| # lpt1 = # avol, # lpt0 = # avol, isbuf2 ↔ pstate = readonly, isbuf0 ↔ pstate = readonly, lpt1[bleb.leb] = mklp(m3, m1, lpf, m2), adr = adr0, ax = ax0, ¬ isbuf0, keyset(gch) = gc-heap(lpt1, log1), log = log1, lpt = lpt0, 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, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate = readonly, bleb, lpt1, avol), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), istore0 ⊑ istore, pstate = unbuffered → isbuf1, 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, isbuf1 → synced(avol), pstate ≠ readonly → bleb.isbuf? ∧ bleb.leb < # avol ∧ lpf = LP_GROUP_NODES ∧ bleb.leb ∈ log1 ∧ avol[bleb.leb].mapped? ∧ (gndx0 ≠ [] ∧ m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # avol[bleb.leb].data), pstate.journal? ∨ pstate = readonly ⊦ [awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, bleb, isbuf2; ; bleb1); persistence_encode_group_nodes#(gndx0, bleb1.leb, lpt1[bleb1.leb].size; ; buf, ax, err); if err = ESUCCESS then if ¬ lpt1[bleb1.leb].size + # buf ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf2); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr0, m, log1, lpt0, ns0, bleb; avol, isbuf2; err); if err = ESUCCESS then lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + # buf, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + bleb1.leb.toString + " failed"); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx)}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax = ax0 ∧ err = err0)), gndx0 = [], dups(log1) |
# lpt0 = # avol, # lpt1 = # avol, pstate.lnum = log1.last, lpt1[log1.last] = mklp(gstore[log1.last].ref-size, m1, LP_GROUP_NODES, m2), avol[log1.last] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, gndx0 ≠ [], log1 ≠ [], pstate ≠ unbuffered, pstate ≠ readonly, pstate.journal?, log1.last < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore[log1.last]), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), log1.last ∈ gstore, istore0 ⊑ istore, ¬ dups(log1), ¬ log1.last ∈ ginval, m1 + gndx0.flashsize ≤ LEB_SIZE → m1 = # buf, isbuf1 → synced(avol), pstate.index? → log1.last ∈ istore ⊦ [awbuf_get_buf#(adr0, m, log1, avol, lpt0, ns0, buffered(log1.last), false; ; bleb1); persistence_encode_group_nodes#(gndx0, bleb1.leb, lpt1[bleb1.leb].size; ; buf, ax, err); isbuf2 := pstate = readonly; bleb := buffered(log1.last); if err = ESUCCESS then if ¬ lpt1[bleb1.leb].size + # buf ≤ LEB_SIZE then {debug#("persistence: trying to write beyond LEB size"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf2); err := ENOSPC} else {awbuf_write_buf#(# buf, buf, adr0, m, log1, lpt0, ns0, bleb; avol, isbuf2; err); if err = ESUCCESS then lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + # buf, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) else {debug#("persistence: adding group node to LEB " + bleb1.leb.toString + " failed"); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx)}} else {debug#("persistence: could not encode group node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb) ∧ # lpt0 = # avol → ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ax = ax0 ∧ err = err0))
Used simplifier rules: fwd-in-gstore-lpt: ⊦ n ∈ gstore ∧ abs-gstore(avol, lpt, gstore, ginval) → n < # lpt ∧ lpt[n].ref-size = gstore[n].ref-size ∧ lpt[n].flags = LP_GROUP_NODES;% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ mapped(buf).data = buf; (s)% ⊦ nx.last = n ∧ nx ≠ [] → n ∈ nx; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ buffered(m).leb = m; (s)%fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fwd-in-log-in-gstore: ⊦ n ∈ nx ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%elems-in-notin-ginval: ⊦ n ∈ nx ∧ elems nx ∩ ns = ∅ → ¬ n ∈ ns; (forward) from specification apersistence-base%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ avol[n].mapped? ↔ (∃ buf. avol[n] = mapped(buf)); (as)% ⊦ bleb.isbuf? ↔ (∃ n. bleb = buffered(n)); (as)