| # lpt = # avol, # lpt0 = # avol, isbuf0 ↔ pstate = readonly, adr = adr0, keyset(gch) = gc-heap(lpt, log1), log = log1, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), synced(avol), istore0 ⊑ istore, pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ ⟪let isbuf = ? in {awbuf_is_readonly#(adr, m, log, avol, lpt0, ns, bleb, isbuf0; ; isbuf); if isbuf then err := EROFS else if freelist = [] then err := ENOSPC else {n := freelist.head; awbuf_remap#(n, adr, m, log, lpt0, ns, bleb, isbuf0; avol; err); if err = ESUCCESS then {freelist := freelist.tail; lpt[n].size := 0; lpt[n].ref-size := 0}}}; if err = ESUCCESS then {awbuf_move_buf#(n, 0, adr0, m, log1, avol, lpt0, ns0, pstate = readonly; bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist else lpt[n].flags := LP_INDEX_NODES}⟫ ⟨pstate0 := pstate; apersistence_allocate_ind#(adr0, istore0, ginval, gstore, gstore0, log1, m, ns0, true; istore, pstate; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err0), dups(log1) |
# lpt0 = # avol, # lpt = # avol, isbuf0 ↔ pstate = readonly, adr = adr0, keyset(gch) = gc-heap(lpt, log1), log = log1, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol), istore0 ⊑ istore, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer ⊦ ⟪awbuf_is_readonly#(adr, m, log, avol, lpt0, ns, bleb, isbuf0; ; isbuf); if isbuf then err := EROFS else if freelist = [] then err := ENOSPC else {n := freelist.head; awbuf_remap#(n, adr, m, log, lpt0, ns, bleb, isbuf0; avol; err); if err = ESUCCESS then {freelist := freelist.tail; lpt[n].size := 0; lpt[n].ref-size := 0}}; if err = ESUCCESS then {awbuf_move_buf#(n, 0, adr0, m, log1, avol, lpt0, ns0, pstate = readonly; bleb; err); if err ≠ ESUCCESS then freelist := n ' + freelist else lpt[n].flags := LP_INDEX_NODES}⟫ ⟨pstate0 := pstate; apersistence_allocate_ind#(adr0, istore0, ginval, gstore, gstore0, log1, m, ns0, true; istore, pstate; err0)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ ginval < # lpt ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err = err0), dups(log1)