| # gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n1 = dom gstore ∪ ginval, isbuf ↔ false, lpt1[n1] = mklp(m1, # buf1, LP_GROUP_NODES, m2), gstore[n1] = groupblock(gndx, lax, m1), avol[n1] = mapped(buf1), err = err0, keyset(gch) = gc-heap(lpt1, nx + n1 '), m = buffered((nx + n1 ').last).leb, n0 = gndx0.flashsize, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, ginval ∩ elems nx = ∅, buffered((nx + n1 ').last).isbuf?, avol[m].mapped?, m < # avol, n1 < # avol, ginval < # avol, n < n0, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), inv(groupblock(gndx, lax, m1)), is-aligned(# avol[m].data + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore, 0 + n ≤ # buf0, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore0 ⊑ istore, isbuf1 → synced(avol), n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [isbuf := true; log1 := nx + n1 '; if err = ESUCCESS then lpt1[buffered(log1.last).leb] := mklp (lpt1[buffered(log1.last).leb].ref-size, lpt1[buffered(log1.last).leb].size + gndx0.flashsize, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(log1.last).leb.toString + " failed"); lpt1[buffered(log1.last).leb] := mklp(lpt1[buffered(log1.last).leb].ref-size, LEB_SIZE, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(n1), log1, lpt1) ∧ # lpt1 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))] ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf, buffered(n1), lpt1, avol[m, mapped(avol[m].data + subarray(buf0, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], buffered(n1)) ∧ # lpt0 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))] → ⟨pstate := journal(log1.last); apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m0, ns0; ax0, gstore, pstate, isbuf1; err1)⟩ ( abs-istore(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], lpt1, istore) ∧ abs-gstore(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))])) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ isbuf) ∧ (pstate ≠ readonly → n1 = pstate.lnum) ∧ lax0.to-adr(n1) = ax0 ∧ err = err1)), nx + n1 ' = [], err = ESUCCESS, gndx0 = [], n = 0, dups(nx), n1 ∈ ginval, n1 ∈ nx |
# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n1 = dom gstore ∪ ginval, isbuf ↔ false, avol[n1] = mapped(buf1), gstore[n1] = groupblock(gndx, lax, m1), lpt1[n1] = mklp(m1, # buf1, LP_GROUP_NODES, m2), err = err0, keyset(gch) = gc-heap(lpt1, nx + n1 '), m = buffered((nx + n1 ').last).leb, n0 = gndx0.flashsize, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, buffered((nx + n1 ').last).isbuf?, avol[m].mapped?, n < n0, ginval < # avol, n1 < # avol, m < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n1)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n1), lpt1, avol), bufs-log-only(buffered(n1), nx + n1 ', lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx, lax, m1)), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), is-aligned(# avol[m].data + n, EB_PAGE_SIZE), log-group-block(nx + n1 ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n1 '), n1 ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, 0 + n ≤ # buf0, istore0 ⊑ istore, n ≠ 0 → n < n0 → avol[m].mapped? ∧ m < # avol, isbuf1 → synced(avol), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [log1 := nx + n1 '; if err = ESUCCESS then lpt1[buffered(log1.last).leb] := mklp (lpt1[buffered(log1.last).leb].ref-size, lpt1[buffered(log1.last).leb].size + gndx0.flashsize, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + buffered(log1.last).leb.toString + " failed"); lpt1[buffered(log1.last).leb] := mklp(lpt1[buffered(log1.last).leb].ref-size, LEB_SIZE, lpt1[buffered(log1.last).leb].flags, lpt1[buffered(log1.last).leb].gcheapidx)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(buffered(n1), log1, lpt1) ∧ # lpt1 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))] ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(true, buffered(n1), lpt1, avol[m, mapped(avol[m].data + subarray(buf0, 0, n))]) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], buffered(n1)) ∧ # lpt0 = # avol[m, mapped(avol[m].data + subarray(buf0, 0, n))] → ⟨pstate := journal(log1.last); apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m0, ns0; ax0, gstore, pstate, isbuf1; err1)⟩ ( abs-istore(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], lpt1, istore) ∧ abs-gstore(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol[m, mapped(avol[m].data + subarray(buf0, 0, n))])) ∧ pstate ≠ unbuffered ∧ (pstate = readonly ↔ true) ∧ (pstate ≠ readonly → n1 = pstate.lnum) ∧ lax0.to-adr(n1) = ax0 ∧ err = err1)), nx + n1 ' = [], err = ESUCCESS, gndx0 = [], n = 0, dups(nx), n1 ∈ nx, n1 ∈ ginval