| import Algorithms.huffman_encoding.lean.spec_lib | |
| namespace Algorithms.huffman_encoding.lean | |
| open AUXLib MaxMinLib | |
| def HuffmanResidualOptimum (input live : List Int) (accumulated : Int) : Prop := | |
| sum live = sum input ∧ ∃ remaining, HuffmanOptimalCost live remaining ∧ HuffmanOptimalCost input (accumulated + remaining) | |
| def HuffmanProgress (input scratch : List Int) (active accumulated : Int) : Prop := | |
| HuffmanResidualOptimum input (sublist 0 active scratch) accumulated | |
| def HuffmanMinScan (scratch : List Int) (scanned best : Int) : Prop := | |
| ∀ k, (0 ≤ k ∧ k < scanned) → Znth best scratch 0 ≤ Znth k scratch 0 | |
| def HuffmanFirstHeld (input scratch : List Int) (active held accumulated : Int) : Prop := | |
| ∃ prior_live, List.Perm prior_live (held :: sublist 0 active scratch) ∧ | |
| (∀ weight, weight ∈ prior_live → held ≤ weight) ∧ HuffmanResidualOptimum input prior_live accumulated | |
| def HuffmanPairReady (input scratch : List Int) (active first second accumulated : Int) : Prop := | |
| ∃ prior_live, List.Perm prior_live (first :: second :: sublist 0 active scratch) ∧ | |
| (∀ weight, weight ∈ prior_live → first ≤ weight) ∧ | |
| (∀ weight, weight ∈ (second :: sublist 0 active scratch) → second ≤ weight) ∧ | |
| HuffmanResidualOptimum input prior_live accumulated | |
| end Algorithms.huffman_encoding.lean | |