| cache_dirs[m2] = mkdir(m6, md3, # links(m2, cache_dirs), m5, entries), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, new_child_inode = new_child_inode0, new_child_inode0 = mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m), new_dent = new_dent0, new_dent0 = mkdentry(str0, entries[str0]), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13), old_dent = old_dent0, old_dent0 = mkdentry(str0, entries[str0]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), dcache-cons (cache_dcache[dentrykey(m2, str0), mkdentry(str0, entries[str0])], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), synced (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m2 ∈ cache_dirs, entries[str0] ∈ cache_files, str0 ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache), links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨ let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, asynced1 = new_dent.dentry? in let asynced0 = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ asynced0 then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[new_dent.name] := old_dent.ino; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?⟩ ( (m2 ∈ cache_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = old_parent_inode ∧ (m2 ∈ cache_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = new_parent_inode ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode ∧ (entries[str0] ∈ cache_dirs0 ⊃ mkinode (entries[str0], (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).meta, true, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nlink, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nsubdirs, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).size) ;mkinode(entries[str0], md0, false, cache_files[entries[str0]].nlink, 0, m) ) = new_child_inode ∧ negdentry(str0) = old_dent ∧ mkdentry(str0, entries[str0]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0[m2, mkdir(m6, md5, # links(m2, cache_dirs0), m5, entries)] ∧ files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0] ⊕ cache_pcache) ⊕ cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs0), 0, m)) ] ∧ (asynced ↔ asynced0)), entries[str0] ∈ cache_dirs |
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str0]] = mkfile(m8, md4, # links(entries[str0], cache_dirs), content0), cache_files[entries[str0]] = mkfile(m1, md, # links(entries[str0], cache_dirs), content), cache_dirs[m2] = mkdir(m6, md3, # links(m2, cache_dirs), m5, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, new_child_inode = new_child_inode0, new_child_inode0 = mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m), new_dent = new_dent0, new_dent0 = mkdentry(str0, entries[str0]), new_parent_inode = new_parent_inode0, new_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), old_child_inode = old_child_inode0, old_child_inode0 = mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs), 0, m13), old_dent = old_dent0, old_dent0 = mkdentry(str0, entries[str0]), old_parent_inode = old_parent_inode0, old_parent_inode0 = mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6), afs-cons (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache[dentrykey(m2, str0), mkdentry(str0, entries[str0])], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)]), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m2, mkdir(m6, md5, # links(m2, cache_dirs), m5, entries)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache), str0 ∈ entries, entries[str0] ∈ cache_files, m2 ∈ cache_dirs, cache_sync → synced (cache_files[entries[str0], mkfile(m, md0, # links(entries[str0], cache_dirs), content)], cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs), 0, m)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m2, cache_dirs) ≠ ∅ ∨ m2 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( (m2 ∈ cache_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = old_parent_inode ∧ (m2 ∈ cache_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = new_parent_inode ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode ∧ (entries[str0] ∈ cache_dirs0 ⊃ mkinode (entries[str0], (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).meta, true, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nlink, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nsubdirs, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).size) ;mkinode(entries[str0], md0, false, cache_files[entries[str0]].nlink, 0, m) ) = new_child_inode ∧ negdentry(str0) = old_dent ∧ mkdentry(str0, entries[str0]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0[m2, mkdir(m6, md5, # links(m2, cache_dirs0), m5, entries)] ∧ files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0] ⊕ cache_pcache) ⊕ cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs0), 0, m)) ] ∧ (asynced ↔ asynced0)), ⟨let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, asynced1 = new_dent.dentry? in let asynced0 = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ asynced0 then {dirs[old_ino].size := dirs[old_ino].size - 1; if old_dent.ino ∈ dirs then dirs[old_ino].nsubdirs := dirs[old_ino].nsubdirs - 1}; dirs[new_ino].entries[new_dent.name] := old_dent.ino; if asynced1 ∧ ¬ asynced0 then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ asynced1 then {dirs[new_ino].size := dirs[new_ino].size + 1; if old_dent.ino ∈ dirs then dirs[new_ino].nsubdirs := dirs[new_ino].nsubdirs + 1}; new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS}; asynced := ?⟩ ( (m2 ∈ cache_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = old_parent_inode ∧ (m2 ∈ cache_dirs0 ⊃ mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6) ;mkinode (m2, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).meta, false, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).nlink, 0, (m2 = entries[str0] ⊃ (cache_files[entries[str0]].size:= m).meta:= md0;cache_files[m2]).size) ) = new_parent_inode ∧ mkinode(entries[str0], md2, false, # links(entries[str0], cache_dirs0), 0, m13) = old_child_inode ∧ (entries[str0] ∈ cache_dirs0 ⊃ mkinode (entries[str0], (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).meta, true, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nlink, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).nsubdirs, (entries[str0] = m2 ⊃ mkdir(m6, md5, # links(entries[str0], cache_dirs0), m5, entries);cache_dirs0[entries[str0]]).size) ;mkinode(entries[str0], md0, false, cache_files[entries[str0]].nlink, 0, m) ) = new_child_inode ∧ negdentry(str0) = old_dent ∧ mkdentry(str0, entries[str0]) = new_dent ∧ ESUCCESS = err ∧ dirs = cache_dirs0[m2, mkdir(m6, md5, # links(m2, cache_dirs0), m5, entries)] ∧ files = (cache_files[entries[str0], (cache_files[entries[str0]].size:= m).meta:= md0] ⊕ cache_pcache) ⊕ cache_icache[m2, mkientry(false, mkinode(m2, md5, true, # links(m2, cache_dirs0), m5, m6))] [entries[str0], mkientry(false, mkinode(entries[str0], md0, false, # links(entries[str0], cache_dirs0), 0, m)) ] ∧ (asynced ↔ asynced0)), entries[str0] ∈ cache_dirs