src/HOL/Tools/Nitpick/nitpick_mono.ML
author blanchet
Tue Jan 03 18:33:17 2012 +0100 (2012-01-03)
changeset 46081 8f6465f7021b
parent 41471 54a58904a598
child 46083 efeaa79f021b
permissions -rw-r--r--
ported mono calculus to handle "set" type constructors
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(*  Title:      HOL/Tools/Nitpick/nitpick_mono.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2009, 2010
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Monotonicity inference for higher-order logic.
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*)
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signature NITPICK_MONO =
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sig
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  type hol_context = Nitpick_HOL.hol_context
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  val trace : bool Unsynchronized.ref
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  val formulas_monotonic :
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    hol_context -> bool -> typ -> term list * term list -> bool
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end;
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structure Nitpick_Mono : NITPICK_MONO =
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struct
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open Nitpick_Util
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open Nitpick_HOL
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datatype sign = Plus | Minus
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type var = int
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datatype annotation = Gen | New | Fls | Tru
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datatype annotation_atom = A of annotation | V of var
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type assign_literal = var * (sign * annotation)
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datatype mtyp =
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  MAlpha |
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  MFun of mtyp * annotation_atom * mtyp |
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  MPair of mtyp * mtyp |
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  MType of string * mtyp list |
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  MRec of string * typ list
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type mdata =
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  {hol_ctxt: hol_context,
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   binarize: bool,
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   alpha_T: typ,
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   max_fresh: int Unsynchronized.ref,
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   datatype_mcache: ((string * typ list) * mtyp) list Unsynchronized.ref,
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   constr_mcache: (styp * mtyp) list Unsynchronized.ref}
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exception UNSOLVABLE of unit
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exception MTYPE of string * mtyp list * typ list
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val trace = Unsynchronized.ref false
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fun trace_msg msg = if !trace then tracing (msg ()) else ()
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fun string_for_sign Plus = "+"
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  | string_for_sign Minus = "-"
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fun negate_sign Plus = Minus
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  | negate_sign Minus = Plus
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val string_for_var = signed_string_of_int
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fun string_for_vars sep [] = "0\<^bsub>" ^ sep ^ "\<^esub>"
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  | string_for_vars sep xs = space_implode sep (map string_for_var xs)
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fun subscript_string_for_vars sep xs =
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  if null xs then "" else "\<^bsub>" ^ string_for_vars sep xs ^ "\<^esub>"
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fun string_for_annotation Gen = "G"
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  | string_for_annotation New = "N"
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  | string_for_annotation Fls = "F"
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  | string_for_annotation Tru = "T"
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fun string_for_annotation_atom (A a) = string_for_annotation a
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  | string_for_annotation_atom (V x) = string_for_var x
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fun string_for_assign_literal (x, (sn, a)) =
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  string_for_var x ^ (case sn of Plus => " = " | Minus => " \<noteq> ") ^
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  string_for_annotation a
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val bool_M = MType (@{type_name bool}, [])
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val dummy_M = MType (nitpick_prefix ^ "dummy", [])
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fun is_MRec (MRec _) = true
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  | is_MRec _ = false
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fun dest_MFun (MFun z) = z
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  | dest_MFun M = raise MTYPE ("Nitpick_Mono.dest_MFun", [M], [])
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val no_prec = 100
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fun precedence_of_mtype (MFun _) = 1
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  | precedence_of_mtype (MPair _) = 2
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  | precedence_of_mtype _ = no_prec
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val string_for_mtype =
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  let
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    fun aux outer_prec M =
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      let
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        val prec = precedence_of_mtype M
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        val need_parens = (prec < outer_prec)
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      in
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        (if need_parens then "(" else "") ^
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        (if M = dummy_M then
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           "_"
