mb | gp
+
+let nonrw-fence = strong-fence | po-rel | acq-po
+let fence = nonrw-fence | wmb | rmb
+let barrier = fencerel(Barrier | Rmb | Wmb | Mb | Sync-rcu | Sync-srcu |
+		Before-atomic | After-atomic | Acquire | Release |
+		Rcu-lock | Rcu-unlock | Srcu-lock | Srcu-unlock) |
+	(po ; [Release]) | ([Acquire] ; po)
+
+(**********************************)
+(* Fundamental coherence ordering *)
+(**********************************)
+
+(* Sequential Consistency Per Variable *)
+let com = rf | co | fr
+acyclic po-loc | com as coherence
+
+(* Atomic Read-Modify-Write *)
+empty rmw & (fre ; coe) as atomic
+
+(**********************************)
+(* Instruction execution ordering *)
+(**********************************)
+
+(* Preserved Program Order *)
+let dep = addr | data
+let rwdep = (dep | ctrl) ; [W]
+let overwrite = co | fr
+let to-w = rwdep | (overwrite & int) | (addr ; [Plain] ; wmb)
+let to-r = (addr ; [R]) | (dep ; [Marked] ; rfi)
+let ppo = to-r | to-w | (fence & int) | (po-unlock-lock-po & int)
+
+(* Propagation: Ordering from release operations and strong fences. *)
+let A-cumul(r) = (rfe ; [Marked])? ; r
+let rmw-sequence = (rf ; rmw)*
+let cumul-fence = [Marked] ; (A-cumul(strong-fence | po-rel) | wmb |
+	po-unlock-lock-po) ; [Marked] ; rmw-sequence
+let prop = [Marked] ; (overwrite & ext)? ; cumul-fence* ;
+	[Marked] ; rfe? ; [Marked]
+
+(*
+ * Happens Before: Ordering from the passage of time.
+ * No fences needed here for prop because relation confined to one process.
+ *)
+let hb = [Marked] ; (ppo | rfe | ((prop \ id) & int)) ; [Marked]
+acyclic hb as happens-before
+
+(****************************************)
+(* Write and fence propagation ordering *)
+(****************************************)
+
+(* Propagation: Each non-rf link needs a strong fence. *)
+let pb = prop ; strong-fence ; hb* ; [Marked]
+acyclic pb as propagation
+
+(*******)
+(* RCU *)
+(*******)
+
+(*
+ * Effects of read-side critical sections proceed from the rcu_read_unlock()
+ * or srcu_read_unlock() backwards on the one hand, and from the
+ * rcu_read_lock() or srcu_read_lock() forwards on the other hand.
+ *
+ * In the definition of rcu-fence below, the po term at the left-hand side
+ * of each disjunct and the po? term at the right-hand end have been factored
+ * out.  They have been moved into the definitions of rcu-link and rb.
+ * This was necessary in order to apply the "& loc" tests correctly.
+ *)
+let rcu-gp = [Sync-rcu]		(* Compare with gp *)
+let srcu-gp = [Sync-srcu]
+let rcu-rscsi = rcu-rscs^-1
+let srcu-rscsi = srcu-rscs^-1
+
+(*
+ * The synchronize_rcu() strong fence is special in that it can order not
+ * one but two non-rf relations, but only in conjunction with an RCU
+ * read-side critical section.
+ *)
+let rcu-link = po? ; hb* ; pb* ; prop ; po
+
+(*
+ * Any sequence containing at least as many grace periods as RCU read-side
+ * critical sections (joined by rcu-link) induces order like a generalized
+ * inter-CPU strong fence.
+ * Likewise for SRCU grace periods and read-side critical sections, provided
+ * the synchronize_srcu() and srcu_read_[un]lock() calls refer to the same
+ * struct srcu_struct location.
