| # lpt2 = # avol, # lpt1 = # avol, isbuf ↔ false, adr = adr3, err = err0, keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt1, maxino = m, ns = ns4, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, dom remove-refsize0(gstore) ∩ ginval = ∅, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, nobuffer), awbuf-inv(avol, bleb0), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt1), lpt-free-unref(lpt2), lpt-leb-size(lpt1), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt1, log1), synced(avol), istore0 ⊑ istore, pstate = unbuffered → bleb0 = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [if err = ESUCCESS then {adr := adr2; m := m2; log := []; lpt := lpt2; ns := ns2} else isbuf := true; ns0 := ?; log0 := log1; bleb := nobuffer; isbuf0 := isbuf, lpt1 := lpt; if err = ESUCCESS then {persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr, m, log, lpt1, ns, bleb, isbuf0; lpt2, freelist, gch, avol)}] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = log ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, log) ∧ bufs-log-only(bleb, log, lpt2) ∧ # lpt2 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt2) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt2, avol) ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt1 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr ∧ maxino = m ∧ log1 = log ∧ ginval < # lpt2 ∧ ns4 = ns ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns0 = ns2 ∧ err = err1)), pstate = readonly, dups(log1) |
# lpt1 = # avol, # lpt2 = # avol, isbuf ↔ false, adr = adr3, err = ESUCCESS, err = err0, keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt1, maxino = m, ns = ns4, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom remove-refsize0(gstore) ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt1), lpt-leb-size(lpt2), lpt-leb-size(lpt1), lpt-ram-flash(lpt2, lpt1, log1), synced(avol), istore0 ⊑ istore, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb0 = nobuffer, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [adr := adr2; m := m2; log := []; lpt := lpt2; ns := ns2; ns0 := ?; log0 := log1; bleb := nobuffer; isbuf0 := isbuf, lpt1 := lpt; if err = ESUCCESS then {persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr, m, log, lpt1, ns, bleb, isbuf0; lpt2, freelist, gch, avol)}] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = log ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, log) ∧ bufs-log-only(bleb, log, lpt2) ∧ # lpt2 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt2) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt2, avol) ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt1 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr ∧ maxino = m ∧ log1 = log ∧ ginval < # lpt2 ∧ ns4 = ns ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns0 = ns2 ∧ err = err1)), pstate = readonly, dups(log1)
# lpt1 = # avol, # lpt2 = # avol, isbuf ↔ false, adr = adr3, err = err0, keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt1, maxino = m, ns = ns4, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom remove-refsize0(gstore) ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt1), lpt-leb-size(lpt2), lpt-leb-size(lpt1), lpt-ram-flash(lpt2, lpt1, log1), synced(avol), istore0 ⊑ istore, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb0 = nobuffer, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [isbuf := true; ns0 := ?; log0 := log1; bleb := nobuffer; isbuf0 := isbuf, lpt1 := lpt; if err = ESUCCESS then {persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr, m, log, lpt1, ns, bleb, isbuf0; lpt2, freelist, gch, avol)}] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = log ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, log) ∧ bufs-log-only(bleb, log, lpt2) ∧ # lpt2 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt2) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt2, avol) ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt1 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr ∧ maxino = m ∧ log1 = log ∧ ginval < # lpt2 ∧ ns4 = ns ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns0 = ns2 ∧ err = err1)), err = ESUCCESS, pstate = readonly, dups(log1)