src/HOL/Tools/Function/function_common.ML

added implementation of pred_of_set

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

Common definitions and other infrastructure for the function package.
*)

signature FUNCTION_DATA =
sig

type info =
 {is_partial : bool,
  defname : string,
    (* contains no logical entities: invariant under morphisms: *)
  add_simps : (binding -> binding) -> string -> (binding -> binding) ->
    Attrib.src list -> thm list -> local_theory -> thm list * local_theory,
  case_names : string list,
  fs : term list,
  R : term,
  psimps: thm list,
  pinducts: thm list,
  simps : thm list option,
  inducts : thm list option,
  termination: thm}

end

structure Function_Data : FUNCTION_DATA =
struct

type info =
 {is_partial : bool,
  defname : string,
    (* contains no logical entities: invariant under morphisms: *)
  add_simps : (binding -> binding) -> string -> (binding -> binding) ->
    Attrib.src list -> thm list -> local_theory -> thm list * local_theory,
  case_names : string list,
  fs : term list,
  R : term,
  psimps: thm list,
  pinducts: thm list,
  simps : thm list option,
  inducts : thm list option,
  termination: thm}

end

structure Function_Common =
struct

open Function_Data

local open Function_Lib in

(* Profiling *)
val profile = Unsynchronized.ref false;

fun PROFILE msg = if !profile then timeap_msg msg else I


val acc_const_name = @{const_name accp}
fun mk_acc domT R =
  Const (acc_const_name, (domT --> domT --> HOLogic.boolT) --> domT --> HOLogic.boolT) $ R 

val function_name = suffix "C"
val graph_name = suffix "_graph"
val rel_name = suffix "_rel"
val dom_name = suffix "_dom"

(* Termination rules *)

structure TerminationRule = Generic_Data
(
  type T = thm list
  val empty = []
  val extend = I
  val merge = Thm.merge_thms
);

val get_termination_rules = TerminationRule.get
val store_termination_rule = TerminationRule.map o cons
val apply_termination_rule = resolve_tac o get_termination_rules o Context.Proof


(* Function definition result data *)

datatype function_result = FunctionResult of
 {fs: term list,
  G: term,
  R: term,
  psimps : thm list,
  simple_pinducts : thm list,
  cases : thm,
  termination : thm,
  domintros : thm list option}

fun transform_function_data ({add_simps, case_names, fs, R, psimps, pinducts,
  simps, inducts, termination, defname, is_partial} : info) phi =
    let
      val term = Morphism.term phi
      val thm = Morphism.thm phi
      val fact = Morphism.fact phi
      val name = Binding.name_of o Morphism.binding phi o Binding.name
    in
      { add_simps = add_simps, case_names = case_names,
        fs = map term fs, R = term R, psimps = fact psimps,
        pinducts = fact pinducts, simps = Option.map fact simps,
        inducts = Option.map fact inducts, termination = thm termination,
        defname = name defname, is_partial=is_partial }
    end

structure FunctionData = Generic_Data
(
  type T = (term * info) Item_Net.T;
  val empty : T = Item_Net.init (op aconv o pairself fst) (single o fst);
  val extend = I;
  fun merge tabs : T = Item_Net.merge tabs;
)

val get_function = FunctionData.get o Context.Proof;


fun lift_morphism thy f =
  let
    val term = Drule.term_rule thy f
  in
    Morphism.thm_morphism f $> Morphism.term_morphism term
    $> Morphism.typ_morphism (Logic.type_map term)
  end

fun import_function_data t ctxt =
  let
    val thy = Proof_Context.theory_of ctxt
    val ct = cterm_of thy t
    val inst_morph = lift_morphism thy o Thm.instantiate

    fun match (trm, data) =
      SOME (transform_function_data data (inst_morph (Thm.match (cterm_of thy trm, ct))))
      handle Pattern.MATCH => NONE
  in
    get_first match (Item_Net.retrieve (get_function ctxt) t)
  end

fun import_last_function ctxt =
  case Item_Net.content (get_function ctxt) of
    [] => NONE
  | (t, data) :: _ =>
    let
      val ([t'], ctxt') = Variable.import_terms true [t] ctxt
    in
      import_function_data t' ctxt'
    end

val all_function_data = Item_Net.content o get_function

fun add_function_data (data : info as {fs, termination, ...}) =
  FunctionData.map (fold (fn f => Item_Net.update (f, data)) fs)
  #> store_termination_rule termination