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         else case M of
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             MAlpha => "\<alpha>"
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           | MFun (M1, aa, M2) =>
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             aux (prec + 1) M1 ^ " \<Rightarrow>\<^bsup>" ^
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             string_for_annotation_atom aa ^ "\<^esup> " ^ aux prec M2
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           | MPair (M1, M2) => aux (prec + 1) M1 ^ " \<times> " ^ aux prec M2
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           | MType (s, []) =>
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             if s = @{type_name prop} orelse s = @{type_name bool} then "o"
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             else s
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           | MType (s, Ms) => "(" ^ commas (map (aux 0) Ms) ^ ") " ^ s
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           | MRec (s, _) => "[" ^ s ^ "]") ^
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        (if need_parens then ")" else "")
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      end
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  in aux 0 end
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fun flatten_mtype (MPair (M1, M2)) = maps flatten_mtype [M1, M2]
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  | flatten_mtype (MType (_, Ms)) = maps flatten_mtype Ms
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  | flatten_mtype M = [M]
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fun initial_mdata hol_ctxt binarize alpha_T =
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  ({hol_ctxt = hol_ctxt, binarize = binarize, alpha_T = alpha_T,
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    max_fresh = Unsynchronized.ref 0, datatype_mcache = Unsynchronized.ref [],
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    constr_mcache = Unsynchronized.ref []} : mdata)
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fun could_exist_alpha_subtype alpha_T (T as Type (_, Ts)) =
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    T = alpha_T orelse (not (is_fp_iterator_type T) andalso
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                        exists (could_exist_alpha_subtype alpha_T) Ts)
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  | could_exist_alpha_subtype alpha_T T = (T = alpha_T)
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fun could_exist_alpha_sub_mtype _ (alpha_T as TFree _) T =
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    could_exist_alpha_subtype alpha_T T
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  | could_exist_alpha_sub_mtype ctxt alpha_T T =
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    (T = alpha_T orelse is_datatype ctxt [(NONE, true)] T)
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fun exists_alpha_sub_mtype MAlpha = true
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  | exists_alpha_sub_mtype (MFun (M1, _, M2)) =
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    exists exists_alpha_sub_mtype [M1, M2]
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  | exists_alpha_sub_mtype (MPair (M1, M2)) =
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    exists exists_alpha_sub_mtype [M1, M2]
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  | exists_alpha_sub_mtype (MType (_, Ms)) = exists exists_alpha_sub_mtype Ms
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  | exists_alpha_sub_mtype (MRec _) = true
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fun exists_alpha_sub_mtype_fresh MAlpha = true
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  | exists_alpha_sub_mtype_fresh (MFun (_, V _, _)) = true
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  | exists_alpha_sub_mtype_fresh (MFun (_, _, M2)) =
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    exists_alpha_sub_mtype_fresh M2
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  | exists_alpha_sub_mtype_fresh (MPair (M1, M2)) =
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    exists exists_alpha_sub_mtype_fresh [M1, M2]
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  | exists_alpha_sub_mtype_fresh (MType (_, Ms)) =
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    exists exists_alpha_sub_mtype_fresh Ms
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  | exists_alpha_sub_mtype_fresh (MRec _) = true
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fun constr_mtype_for_binders z Ms =
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  fold_rev (fn M => curry3 MFun M (A Gen)) Ms (MRec z)
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fun repair_mtype _ _ MAlpha = MAlpha
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  | repair_mtype cache seen (MFun (M1, aa, M2)) =
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    MFun (repair_mtype cache seen M1, aa, repair_mtype cache seen M2)
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  | repair_mtype cache seen (MPair Mp) =
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    MPair (pairself (repair_mtype cache seen) Mp)
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  | repair_mtype cache seen (MType (s, Ms)) =
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    MType (s, maps (flatten_mtype o repair_mtype cache seen) Ms)
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  | repair_mtype cache seen (MRec (z as (s, _))) =
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    case AList.lookup (op =) cache z |> the of
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      MRec _ => MType (s, [])
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    | M => if member (op =) seen M then MType (s, [])
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           else repair_mtype cache (M :: seen) M
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fun repair_datatype_mcache cache =
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  let
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    fun repair_one (z, M) =
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      Unsynchronized.change cache
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          (AList.update (op =) (z, repair_mtype (!cache) [] M))
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  in List.app repair_one (rev (!cache)) end
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fun repair_constr_mcache dtype_cache constr_mcache =
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  let
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    fun repair_one (x, M) =
