This is a listing of all goals defined over the current specification. Axioms are marked yellow, proved theorems green and unproved theorems blue. Click on individual names to get more information on the proof.
| Name: | Sequent: | Type: |
|---|---|---|
| init | tree_buffer_heap_init#(n0; ; H, rxs, rys, h, xs_len, to_delete){h := n0; rxs := null; rys := null; to_delete := []; xs_len := 0; H := ∅} | An Axiom |
| get | tree_buffer_heap_get#(H, rxs, rys, h; ; x) {x := []; let n = 0, r = rxs in {while n < h ∧ r ≠ null do {x := x + H[r].val; r := H[r].nxt; n := n + 1}; r := rys; while n < h ∧ r ≠ null do {x := x + H[r].val; r := H[r].nxt; n := n + 1}} } | An Axiom |
| add | tree_buffer_heap_add#(a, h; H, rxs, rys, xs_len, to_delete) {tree_buffer_heap_process_queue#(; H, to_delete); choose r with ¬ r ∈ H ∧ r ≠ null in {H := H ++ r; H[r].val := a; H[r].nxt := rxs; if xs_len + 1 = h then {if rys ≠ null then to_delete := rys + to_delete; rys := r; xs_len := 0; rxs := null} else {rxs := r; xs_len := 1 + xs_len}} } | An Axiom |
| infinite-memory | ⊦ ∃ r. r ≠ null ∧ ¬ r ∈ H | An Axiom |
| process-queue | tree_buffer_heap_process_queue#(; H, to_delete) {tree_buffer_heap_process_one#(; H, to_delete); tree_buffer_heap_process_one#(; H, to_delete)} | An Axiom |
| process-one | tree_buffer_heap_process_one#(; H, to_delete) {if to_delete ≠ [] then let r = to_delete.head in {to_delete := to_delete.tail; if H[r].nxt ≠ null then to_delete := H[r].nxt + to_delete; H := H -- r} } | An Axiom |