(* Simp rules for termination proofs *)

structure Termination_Simps = Named_Thms
(
  val name = @{binding termination_simp}
  val description = "simplification rules for termination proofs"
)


(* Default Termination Prover *)

structure TerminationProver = Generic_Data
(
  type T = Proof.context -> tactic
  val empty = (fn _ => error "Termination prover not configured")
  val extend = I
  fun merge (a, _) = a
)

val set_termination_prover = TerminationProver.put
val get_termination_prover = TerminationProver.get o Context.Proof


(* Configuration management *)
datatype function_opt
  = Sequential
  | Default of string
  | DomIntros
  | No_Partials

datatype function_config = FunctionConfig of
 {sequential: bool,
  default: string option,
  domintros: bool,
  partials: bool}

fun apply_opt Sequential (FunctionConfig {sequential, default, domintros, partials}) =
    FunctionConfig {sequential=true, default=default, domintros=domintros, partials=partials}
  | apply_opt (Default d) (FunctionConfig {sequential, default, domintros, partials}) =
    FunctionConfig {sequential=sequential, default=SOME d, domintros=domintros, partials=partials}
  | apply_opt DomIntros (FunctionConfig {sequential, default, domintros, partials}) =
    FunctionConfig {sequential=sequential, default=default, domintros=true, partials=partials}
  | apply_opt No_Partials (FunctionConfig {sequential, default, domintros, partials}) =
    FunctionConfig {sequential=sequential, default=default, domintros=domintros, partials=false}

val default_config =
  FunctionConfig { sequential=false, default=NONE,
    domintros=false, partials=true}


(* Analyzing function equations *)

fun split_def ctxt check_head geq =
  let
    fun input_error msg = cat_lines [msg, Syntax.string_of_term ctxt geq]
    val qs = Term.strip_qnt_vars "all" geq
    val imp = Term.strip_qnt_body "all" geq
    val (gs, eq) = Logic.strip_horn imp

    val (f_args, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
      handle TERM _ => error (input_error "Not an equation")

    val (head, args) = strip_comb f_args

    val fname = fst (dest_Free head) handle TERM _ => ""
    val _ = check_head fname
  in
    (fname, qs, gs, args, rhs)
  end

(* Check for all sorts of errors in the input *)
fun check_defs ctxt fixes eqs =
  let
    val fnames = map (fst o fst) fixes

    fun check geq =
      let
        fun input_error msg = error (cat_lines [msg, Syntax.string_of_term ctxt geq])

        fun check_head fname =
          member (op =) fnames fname orelse
          input_error ("Illegal equation head. Expected " ^ commas_quote fnames)

        val (fname, qs, gs, args, rhs) = split_def ctxt check_head geq

        val _ = length args > 0 orelse input_error "Function has no arguments:"

        fun add_bvs t is = add_loose_bnos (t, 0, is)
        val rvs = (subtract (op =) (fold add_bvs args []) (add_bvs rhs []))
                    |> map (fst o nth (rev qs))

        val _ = null rvs orelse input_error
          ("Variable" ^ plural " " "s " rvs ^ commas_quote rvs ^
           " occur" ^ plural "s" "" rvs ^ " on right hand side only:")

        val _ = forall (not o Term.exists_subterm
          (fn Free (n, _) => member (op =) fnames n | _ => false)) (gs @ args)
          orelse input_error "Defined function may not occur in premises or arguments"