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      Unsynchronized.change constr_mcache
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          (AList.update (op =) (x, repair_mtype dtype_cache [] M))
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  in List.app repair_one (!constr_mcache) end
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fun is_fin_fun_supported_type @{typ prop} = true
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  | is_fin_fun_supported_type @{typ bool} = true
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  | is_fin_fun_supported_type (Type (@{type_name option}, _)) = true
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  | is_fin_fun_supported_type _ = false
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(* TODO: clean this up *)
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fun fin_fun_body _ _ (t as @{term False}) = SOME t
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  | fin_fun_body _ _ (t as Const (@{const_name None}, _)) = SOME t
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  | fin_fun_body dom_T ran_T
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                 ((t0 as Const (@{const_name If}, _))
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                  $ (t1 as Const (@{const_name HOL.eq}, _) $ Bound 0 $ t1')
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                  $ t2 $ t3) =
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    (if loose_bvar1 (t1', 0) then
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       NONE
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     else case fin_fun_body dom_T ran_T t3 of
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       NONE => NONE
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     | SOME t3 =>
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       SOME (t0 $ (Const (@{const_name is_unknown}, dom_T --> bool_T) $ t1')
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                $ (Const (@{const_name unknown}, ran_T)) $ (t0 $ t1 $ t2 $ t3)))
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  | fin_fun_body _ _ _ = NONE
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(* FIXME: make sure well-annotated *)
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fun fresh_mfun_for_fun_type (mdata as {max_fresh, ...} : mdata) all_minus
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                            T1 T2 =
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  let
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    val M1 = fresh_mtype_for_type mdata all_minus T1
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    val M2 = fresh_mtype_for_type mdata all_minus T2
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    val aa = if not all_minus andalso exists_alpha_sub_mtype_fresh M1 andalso
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                is_fin_fun_supported_type (body_type T2) then
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               V (Unsynchronized.inc max_fresh)
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             else
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               A Gen
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  in (M1, aa, M2) end
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and fresh_mtype_for_type (mdata as {hol_ctxt as {ctxt, ...}, binarize, alpha_T,
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                                    datatype_mcache, constr_mcache, ...})
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                         all_minus =
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  let
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    fun do_type T =
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      if T = alpha_T then
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        MAlpha
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      else case T of
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        Type (@{type_name fun}, [T1, T2]) =>
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        MFun (fresh_mfun_for_fun_type mdata all_minus T1 T2)
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      | Type (@{type_name prod}, [T1, T2]) => MPair (pairself do_type (T1, T2))
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      | Type (@{type_name set}, [T']) => do_type (T' --> bool_T)
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      | Type (z as (s, _)) =>
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        if could_exist_alpha_sub_mtype ctxt alpha_T T then
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          case AList.lookup (op =) (!datatype_mcache) z of
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            SOME M => M
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          | NONE =>
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            let
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              val _ = Unsynchronized.change datatype_mcache (cons (z, MRec z))
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              val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize T
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              val (all_Ms, constr_Ms) =
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                fold_rev (fn (_, T') => fn (all_Ms, constr_Ms) =>
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                             let
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                               val binder_Ms = map do_type (binder_types T')
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                               val new_Ms = filter exists_alpha_sub_mtype_fresh
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                                                   binder_Ms
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                               val constr_M = constr_mtype_for_binders z
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                                                                       binder_Ms
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                             in
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                               (union (op =) new_Ms all_Ms,
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                                constr_M :: constr_Ms)
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                             end)
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                         xs ([], [])
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              val M = MType (s, all_Ms)
