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: |
|---|---|---|
| max-sub-array-sum | maxSubArraySum#(a; ; res) {let size = # a, max_so_far = 0, max_ending_here = 0, n = 0 in {while n < size do {/* kadane-correct : invariant 0 ≤ max_ending_here ∧ max_ending_here ≤ max_so_far ∧ n ≤ size ∧ maximum-sum(subarray(a, 0, n), max_so_far) ∧ (∃ m. maximum-suffix-sum(subarray(a, 0, n), m, max_ending_here)) wfbound size - n; */; max_ending_here := max_ending_here + a[n]; if max_ending_here < 0 then max_ending_here := 0 else if max_so_far < max_ending_here then max_so_far := max_ending_here; n := n + 1}; res := max_so_far} } | An Axiom |
| kadane-correct | ⊦ ⟪maxSubArraySum#(a; ; res)⟫ maximum-sum(a, res) | A User Theorem |