| afs-cons(dirs, files), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ino ∈ dirs ∨ ino ∈ files, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ ⟪choose err0 with ⌊err0⌋ in err := err0; if err = ESUCCESS then if ¬ inode.directory then err := ENOENT else if ¬ px(user, inode.meta) then err := EACCESS; if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}; while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}⟫ true, p = ε |
afs-cons(dirs, files), ⌊err0⌋ , ino ∈ dirs ∨ ino ∈ files, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ ⟪err := err0; if err = ESUCCESS then if ¬ inode.directory then err := ENOENT else if ¬ px(user, inode.meta) then err := EACCESS; if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}; while p ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p := p.tail}}}⟫ true, p = ε
afs-cons(dirs, files), ino ∈ dirs ∨ ino ∈ files, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, ∀ p0, err, dirs, files, ino, user, asynced. # p0 < # p → err = ESUCCESS ∧ afs-cons(dirs, files) ∧ (ino ∈ dirs ∨ ino ∈ files) ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO) → ⟪while p0 ≠ ε ∧ err = ESUCCESS do {choose inode with true in vfs_may_lookup#(ino, user, dirs, files, asynced; inode, err); if err = ESUCCESS then let dent = negdentry(p0.head) in {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then {ino := dent.ino; p0 := p0.tail}}}⟫ true ⊦ p = ε, ∃ err0. ⌊err0⌋