        val freeargs = map (fn t => subst_bounds (rev (map Free qs), t)) args
        val funvars = filter (fn q => exists (exists_subterm (fn (Free q') $ _ => q = q' | _ => false)) freeargs) qs
        val _ = null funvars orelse (warning (cat_lines
          ["Bound variable" ^ plural " " "s " funvars ^
          commas_quote (map fst funvars) ^ " occur" ^ plural "s" "" funvars ^
          " in function position.", "Misspelled constructor???"]); true)
      in
        (fname, length args)
      end

    val grouped_args = AList.group (op =) (map check eqs)
    val _ = grouped_args
      |> map (fn (fname, ars) =>
        length (distinct (op =) ars) = 1
        orelse error ("Function " ^ quote fname ^
          " has different numbers of arguments in different equations"))

    val not_defined = subtract (op =) (map fst grouped_args) fnames
    val _ = null not_defined
      orelse error ("No defining equations for function" ^
        plural " " "s " not_defined ^ commas_quote not_defined)

    fun check_sorts ((fname, fT), _) =
      Sorts.of_sort (Sign.classes_of (Proof_Context.theory_of ctxt)) (fT, HOLogic.typeS)
      orelse error (cat_lines
      ["Type of " ^ quote fname ^ " is not of sort " ^ quote "type" ^ ":",
       Syntax.string_of_typ (Config.put show_sorts true ctxt) fT])

    val _ = map check_sorts fixes
  in
    ()
  end

(* Preprocessors *)

type fixes = ((string * typ) * mixfix) list
type 'a spec = (Attrib.binding * 'a list) list
type preproc = function_config -> Proof.context -> fixes -> term spec ->
  (term list * (thm list -> thm spec) * (thm list -> thm list list) * string list)

val fname_of = fst o dest_Free o fst o strip_comb o fst o HOLogic.dest_eq o
  HOLogic.dest_Trueprop o Logic.strip_imp_concl o snd o dest_all_all

fun mk_case_names i "" k = mk_case_names i (string_of_int (i + 1)) k
  | mk_case_names _ n 0 = []
  | mk_case_names _ n 1 = [n]
  | mk_case_names _ n k = map (fn i => n ^ "_" ^ string_of_int i) (1 upto k)

fun empty_preproc check _ ctxt fixes spec =
  let
    val (bnds, tss) = split_list spec
    val ts = flat tss
    val _ = check ctxt fixes ts
    val fnames = map (fst o fst) fixes
    val indices = map (fn eq => find_index (curry op = (fname_of eq)) fnames) ts

    fun sort xs = partition_list (fn i => fn (j,_) => i = j) 0 (length fnames - 1) 
      (indices ~~ xs) |> map (map snd)

    (* using theorem names for case name currently disabled *)
    val cnames = map_index (fn (i, _) => mk_case_names i "" 1) bnds |> flat
  in
    (ts, curry op ~~ bnds o Library.unflat tss, sort, cnames)
  end

structure Preprocessor = Generic_Data
(
  type T = preproc
  val empty : T = empty_preproc check_defs
  val extend = I
  fun merge (a, _) = a
)

val get_preproc = Preprocessor.get o Context.Proof
val set_preproc = Preprocessor.map o K



local
  val option_parser = Parse.group (fn () => "option")
    ((Parse.reserved "sequential" >> K Sequential)
     || ((Parse.reserved "default" |-- Parse.term) >> Default)
     || (Parse.reserved "domintros" >> K DomIntros)
     || (Parse.reserved "no_partials" >> K No_Partials))

  fun config_parser default =
    (Scan.optional (Parse.$$$ "(" |-- Parse.!!! (Parse.list1 option_parser) --| Parse.$$$ ")") [])
     >> (fn opts => fold apply_opt opts default)
in
  fun function_parser default_cfg =
      config_parser default_cfg -- Parse.fixes -- Parse_Spec.where_alt_specs
end


end
end