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              val _ = Unsynchronized.change datatype_mcache
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                          (AList.update (op =) (z, M))
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              val _ = Unsynchronized.change constr_mcache
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                          (append (xs ~~ constr_Ms))
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            in
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              if forall (not o is_MRec o snd) (!datatype_mcache) then
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                (repair_datatype_mcache datatype_mcache;
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                 repair_constr_mcache (!datatype_mcache) constr_mcache;
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                 AList.lookup (op =) (!datatype_mcache) z |> the)
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              else
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                M
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            end
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        else
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          MType (s, [])
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      | _ => MType (simple_string_of_typ T, [])
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  in do_type end
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val ground_and_sole_base_constrs = []
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(* FIXME: [@{const_name Nil}, @{const_name None}], cf. lists_empty *)
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fun prodM_factors (MPair (M1, M2)) = maps prodM_factors [M1, M2]
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  | prodM_factors M = [M]
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fun curried_strip_mtype (MFun (M1, _, M2)) =
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    curried_strip_mtype M2 |>> append (prodM_factors M1)
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  | curried_strip_mtype M = ([], M)
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fun sel_mtype_from_constr_mtype s M =
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  let
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    val (arg_Ms, dataM) = curried_strip_mtype M
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    val a = if member (op =) ground_and_sole_base_constrs
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                             (constr_name_for_sel_like s) then
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              Fls
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            else
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              Gen
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  in
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    MFun (dataM, A a,
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          case sel_no_from_name s of ~1 => bool_M | n => nth arg_Ms n)
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  end
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fun mtype_for_constr (mdata as {hol_ctxt = {ctxt, ...}, alpha_T, constr_mcache,
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                                ...}) (x as (_, T)) =
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  if could_exist_alpha_sub_mtype ctxt alpha_T T then
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    case AList.lookup (op =) (!constr_mcache) x of
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      SOME M => M
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    | NONE => if T = alpha_T then
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                let val M = fresh_mtype_for_type mdata false T in
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                  (Unsynchronized.change constr_mcache (cons (x, M)); M)
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                end
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              else
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                (fresh_mtype_for_type mdata false (body_type T);
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                 AList.lookup (op =) (!constr_mcache) x |> the)
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  else
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    fresh_mtype_for_type mdata false T
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fun mtype_for_sel (mdata as {hol_ctxt, binarize, ...}) (x as (s, _)) =
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  x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize
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    |> mtype_for_constr mdata |> sel_mtype_from_constr_mtype s
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fun resolve_annotation_atom asgs (V x) =
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    x |> AList.lookup (op =) asgs |> Option.map A |> the_default (V x)
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  | resolve_annotation_atom _ aa = aa
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fun resolve_mtype asgs =
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  let
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   311
    fun aux MAlpha = MAlpha
blanchet@40988
   312
      | aux (MFun (M1, aa, M2)) =
blanchet@40989
   313
        MFun (aux M1, resolve_annotation_atom asgs aa, aux M2)
blanchet@35385
   314
      | aux (MPair Mp) = MPair (pairself aux Mp)
blanchet@35385
   315
      | aux (MType (s, Ms)) = MType (s, map aux Ms)
blanchet@35385
   316
      | aux (MRec z) = MRec z
blanchet@33192
   317
  in aux end
blanchet@33192
   318
blanchet@40996
   319
datatype comp_op = Eq | Neq | Leq
blanchet@33192
   320
blanchet@40985
   321
type comp = annotation_atom * annotation_atom * comp_op * var list
blanchet@40995
   322
type assign_clause = assign_literal list
blanchet@33192
   323
blanchet@40994
   324
type constraint_set = comp list * assign_clause list
blanchet@33192
   325
blanchet@33192
   326
fun string_for_comp_op Eq = "="
blanchet@40996
   327
  | string_for_comp_op Neq = "\<noteq>"
blanchet@33192
   328
  | string_for_comp_op Leq = "\<le>"
blanchet@33192
   329
blanchet@40990
   330
fun string_for_comp (aa1, aa2, cmp, xs) =
blanchet@40990
   331
  string_for_annotation_atom aa1 ^ " " ^ string_for_comp_op cmp ^
blanchet@40990
   332
  subscript_string_for_vars " \<and> " xs ^ " " ^ string_for_annotation_atom aa2
blanchet@33192
   333
blanchet@40999
   334
fun string_for_assign_clause NONE = "\<top>"
blanchet@40999
