File measure_functions.ML


(*  Title:       HOL/Tools/Function/measure_functions.ML
Author: Alexander Krauss, TU Muenchen

Measure functions, generated heuristically.
*)

signature MEASURE_FUNCTIONS =
sig

val get_measure_functions : Proof.context -> typ -> term list
val setup : theory -> theory

end

structure MeasureFunctions : MEASURE_FUNCTIONS =
struct

(** User-declared size functions **)
structure Measure_Heuristic_Rules = Named_Thms
(
val name = "measure_function"
val description =
"Rules that guide the heuristic generation of measure functions"
);

fun mk_is_measure t =
Const (@{const_name is_measure}, fastype_of t --> HOLogic.boolT) $ t

fun find_measures ctxt T =
DEPTH_SOLVE (resolve_tac (Measure_Heuristic_Rules.get ctxt) 1)
(HOLogic.mk_Trueprop (mk_is_measure (Var (("f",0), T --> HOLogic.natT)))
|> cterm_of (ProofContext.theory_of ctxt) |> Goal.init)
|> Seq.map (prop_of #> (fn _ $ (_ $ (_ $ f)) => f))
|> Seq.list_of


(** Generating Measure Functions **)

fun constant_0 T = Abs ("x", T, HOLogic.zero)
fun constant_1 T = Abs ("x", T, HOLogic.Suc_zero)

fun mk_funorder_funs (Type ("+", [fT, sT])) =
map (fn m => SumTree.mk_sumcase fT sT HOLogic.natT m (constant_0 sT)) (mk_funorder_funs fT)
@ map (fn m => SumTree.mk_sumcase fT sT HOLogic.natT (constant_0 fT) m) (mk_funorder_funs sT)
| mk_funorder_funs T = [ constant_1 T ]

fun mk_ext_base_funs ctxt (Type ("+", [fT, sT])) =
map_product (SumTree.mk_sumcase fT sT HOLogic.natT)
(mk_ext_base_funs ctxt fT) (mk_ext_base_funs ctxt sT)
| mk_ext_base_funs ctxt T = find_measures ctxt T

fun mk_all_measure_funs ctxt (T as Type ("+", _)) =
mk_ext_base_funs ctxt T @ mk_funorder_funs T
| mk_all_measure_funs ctxt T = find_measures ctxt T

val get_measure_functions = mk_all_measure_funs

val setup = Measure_Heuristic_Rules.setup

end