Theory Sorting_Algorithms_Examples

(*  Title:      HOL/ex/Sorting_Algorithms_Examples.thy
    Author:     Florian Haftmann, TU Muenchen
*)

theory Sorting_Algorithms_Examples
  imports Main "HOL-Library.Sorting_Algorithms"
begin

subsection ‹Evaluation examples›

definition int_abs_reversed :: "int comparator"
  where "int_abs_reversed = key abs (reversed default)"

definition example_1 :: "int list"
  where "example_1 = [65, 1705, -2322, 734, 4, (-17::int)]"

definition example_2 :: "int list"
  where "example_2 = [-3000..3000]"

ML local

  val term_of_int_list = HOLogic.mk_list typint
    o map (HOLogic.mk_number typint o @{code integer_of_int});

  fun raw_sort (ctxt, ct, ks) =
    instantiatex = ct and y = Thm.cterm_of ctxt (term_of_int_list ks)
      in cterm x  y for x y :: int list;

  val (_, sort_oracle) = Theory.setup_result (Thm.add_oracle (bindingsort, raw_sort));

in

  val sort_int_abs_reversed_conv = @{computation_conv "int list" terms: int_abs_reversed
    "sort :: int comparator  _"
    "quicksort :: int comparator  _"
    "mergesort :: int comparator  _"
    example_1 example_2
  } (fn ctxt => fn ct => fn ks => sort_oracle (ctxt, ks, ct))

end

declare [[code_timing]]

ML_val sort_int_abs_reversed_conv context
  ctermsort int_abs_reversed example_1

ML_val sort_int_abs_reversed_conv context
  ctermquicksort int_abs_reversed example_1

ML_val sort_int_abs_reversed_conv context
  ctermmergesort int_abs_reversed example_1

ML_val sort_int_abs_reversed_conv context
  ctermsort int_abs_reversed example_2

ML_val sort_int_abs_reversed_conv context
  ctermquicksort int_abs_reversed example_2

ML_val sort_int_abs_reversed_conv context
  ctermmergesort int_abs_reversed example_2

end