   335
  | string_for_assign_clause (SOME []) = "\<bot>"
blanchet@40999
   336
  | string_for_assign_clause (SOME asgs) =
blanchet@40995
   337
    space_implode " \<or> " (map string_for_assign_literal asgs)
blanchet@40990
   338
blanchet@40996
   339
fun add_assign_literal (x, (sn, a)) clauses =
blanchet@40996
   340
  if exists (fn [(x', (sn', a'))] =>
blanchet@40996
   341
                x = x' andalso ((sn = sn' andalso a <> a') orelse
blanchet@40996
   342
                                (sn <> sn' andalso a = a'))
blanchet@40996
   343
              | _ => false) clauses then
blanchet@40994
   344
    NONE
blanchet@40994
   345
  else
blanchet@41017
   346
    SOME ([(x, (sn, a))] :: clauses)
blanchet@33192
   347
blanchet@40991
   348
fun add_assign_disjunct _ NONE = NONE
blanchet@40991
   349
  | add_assign_disjunct asg (SOME asgs) = SOME (insert (op =) asg asgs)
blanchet@40991
   350
blanchet@40999
   351
fun add_assign_clause NONE = I
blanchet@40999
   352
  | add_assign_clause (SOME clause) = insert (op =) clause
blanchet@40997
   353
blanchet@40996
   354
fun annotation_comp Eq a1 a2 = (a1 = a2)
blanchet@40996
   355
  | annotation_comp Neq a1 a2 = (a1 <> a2)
blanchet@40996
   356
  | annotation_comp Leq a1 a2 = (a1 = a2 orelse a2 = Gen)
blanchet@40996
   357
blanchet@40997
   358
fun sign_for_comp_op Eq = Plus
blanchet@40997
   359
  | sign_for_comp_op Neq = Minus
blanchet@40997
   360
  | sign_for_comp_op Leq = raise BAD ("sign_for_comp_op", "unexpected \"Leq\"")
blanchet@40996
   361
blanchet@40996
   362
fun do_annotation_atom_comp Leq [] aa1 aa2 (cset as (comps, clauses)) =
blanchet@40988
   363
    (case (aa1, aa2) of
blanchet@40996
   364
       (A a1, A a2) => if annotation_comp Leq a1 a2 then SOME cset else NONE
blanchet@40996
   365
     | _ => SOME (insert (op =) (aa1, aa2, Leq, []) comps, clauses))
blanchet@40996
   366
  | do_annotation_atom_comp cmp [] aa1 aa2 (cset as (comps, clauses)) =
blanchet@40996
   367
    (case (aa1, aa2) of
blanchet@40996
   368
       (A a1, A a2) => if annotation_comp cmp a1 a2 then SOME cset else NONE
blanchet@40988
   369
     | (V x1, A a2) =>
blanchet@40997
   370
       clauses |> add_assign_literal (x1, (sign_for_comp_op cmp, a2))
blanchet@40996
   371
               |> Option.map (pair comps)
blanchet@40996
   372
     | (A _, V _) => do_annotation_atom_comp cmp [] aa2 aa1 cset
blanchet@40996
   373
     | (V _, V _) => SOME (insert (op =) (aa1, aa2, cmp, []) comps, clauses))
blanchet@40994
   374
  | do_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) =
blanchet@40994
   375
    SOME (insert (op =) (aa1, aa2, cmp, xs) comps, clauses)
blanchet@33192
   376
blanchet@40997
   377
fun add_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) =
blanchet@40998
   378
  (trace_msg (fn () => "*** Add " ^ string_for_comp (aa1, aa2, cmp, xs));
blanchet@40994
   379
   case do_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) of
blanchet@40993
   380
     NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
blanchet@40994
   381
   | SOME cset => cset)
blanchet@40993
   382
blanchet@35385
   383
fun do_mtype_comp _ _ _ _ NONE = NONE
blanchet@40994
   384
  | do_mtype_comp _ _ MAlpha MAlpha cset = cset
blanchet@40988
   385
  | do_mtype_comp Eq xs (MFun (M11, aa1, M12)) (MFun (M21, aa2, M22))
blanchet@40994
   386
                  (SOME cset) =
blanchet@40994
   387
    cset |> do_annotation_atom_comp Eq xs aa1 aa2
blanchet@40994
   388
         |> do_mtype_comp Eq xs M11 M21 |> do_mtype_comp Eq xs M12 M22
blanchet@40988
   389
  | do_mtype_comp Leq xs (MFun (M11, aa1, M12)) (MFun (M21, aa2, M22))
blanchet@40994
   390
                  (SOME cset) =
blanchet@35385
   391
    (if exists_alpha_sub_mtype M11 then
blanchet@40994
   392
       cset |> do_annotation_atom_comp Leq xs aa1 aa2
blanchet@40994
   393
            |> do_mtype_comp Leq xs M21 M11
blanchet@40994
   394
            |> (case aa2 of
blanchet@40994
   395
                  A Gen => I
blanchet@40994
   396
                | A _ => do_mtype_comp Leq xs M11 M21
blanchet@40994
   397
                | V x => do_mtype_comp Leq (x :: xs) M11 M21)
blanchet@33192
   398
     else
blanchet@40994
   399
       SOME cset)
blanchet@35385
   400
    |> do_mtype_comp Leq xs M12 M22
blanchet@35385
   401
  | do_mtype_comp cmp xs (M1 as MPair (M11, M12)) (M2 as MPair (M21, M22))
blanchet@40994
   402
                  cset =
blanchet@40994
   403
    (cset |> fold (uncurry (do_mtype_comp cmp xs)) [(M11, M21), (M12, M22)]
blanchet@41017
   404
     handle ListPair.UnequalLengths =>
blanchet@35665
   405
            raise MTYPE ("Nitpick_Mono.do_mtype_comp", [M1, M2], []))
blanchet@40994
   406
  | do_mtype_comp _ _ (MType _) (MType _) cset =
blanchet@40994
   407
    cset (* no need to compare them thanks to the cache *)
blanchet@35665
   408
  | do_mtype_comp cmp _ M1 M2 _ =
blanchet@35665
   409
    raise MTYPE ("Nitpick_Mono.do_mtype_comp (" ^ string_for_comp_op cmp ^ ")",
blanchet@35665
   410
                 [M1, M2], [])
blanchet@33192
   411
blanchet@40994
   412
fun add_mtype_comp cmp M1 M2 cset =
blanchet@40991
   413
  (trace_msg (fn () => "*** Add " ^ string_for_mtype M1 ^ " " ^
blanchet@40991
   414
                       string_for_comp_op cmp ^ " " ^ string_for_mtype M2);
blanchet@40994
   415
   case SOME cset |> do_mtype_comp cmp [] M1 M2 of
blanchet@40991
   416
     NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
blanchet@40994
   417
   | SOME cset => cset)
blanchet@33192
   418
blanchet@35385
   419
val add_mtypes_equal = add_mtype_comp Eq
blanchet@35385
   420
val add_is_sub_mtype = add_mtype_comp Leq
blanchet@33192
   421
blanchet@35385
   422
fun do_notin_mtype_fv _ _ _ NONE = NONE
blanchet@40994
   423
  | do_notin_mtype_fv Minus _ MAlpha cset = cset
blanchet@35385
   424
  | do_notin_mtype_fv Plus [] MAlpha _ = NONE
blanchet@40996
   425
  | do_notin_mtype_fv Plus [asg] MAlpha (SOME clauses) =
blanchet@40996
   426
    clauses |> add_assign_literal asg
blanchet@41000
   427
  | do_notin_mtype_fv Plus unless MAlpha (SOME clauses) =
blanchet@41000
   428
    SOME (insert (op =) unless clauses)
blanchet@41000
   429
  | do_notin_mtype_fv sn unless (MFun (M1, A a, M2)) cset =
blanchet@41000
   430
    cset |> (if a <> Gen andalso sn = Plus then do_notin_mtype_fv Plus unless M1
blanchet@40994
   431
             else I)
blanchet@41000
   432
         |> (if a = Gen orelse sn = Plus then do_notin_mtype_fv Minus unless M1
blanchet@40994
   433
             else I)
blanchet@41000
   434
         |> do_notin_mtype_fv sn unless M2
blanchet@41000
   435
  | do_notin_mtype_fv Plus unless (MFun (M1, V x, M2)) cset =
blanchet@41000
   436
    cset |> (case add_assign_disjunct (x, (Plus, Gen)) (SOME unless) of
blanchet@40994
   437
