| (m = m3 ⊃ mkdir(m0, md5, # links(m3, cache_dirs), m1, entries0 -- str0);mkdir(m2, md4, # links(m, cache_dirs), m5, entries)) = mkdir(m8, md3, m10, m11, entries2), (entries[str] = m ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;(entries[str] = m3 ⊃ mkdir(m0, md5, # links(entries[str], cache_dirs), m1, entries0 -- str0) ;mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅) ) ) = mkdir(m13, md8, m12 + 1, m15, entries4), cache_dirs[entries0[str0]] = mkdir(m6, md6, # links(entries0[str0], cache_dirs), m9, entries3), cache_dirs[entries[str]] = mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅), cache_dirs[m] = mkdir(m2, md4, # links(m, cache_dirs), m5, entries), cache_dirs[m3] = mkdir(m0 + 1, md5, # links(m3, cache_dirs), m1 + 1, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m3, (m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m3 = m ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m3, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m, (m = m3 ⊃ (m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ], err = ESUCCESS, files = cache_files, ino = inode.ino, inode = mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4), new_child_inode = (entries[str] ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (entries[str], dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].size) ;mkinode(entries[str], files[entries[str]].meta, false, files[entries[str]].nlink, 0, files[entries[str]].size) ), new_parent_inode = (m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), old_parent_inode = (m3 ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m3, dirs[ino, dirs[ino].meta:= inode.meta][m3].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m3].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m3].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m3].size) ;mkinode(m3, files[m3].meta, false, files[m3].nlink, 0, files[m3].size) ), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, entries0[str0] ∈ cache_dirs, str0 ∈ entries0, m3 ∈ cache_dirs, ino ∈ dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, (entries[str] ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ;str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ [asynced := ?; entries1 := entries; new_dent := mkdentry(mkdentry(str, entries[str]).name, mkdentry(str0, entries0[str0]).ino); old_dent1 := negdentry(mkdentry(str0, entries0[str0]).name); if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries1[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent1.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(cache_dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(cache_pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries1[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m5, m2); old_parent_inode0 := mkinode(m3, md0, true, # links(m3, cache_dirs), m1 + 1, m0 + 1); new_child_inode0 := mkinode (entries1[str], md1, true, # links(entries1[str], cache_dirs), cache_dirs[entries1[str]].nsubdirs, cache_dirs[entries1[str]].size); old_child_inode0 := mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m9, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode (entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), cache_dirs1[entries0[str0]].nsubdirs, cache_dirs2[entries0[str0]].size) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent1 = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = dirs[ino, dirs[ino].meta:= inode.meta] ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced))), entries[str] = ROOT_INO, ino ∈ files, m3 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0]) |
(entries[str] = m ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]) ;(entries[str] = m3 ⊃ mkdir(m0, md5, # links(entries[str], cache_dirs), m1, entries0 -- str0) ;mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅) ) ) = mkdir(m13, md8, m12 + 1, m15, entries4), (m = m3 ⊃ mkdir(m0, md5, # links(m3, cache_dirs), m1, entries0 -- str0);mkdir(m2, md4, # links(m, cache_dirs), m5, entries)) = mkdir(m8, md3, m10, m11, entries2), cache_dirs[m3] = mkdir(m0 + 1, md5, # links(m3, cache_dirs), m1 + 1, entries0), cache_dirs[m] = mkdir(m2, md4, # links(m, cache_dirs), m5, entries), cache_dirs[entries[str]] = mkdir(m4, md7, # links(entries[str], cache_dirs), m7, ∅), cache_dirs[entries0[str0]] = mkdir(m6, md6, # links(entries0[str0], cache_dirs), m9, entries3), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[entries[str], mkdir(m13, md8, m12, m15, entries4)] [m3, (m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4) ;(m3 = m ⊃ mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]]);mkdir(m0, md5, # links(m3, cache_dirs), m1, entries0 -- str0)) ) .meta:= md0 ] [m, (m = m3 ⊃ (m3 = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])).meta:= md0 ;(m = entries[str] ⊃ mkdir(m13, md8, m12, m15, entries4);mkdir(m8, md3, m10, m11, entries2[str, entries0[str0]])) ) .meta:= md ], err = ESUCCESS, files = cache_files, ino = inode.ino, inode = mkinode(entries[str], md1, true, # links(entries[str], cache_dirs), m7, m4), new_child_inode = (entries[str] ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (entries[str], dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].nlink, dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][entries[str]].size) ;mkinode(entries[str], files[entries[str]].meta, false, files[entries[str]].nlink, 0, files[entries[str]].size) ), new_parent_inode = (m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), old_parent_inode = (m3 ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m3, dirs[ino, dirs[ino].meta:= inode.meta][m3].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m3].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m3].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m3].size) ;mkinode(m3, files[m3].meta, false, files[m3].nlink, 0, files[m3].size) ), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ dirs, m3 ∈ cache_dirs, str0 ∈ entries0, entries0[str0] ∈ cache_dirs, entries[str] ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), (entries[str] ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ;str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries ), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [entries1 := entries; new_dent := mkdentry(mkdentry(str, entries[str]).name, mkdentry(str0, entries0[str0]).ino); old_dent1 := negdentry(mkdentry(str0, entries0[str0]).name); if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); if mkdentry(str, entries1[str]).dentry? then icache_set#(new_child_inode, asynced; err, cache_icache); dcache_delete#(old_parent_inode.ino, old_dent1.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}] ( icache-cons(cache_icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(cache_dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(cache_pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], cache_icache, cache_pcache) ∧ (cache_sync → synced(files, cache_icache, cache_pcache)) → ⟨new_dent0 := mkdentry(str, entries1[str]); old_dent0 := mkdentry(str0, entries0[str0]); new_parent_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m5, m2); old_parent_inode0 := mkinode(m3, md0, true, # links(m3, cache_dirs), m1 + 1, m0 + 1); new_child_inode0 := mkinode (entries1[str], md1, true, # links(entries1[str], cache_dirs), cache_dirs[entries1[str]].nsubdirs, cache_dirs[entries1[str]].size); old_child_inode0 := mkinode(entries0[str0], md2, true, # links(entries0[str0], cache_dirs), m9, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ mkinode (entries0[str0], md2, true, # links(entries0[str0], cache_dirs0), cache_dirs1[entries0[str0]].nsubdirs, cache_dirs2[entries0[str0]].size) = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent1 = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ cache_dirs = dirs[ino, dirs[ino].meta:= inode.meta] ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced))), entries[str] = ROOT_INO, ino ∈ files, m3 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0])