+ *)
+let rec rcu-order = rcu-gp | srcu-gp |
+	(rcu-gp ; rcu-link ; rcu-rscsi) |
+	((srcu-gp ; rcu-link ; srcu-rscsi) & loc) |
+	(rcu-rscsi ; rcu-link ; rcu-gp) |
+	((srcu-rscsi ; rcu-link ; srcu-gp) & loc) |
+	(rcu-gp ; rcu-link ; rcu-order ; rcu-link ; rcu-rscsi) |
+	((srcu-gp ; rcu-link ; rcu-order ; rcu-link ; srcu-rscsi) & loc) |
+	(rcu-rscsi ; rcu-link ; rcu-order ; rcu-link ; rcu-gp) |
+	((srcu-rscsi ; rcu-link ; rcu-order ; rcu-link ; srcu-gp) & loc) |
+	(rcu-order ; rcu-link ; rcu-order)
+let rcu-fence = po ; rcu-order ; po?
+let fence = fence | rcu-fence
+let strong-fence = strong-fence | rcu-fence
+
+(* rb orders instructions just as pb does *)
+let rb = prop ; rcu-fence ; hb* ; pb* ; [Marked]
+
+irreflexive rb as rcu
+
+(*
+ * The happens-before, propagation, and rcu constraints are all
+ * expressions of temporal ordering.  They could be replaced by
+ * a single constraint on an "executes-before" relation, xb:
+ *
+ * let xb = hb | pb | rb
+ * acyclic xb as executes-before
+ *)
+
+(*********************************)
+(* Plain accesses and data races *)
+(*********************************)
+
+(* Warn about plain writes and marked accesses in the same region *)
+let mixed-accesses = ([Plain & W] ; (po-loc \ barrier) ; [Marked]) |
+	([Marked] ; (po-loc \ barrier) ; [Plain & W])
+flag ~empty mixed-accesses as mixed-accesses
+
+(* Executes-before and visibility *)
+let xbstar = (hb | pb | rb)*
+let vis = cumul-fence* ; rfe? ; [Marked] ;
+	((strong-fence ; [Marked] ; xbstar) | (xbstar & int))
+
+(* Boundaries for lifetimes of plain accesses *)
+let w-pre-bounded = [Marked] ; (addr | fence)?
+let r-pre-bounded = [Marked] ; (addr | nonrw-fence |
+	([R4rmb] ; fencerel(Rmb) ; [~Noreturn]))?
+let w-post-bounded = fence? ; [Marked] ; rmw-sequence
+let r-post-bounded = (nonrw-fence | ([~Noreturn] ; fencerel(Rmb) ; [R4rmb]))? ;
+	[Marked]
+
+(* Visibility and executes-before for plain accesses *)
+let ww-vis = fence | (strong-fence ; xbstar ; w-pre-bounded) |
+	(w-post-bounded ; vis ; w-pre-bounded)
+let wr-vis = fence | (strong-fence ; xbstar ; r-pre-bounded) |
+	(w-post-bounded ; vis ; r-pre-bounded)
+let rw-xbstar = fence | (r-post-bounded ; xbstar ; w-pre-bounded)
+
+(* Potential races *)
+let pre-race = ext & ((Plain * M) | ((M \ IW) * Plain))
+
+(* Coherence requirements for plain accesses *)
+let wr-incoh = pre-race & rf & rw-xbstar^-1
+let rw-incoh = pre-race & fr & wr-vis^-1
+let ww-incoh = pre-race & co & ww-vis^-1
+empty (wr-incoh | rw-incoh | ww-incoh) as plain-coherence
+
+(* Actual races *)
+let ww-nonrace = ww-vis & ((Marked * W) | rw-xbstar) & ((W * Marked) | wr-vis)
+let ww-race = (pre-race & co) \ ww-nonrace
+let wr-race = (pre-race & (co? ; rf)) \ wr-vis \ rw-xbstar^-1
+let rw-race = (pre-race & fr) \ rw-xbstar
+
+flag ~empty (ww-race | wr-race | rw-race) as data-race