               NONE => I
blanchet@41000
   438
             | SOME unless' => do_notin_mtype_fv Plus unless' M1)
blanchet@41000
   439
         |> do_notin_mtype_fv Minus unless M1
blanchet@41000
   440
         |> do_notin_mtype_fv Plus unless M2
blanchet@41000
   441
  | do_notin_mtype_fv Minus unless (MFun (M1, V x, M2)) cset =
blanchet@40996
   442
    cset |> (case fold (fn a => add_assign_disjunct (x, (Plus, a))) [Fls, Tru]
blanchet@41000
   443
                       (SOME unless) of
blanchet@40994
   444
               NONE => I
blanchet@41000
   445
             | SOME unless' => do_notin_mtype_fv Plus unless' M1)
blanchet@41000
   446
         |> do_notin_mtype_fv Minus unless M2
blanchet@41000
   447
  | do_notin_mtype_fv sn unless (MPair (M1, M2)) cset =
blanchet@41000
   448
    cset |> fold (do_notin_mtype_fv sn unless) [M1, M2]
blanchet@41000
   449
  | do_notin_mtype_fv sn unless (MType (_, Ms)) cset =
blanchet@41000
   450
    cset |> fold (do_notin_mtype_fv sn unless) Ms
blanchet@40994
   451
 | do_notin_mtype_fv _ _ M _ =
blanchet@40994
   452
   raise MTYPE ("Nitpick_Mono.do_notin_mtype_fv", [M], [])
blanchet@33192
   453
blanchet@41000
   454
fun add_notin_mtype_fv sn unless M (comps, clauses) =
blanchet@40985
   455
  (trace_msg (fn () => "*** Add " ^ string_for_mtype M ^ " is " ^
blanchet@40985
   456
                       (case sn of Minus => "concrete" | Plus => "complete"));
blanchet@41000
   457
   case SOME clauses |> do_notin_mtype_fv sn unless M of
blanchet@40985
   458
     NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
blanchet@40994
   459
   | SOME clauses => (comps, clauses))
blanchet@33192
   460
krauss@41109
   461
fun add_mtype_is_concrete x y z = add_notin_mtype_fv Minus x y z
krauss@41109
   462
fun add_mtype_is_complete x y z = add_notin_mtype_fv Plus x y z
blanchet@33192
   463
blanchet@40986
   464
val bool_table =
blanchet@40986
   465
  [(Gen, (false, false)),
blanchet@40986
   466
   (New, (false, true)),
blanchet@40986
   467
   (Fls, (true, false)),
blanchet@40986
   468
   (Tru, (true, true))]
blanchet@40986
   469
blanchet@40993
   470
fun fst_var n = 2 * n
blanchet@40993
   471
fun snd_var n = 2 * n + 1
blanchet@40993
   472
blanchet@40986
   473
val bools_from_annotation = AList.lookup (op =) bool_table #> the
blanchet@40986
   474
val annotation_from_bools = AList.find (op =) bool_table #> the_single
blanchet@33192
   475
wenzelm@41471
   476
fun prop_for_bool b = if b then Prop_Logic.True else Prop_Logic.False
blanchet@40990
   477
fun prop_for_bool_var_equality (v1, v2) =
blanchet@46081
   478
  Prop_Logic.SAnd (Prop_Logic.SOr (Prop_Logic.BoolVar v1,
blanchet@46081
   479
                                   Prop_Logic.SNot (Prop_Logic.BoolVar v2)),
blanchet@46081
   480
                   Prop_Logic.SOr (Prop_Logic.SNot (Prop_Logic.BoolVar v1),
blanchet@46081
   481
                                   Prop_Logic.BoolVar v2))
blanchet@40996
   482
fun prop_for_assign (x, a) =
blanchet@40986
   483
  let val (b1, b2) = bools_from_annotation a in
wenzelm@41471
   484
    Prop_Logic.SAnd (Prop_Logic.BoolVar (fst_var x) |> not b1 ? Prop_Logic.SNot,
blanchet@46081
   485
                     Prop_Logic.BoolVar (snd_var x) |> not b2 ? Prop_Logic.SNot)
blanchet@40986
   486
  end
blanchet@40996
   487
fun prop_for_assign_literal (x, (Plus, a)) = prop_for_assign (x, a)
blanchet@46081
   488
  | prop_for_assign_literal (x, (Minus, a)) =
blanchet@46081
   489
    Prop_Logic.SNot (prop_for_assign (x, a))
blanchet@40990
   490
fun prop_for_atom_assign (A a', a) = prop_for_bool (a = a')
blanchet@40996
   491
  | prop_for_atom_assign (V x, a) = prop_for_assign_literal (x, (Plus, a))
blanchet@40990
   492
fun prop_for_atom_equality (aa1, A a2) = prop_for_atom_assign (aa1, a2)
blanchet@40990
   493
  | prop_for_atom_equality (A a1, aa2) = prop_for_atom_assign (aa2, a1)
blanchet@40990
   494
  | prop_for_atom_equality (V x1, V x2) =
wenzelm@41471
   495
    Prop_Logic.SAnd (prop_for_bool_var_equality (pairself fst_var (x1, x2)),
blanchet@40999
   496
             prop_for_bool_var_equality (pairself snd_var (x1, x2)))
wenzelm@41471
   497
val prop_for_assign_clause = Prop_Logic.exists o map prop_for_assign_literal
blanchet@40995
   498
fun prop_for_exists_var_assign_literal xs a =
wenzelm@41471
   499
  Prop_Logic.exists (map (fn x => prop_for_assign_literal (x, (Plus, a))) xs)
blanchet@40988
   500
fun prop_for_comp (aa1, aa2, Eq, []) =
wenzelm@41471
   501
    Prop_Logic.SAnd (prop_for_comp (aa1, aa2, Leq, []),
blanchet@40990
   502
             prop_for_comp (aa2, aa1, Leq, []))
blanchet@40996
   503
  | prop_for_comp (aa1, aa2, Neq, []) =
wenzelm@41471
   504
    Prop_Logic.SNot (prop_for_comp (aa1, aa2, Eq, []))
blanchet@40988
   505
  | prop_for_comp (aa1, aa2, Leq, []) =
blanchet@46081
   506
    Prop_Logic.SOr (prop_for_atom_equality (aa1, aa2),
blanchet@46081
   507
                    prop_for_atom_assign (aa2, Gen))
blanchet@40988
   508
  | prop_for_comp (aa1, aa2, cmp, xs) =
wenzelm@41471
   509
    Prop_Logic.SOr (prop_for_exists_var_assign_literal xs Gen,
blanchet@40990
   510
            prop_for_comp (aa1, aa2, cmp, []))
blanchet@33192
   511
blanchet@40990
   512
fun extract_assigns max_var assigns asgs =
blanchet@33192
   513
  fold (fn x => fn accum =>
blanchet@40989
   514
           if AList.defined (op =) asgs x then
blanchet@33192
   515
             accum
blanchet@40986
   516
           else case (fst_var x, snd_var x) |> pairself assigns of
blanchet@40986
   517
             (NONE, NONE) => accum
blanchet@40993
   518
           | bp => (x, annotation_from_bools (pairself (the_default false) bp))
blanchet@40993
   519
                   :: accum)
blanchet@40989
   520
       (max_var downto 1) asgs
blanchet@33192
   521
blanchet@41001
   522
fun print_problem comps clauses =
blanchet@41001
   523
  trace_msg (fn () => "*** Problem:\n" ^
blanchet@41001
   524
                      cat_lines (map string_for_comp comps @
blanchet@41001
   525
                                 map (string_for_assign_clause o SOME) clauses))
blanchet@33192
   526
blanchet@40989
   527
fun print_solution asgs =
blanchet@40989
   528
  trace_msg (fn () => "*** Solution:\n" ^
blanchet@40989
   529
      (asgs
blanchet@40989
   530
       |> map swap
blanchet@40989
   531
       |> AList.group (op =)
blanchet@40989
   532
       |> map (fn (a, xs) => string_for_annotation a ^ ": " ^
blanchet@41005
   533
                             string_for_vars ", " (sort int_ord xs))
blanchet@40989
   534
       |> space_implode "\n"))
blanchet@33192
   535
blanchet@41007
   536
(* The ML solver timeout should correspond more or less to the overhead of
blanchet@41007
   537
   invoking an external prover. *)
blanchet@41007
   538
