def msort_by_perm

bend-mathlib@0.8.1.0 · perm.bend:233

import Base
import bendlib-kernel-list@1.0.0.0/list.bend as K

233# Merge sort permutes its input, for any fuel.
234def msort_by_perm(~A: Data, ~le: A -> A -> Bool, fuel: Nat, +xs: List<&2, A>) -> K.perm(A, xs, msort_by(~A, ~le, fuel, xs)):
235  match fuel:
236    case 0n:
237      perm_refl(A, xs)
238    case 1n++f:
239      perm_trans(A, xs, List.append(&2, A, evens(A, xs), odds(A, xs)), msort_by(~A, ~le, 1n+f, xs), split_perm(A, xs), perm_trans(A, List.append(&2, A, evens(A, xs), odds(A, xs)), List.append(&2, A, msort_by(~A, ~le, f, evens(A, xs)), msort_by(~A, ~le, f, odds(A, xs))), msort_by(~A, ~le, 1n+f, xs), perm_append(A, evens(A, xs), msort_by(~A, ~le, f, evens(A, xs)), odds(A, xs), msort_by(~A, ~le, f, odds(A, xs)), msort_by_perm(~A, ~le, f, evens(A, xs)), msort_by_perm(~A, ~le, f, odds(A, xs))), merge_by_perm(~A, ~le, msort_by(~A, ~le, f, evens(A, xs)), msort_by(~A, ~le, f, odds(A, xs)))))