| fs[ri[inodekey(m0)]] = inodenode(key4, md6, true, m14 + 1, m10, m12), fs[ri[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs[ri[dentrykey(m11, str)]] = dentrynode(key, m), fs[ri[inodekey(m)]] = inodenode(key1, md3, true, m1, m2, m3), fs[ri[inodekey(m7)]] = inodenode(key3, md5, true, m5, m6, m8), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, dirs = abs-dirs(fs, ri), err = err1, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent1, new_dent_inode = mkinode(m0, md0, true, m14 + 1, m10, m12), new_inode = mkinode(m7, md1, true, m5, m6, m8), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent0, old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, true, m1, m2, m3), old_inode = mkinode(m11, md2, true, m4, m16 + 1, m13 + 1), old_parent_inode = old_inode, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m11, str) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, inodekey(m11) ∈ ri, ri[inodekey(m11)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, ⌊err0⌋ , m14 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar1) ∧ mkinode(m11, md2, true, m4, m16 + 1, m13 + 1) = old_parent_inode ∧ mkinode(m7, md1, true, m5, m6, m8) = new_parent_inode ∧ mkinode(m, md, true, m1, m2, m3) = old_child_inode ∧ mkinode(m0, md0, true, m14 + 1, m10, m12) = new_child_inode ∧ mkdentry(str, m) = old_dent ∧ mkdentry(str0, m0) = new_dent ∧ err0 = err), ⟨let old_ino = old_parent_inode.ino, new_ino = new_parent_inode.ino, boolvar0 = new_dent.dentry? in let boolvar = old_ino = new_ino ∧ new_dent = old_dent in {dirs[old_ino].entries := dirs[old_ino].entries -- old_dent.name; if ¬ boolvar 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 boolvar0 ∧ ¬ boolvar then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ boolvar0 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 boolvar0 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 := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar1) ∧ mkinode(m11, md2, true, m4, m16 + 1, m13 + 1) = old_parent_inode ∧ mkinode(m7, md1, true, m5, m6, m8) = new_parent_inode ∧ mkinode(m, md, true, m1, m2, m3) = old_child_inode ∧ mkinode(m0, md0, true, m14 + 1, m10, m12) = new_child_inode ∧ mkdentry(str, m) = old_dent ∧ mkdentry(str0, m0) = new_dent ∧ err0 = err), m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, m4 = 0 ∧ m11 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ ROOT_INO |
m14 + 1 = fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m7)]] = inodenode(key3, md5, true, m5, m6, m8), fs[ri[inodekey(m0)]] = inodenode(key4, md6, true, m14 + 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), fs[ri[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs[ri[dentrykey(m11, str)]] = dentrynode(key, m), fs[ri[inodekey(m)]] = inodenode(key1, md3, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, m0 ≠ 0, m0 ≠ ROOT_INO, m11 ≠ 0, m11 ≠ m7, m7 ≠ 0, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m0)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m11, str) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, inodekey(m11) ∈ ri, ri[inodekey(m11)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, ⌊err0⌋ , m14 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar1) ∧ err0 = err), ⟨let old_ino = m11, new_ino = m7, boolvar0 = true in let boolvar = old_ino = new_ino ∧ mkdentry(str0, m0) = mkdentry(str, m) in {dirs := abs-dirs(fs, ri)[old_ino, abs-dirs(fs, ri)[old_ino].entries:= (abs-dirs(fs, ri)[old_ino].entries -- str)]; old_dent := mkdentry(str, m); if ¬ boolvar 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[str0] := old_dent.ino; new_dent := mkdentry(str0, m0); files := abs-files(fs, ri); if boolvar0 ∧ ¬ boolvar then let ino = new_dent.ino in afs_drop_nlink#(ino; dirs, files); if ¬ boolvar0 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#(mkinode(m11, md2, true, m4, m16 + 1, m13 + 1); dirs, files); afs_inode_sync#(mkinode(m7, md1, true, m5, m6, m8); dirs, files); new_child_inode := mkinode(m0, md0, true, m14 + 1, fs[ri[inodekey(dentrynode(key0, m0).ino)]].nsubdirs, fs[ri[inodekey(dentrynode(key0, m0).ino)]].size); if boolvar0 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode (new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.ino].size) )}; old_inode := (m11 ∈ dirs ⊃ mkinode(m11, dirs[m11].meta, true, dirs[m11].nlink, dirs[m11].nsubdirs, dirs[m11].size) ;mkinode(m11, files[m11].meta, false, files[m11].nlink, 0, files[m11].size) ); new_inode := (m7 ∈ dirs ⊃ mkinode(m7, dirs[m7].meta, true, dirs[m7].nlink, dirs[m7].nsubdirs, dirs[m7].size) ;mkinode(m7, files[m7].meta, false, files[m7].nlink, 0, files[m7].size) ); err := ESUCCESS}; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar1) ∧ mkinode(m11, md2, true, m4, m16 + 1, m13 + 1) = old_inode ∧ mkinode(m7, md1, true, m5, m6, m8) = new_inode ∧ mkinode(m0, md0, true, m14 + 1, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size) = new_child_inode ∧ mkdentry(str, m) = old_dent ∧ mkdentry(str0, m0) = new_dent ∧ err0 = err), m4 = 0 ∧ m11 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ ROOT_INO
Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ dentrynode(key, m).ino = m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).size = m1; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nsubdirs = m0; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ dentrykey(ino, str) ∈ ri → abs-children(ino, fs, ri)[str] = fs[ri[dentrykey(ino, str)]].ino; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ str ∈ abs-children(ino, fs, ri) ↔ dentrykey(ino, str) ∈ ri; (s)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)