val ml_solver_timeout = SOME (seconds 0.02)
blanchet@41007
   539
blanchet@41007
   540
fun solve tac_timeout max_var (comps, clauses) =
blanchet@40146
   541
  let
blanchet@41013
   542
    val asgs =
blanchet@41013
   543
      map_filter (fn [(x, (Plus, a))] => SOME (x, a) | _ => NONE) clauses
blanchet@40146
   544
    fun do_assigns assigns =
blanchet@40990
   545
      SOME (extract_assigns max_var assigns asgs |> tap print_solution)
blanchet@41001
   546
    val _ = print_problem comps clauses
blanchet@40993
   547
    val prop =
blanchet@46081
   548
      Prop_Logic.all (map prop_for_comp comps @
blanchet@46081
   549
                      map prop_for_assign_clause clauses)
blanchet@40146
   550
  in
wenzelm@41471
   551
    if Prop_Logic.eval (K false) prop then
blanchet@40990
   552
      do_assigns (K (SOME false))
wenzelm@41471
   553
    else if Prop_Logic.eval (K true) prop then
blanchet@40990
   554
      do_assigns (K (SOME true))
blanchet@40146
   555
    else
blanchet@40146
   556
      let
blanchet@40146
   557
        (* use the first ML solver (to avoid startup overhead) *)
blanchet@41007
   558
        val (ml_solvers, nonml_solvers) =
blanchet@41007
   559
          !SatSolver.solvers
blanchet@41007
   560
          |> List.partition (member (op =) ["dptsat", "dpll"] o fst)
blanchet@41007
   561
        val res =
blanchet@41007
   562
          if null nonml_solvers then
blanchet@41007
   563
            time_limit tac_timeout (snd (hd ml_solvers)) prop
blanchet@41007
   564
          else
blanchet@41007
   565
            time_limit ml_solver_timeout (snd (hd ml_solvers)) prop
blanchet@41007
   566
            handle TimeLimit.TimeOut =>
blanchet@41007
   567
                   time_limit tac_timeout (SatSolver.invoke_solver "auto") prop
blanchet@40146
   568
      in
blanchet@41007
   569
        case res of
blanchet@40146
   570
          SatSolver.SATISFIABLE assigns => do_assigns assigns
blanchet@40994
   571
        | _ => (trace_msg (K "*** Unsolvable"); NONE)
blanchet@40146
   572
      end
blanchet@41007
   573
      handle TimeLimit.TimeOut => (trace_msg (K "*** Timed out"); NONE)
blanchet@40146
   574
  end
blanchet@33192
   575
blanchet@40998
   576
type mcontext =
blanchet@35665
   577
  {bound_Ts: typ list,
blanchet@35665
   578
   bound_Ms: mtyp list,
blanchet@40998
   579
   frame: (int * annotation_atom) list,
blanchet@35385
   580
   frees: (styp * mtyp) list,
blanchet@35385
   581
   consts: (styp * mtyp) list}
blanchet@33192
   582
blanchet@40998
   583
fun string_for_bound ctxt Ms (j, aa) =
blanchet@40998
   584
  Syntax.string_of_term ctxt (Bound (length Ms - j - 1)) ^ " :\<^bsup>" ^
blanchet@40998
   585
  string_for_annotation_atom aa ^ "\<^esup> " ^
blanchet@40998
   586
  string_for_mtype (nth Ms (length Ms - j - 1))
blanchet@40998
   587
fun string_for_free relevant_frees ((s, _), M) =
blanchet@40998
   588
  if member (op =) relevant_frees s then SOME (s ^ " : " ^ string_for_mtype M)
blanchet@40998
   589
  else NONE
krauss@41109
   590
fun string_for_mcontext ctxt t ({bound_Ms, frame, frees, ...} : mcontext) =
blanchet@40998
   591
  (map_filter (string_for_free (Term.add_free_names t [])) frees @
blanchet@40998
   592
   map (string_for_bound ctxt bound_Ms) frame)
blanchet@40998
   593
  |> commas |> enclose "[" "]"
blanchet@33192
   594
blanchet@40987
   595
val initial_gamma =
blanchet@40998
   596
  {bound_Ts = [], bound_Ms = [], frame = [], frees = [], consts = []}
blanchet@33192
   597
blanchet@40998
   598
fun push_bound aa T M {bound_Ts, bound_Ms, frame, frees, consts} =
blanchet@40987
   599
  {bound_Ts = T :: bound_Ts, bound_Ms = M :: bound_Ms,
blanchet@40998
   600
   frame = frame @ [(length bound_Ts, aa)], frees = frees, consts = consts}
blanchet@40998
   601
fun pop_bound {bound_Ts, bound_Ms, frame, frees, consts} =
blanchet@40993
   602
  {bound_Ts = tl bound_Ts, bound_Ms = tl bound_Ms,
blanchet@40998
   603
   frame = frame |> filter_out (fn (j, _) => j = length bound_Ts - 1),
blanchet@40987
   604
   frees = frees, consts = consts}
blanchet@35665
   605
  handle List.Empty => initial_gamma (* FIXME: needed? *)
blanchet@33192
   606
blanchet@40998
   607
fun set_frame frame ({bound_Ts, bound_Ms, frees, consts, ...} : mcontext) =
blanchet@40998
   608
  {bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame, frees = frees,
blanchet@40998
   609
   consts = consts}
blanchet@40994
   610
blanchet@40998
   611
fun add_comp_frame aa cmp = fold (add_annotation_atom_comp cmp [] aa o snd)
blanchet@40994
   612
blanchet@40994
   613
fun add_bound_frame j frame =
blanchet@40994
   614
  let
blanchet@40994
   615
    val (new_frame, gen_frame) = List.partition (curry (op =) j o fst) frame
blanchet@40994
   616
  in
blanchet@40998
   617
    add_comp_frame (A New) Leq new_frame
blanchet@40998
   618
    #> add_comp_frame (A Gen) Eq gen_frame
blanchet@40994
   619
  end
blanchet@40994
   620
blanchet@40997
   621
fun fresh_frame ({max_fresh, ...} : mdata) fls tru =
blanchet@40997
   622
  map (apsnd (fn aa =>
blanchet@40997
   623
                 case (aa, fls, tru) of
blanchet@40997
   624
                   (A Fls, SOME a, _) => A a
blanchet@40997
   625
                 | (A Tru, _, SOME a) => A a
blanchet@40997
   626
                 | (A Gen, _, _) => A Gen
blanchet@40997
   627
                 | _ => V (Unsynchronized.inc max_fresh)))
blanchet@40994
   628
blanchet@40997
   629
fun conj_clauses res_aa aa1 aa2 =
blanchet@40997
   630
  [[(aa1, (Neq, Tru)), (aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
blanchet@40997
   631
   [(aa1, (Neq, Fls)), (res_aa, (Eq, Fls))],
blanchet@40997
   632
   [(aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
blanchet@40997
   633
   [(aa1, (Neq, Gen)), (aa2, (Eq, Fls)), (res_aa, (Eq, Gen))],
blanchet@40997
   634
   [(aa1, (Neq, New)), (aa2, (Eq, Fls)), (res_aa, (Eq, Gen))],
blanchet@40997
   635
   [(aa1, (Eq, Fls)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
blanchet@40997
   636
   [(aa1, (Eq, Fls)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
blanchet@40997
   637
blanchet@40997
   638
fun disj_clauses res_aa aa1 aa2 =
blanchet@40997
   639
  [[(aa1, (Neq, Tru)), (res_aa, (Eq, Tru))],
blanchet@40997
   640
   [(aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
blanchet@40997
   641
   [(aa1, (Neq, Fls)), (aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
blanchet@40997
   642
   [(aa1, (Neq, Gen)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
blanchet@40997
   643
   [(aa1, (Neq, New)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
blanchet@40997
   644
   [(aa1, (Eq, Tru)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
blanchet@40997
   645
   [(aa1, (Eq, Tru)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
blanchet@40994
   646
blanchet@40997
   647
fun imp_clauses res_aa aa1 aa2 =
blanchet@40997
   648
  [[(aa1, (Neq, Fls)), (res_aa, (Eq, Tru))],
blanchet@40997
   649
   [(aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
blanchet@40997
   650
   [(aa1, (Neq, Tru)), (aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
blanchet@40997
   651
   [(aa1, (Neq, Gen)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
blanchet@40997
   652
   [(aa1, (Neq, New)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
blanchet@40997
   653
   [(aa1, (Eq, Fls)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
blanchet@40997
   654
   [(aa1, (Eq, Fls)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
blanchet@40997
   655
blanchet@41054
   656
val meta_conj_spec = ("\<and>", conj_clauses)
blanchet@41054
   657
val meta_imp_spec = ("\<implies>", imp_clauses)
blanchet@41054
   658
val conj_spec = ("\<and>", conj_clauses)
blanchet@41054
   659
val disj_spec = ("\<or>", disj_clauses)
blanchet@41054
   660
val imp_spec = ("\<implies>", imp_clauses)
blanchet@41003
   661
blanchet@40999
   662
fun add_annotation_clause_from_quasi_clause _ NONE = NONE
blanchet@40999
   663
  | add_annotation_clause_from_quasi_clause [] accum = accum
blanchet@40999
   664
  | add_annotation_clause_from_quasi_clause ((aa, (cmp, a)) :: rest) accum =
blanchet@40999
   665
    case aa of
blanchet@40999
   666
      A a' => if annotation_comp cmp a' a then NONE
blanchet@40999
   667
              else add_annotation_clause_from_quasi_clause rest accum
blanchet@40999
   668
    | V x => add_annotation_clause_from_quasi_clause rest accum
blanchet@40999
   669
             |> Option.map (cons (x, (sign_for_comp_op cmp, a)))
blanchet@40995
   670
blanchet@41000
   671
fun assign_clause_from_quasi_clause unless =
blanchet@41000
   672
  add_annotation_clause_from_quasi_clause unless (SOME [])
blanchet@40995
   673
blanchet@40997
   674
fun add_connective_var conn mk_quasi_clauses res_aa aa1 aa2 =
blanchet@40997
   675
  (trace_msg (fn () => "*** Add " ^ string_for_annotation_atom res_aa ^ " = " ^
blanchet@40997
   676
                       string_for_annotation_atom aa1 ^ " " ^ conn ^ " " ^
blanchet@40997
   677
                       string_for_annotation_atom aa2);
blanchet@40999
   678
   fold (add_assign_clause o assign_clause_from_quasi_clause)
blanchet@40999
   679
        (mk_quasi_clauses res_aa aa1 aa2))
blanchet@40997
   680
fun add_connective_frames conn mk_quasi_clauses res_frame frame1 frame2 =
blanchet@40997
   681
  fold I (map3 (fn (_, res_aa) => fn (_, aa1) => fn (_, aa2) =>
blanchet@40997
   682
                   add_connective_var conn mk_quasi_clauses res_aa aa1 aa2)
blanchet@40997
   683
               res_frame frame1 frame2)
blanchet@40995
   684
krauss@41109
   685
fun kill_unused_in_frame is_in (accum as ({frame, ...} : mcontext, _)) =
blanchet@40998
   686
  let val (used_frame, unused_frame) = List.partition is_in frame in
blanchet@40998
   687
    accum |>> set_frame used_frame
blanchet@40998
   688
          ||> add_comp_frame (A Gen) Eq unused_frame
blanchet@40998
   689
  end
blanchet@40998
   690
krauss@41109
   691
fun split_frame is_in_fun (gamma as {frame, ...} : mcontext, cset) =
blanchet@40998
   692
  let
blanchet@40998
   693
    fun bubble fun_frame arg_frame [] cset =
blanchet@40998
   694
        ((rev fun_frame, rev arg_frame), cset)
blanchet@40998
   695
      | bubble fun_frame arg_frame ((bound as (_, aa)) :: rest) cset =
blanchet@40998
   696
        if is_in_fun bound then
blanchet@40998
   697
          bubble (bound :: fun_frame) arg_frame rest
blanchet@40998
   698
                 (cset |> add_comp_frame aa Leq arg_frame)
blanchet@40998
   699
        else
blanchet@40998
   700
          bubble fun_frame (bound :: arg_frame) rest cset
blanchet@40998
   701
  in cset |> bubble [] [] frame ||> pair gamma end
blanchet@40998
   702
blanchet@40998
   703
fun add_annotation_atom_comp_alt _ (A Gen) _ _ = I
blanchet@40998
   704
  | add_annotation_atom_comp_alt _ (A _) _ _ =
blanchet@40998
   705
    (trace_msg (K "*** Expected G"); raise UNSOLVABLE ())
blanchet@40998
   706
  | add_annotation_atom_comp_alt cmp (V x) aa1 aa2 =
blanchet@40998
   707
    add_annotation_atom_comp cmp [x] aa1 aa2
blanchet@40998
   708
blanchet@40999
   709
fun add_arg_order1 ((_, aa), (_, prev_aa)) = I
blanchet@40998
   710
  add_annotation_atom_comp_alt Neq prev_aa (A Gen) aa
blanchet@40999
   711
fun add_app1 fun_aa ((_, res_aa), (_, arg_aa)) = I
blanchet@40999
   712
  let
blanchet@40999
   713
    val clause = [(arg_aa, (Eq, New)), (res_aa, (Eq, Gen))]
blanchet@40999
   714
                 |> assign_clause_from_quasi_clause
blanchet@40999
   715
  in
blanchet@40999
   716
    trace_msg (fn () => "*** Add " ^ string_for_assign_clause clause);
blanchet@40999
   717
    apsnd (add_assign_clause clause)
blanchet@40999
   718
    #> add_annotation_atom_comp_alt Leq arg_aa fun_aa res_aa
blanchet@40999
   719
  end
blanchet@40998
   720
fun add_app _ [] [] = I
blanchet@40998
   721
  | add_app fun_aa res_frame arg_frame =
blanchet@40998
   722
    add_comp_frame (A New) Leq arg_frame
blanchet@40998
   723
    #> fold add_arg_order1 (tl arg_frame ~~ (fst (split_last arg_frame)))
blanchet@40998
   724
    #> fold (add_app1 fun_aa) (res_frame ~~ arg_frame)
blanchet@40998
   725
blanchet@41054
   726
fun consider_connective mdata (conn, mk_quasi_clauses) do_t1 do_t2
blanchet@41003
   727
                        (accum as ({frame, ...}, _)) =
blanchet@41003
   728
  let
blanchet@41003
   729
    val frame1 = fresh_frame mdata (SOME Tru) NONE frame
blanchet@41003
   730
    val frame2 = fresh_frame mdata (SOME Fls) NONE frame
blanchet@41003
   731
  in
blanchet@41054
   732
    accum |>> set_frame frame1 |> do_t1
blanchet@41054
   733
          |>> set_frame frame2 |> do_t2
blanchet@41054
   734
          |>> set_frame frame
blanchet@41054
   735
          ||> apsnd (add_connective_frames conn mk_quasi_clauses frame frame1
blanchet@41054
   736
                                           frame2)
blanchet@41003
   737
  end
blanchet@41003
   738
blanchet@39359
   739
fun consider_term (mdata as {hol_ctxt = {thy, ctxt, stds, ...}, alpha_T,
blanchet@39359
   740
                             max_fresh, ...}) =
blanchet@33192
   741
  let
blanchet@37476
   742
    fun is_enough_eta_expanded t =
blanchet@37476
   743
      case strip_comb t of
blanchet@39359
   744
        (Const x, ts) => the_default 0 (arity_of_built_in_const thy stds x)
blanchet@37476
   745
        <= length ts
blanchet@37476
   746
      | _ => true
blanchet@35672
   747
    val mtype_for = fresh_mtype_for_type mdata false
blanchet@46081
   748
    fun mtype_for_set x T = MFun (mtype_for (elem_type T), V x, bool_M)
blanchet@35385
   749
    fun do_all T (gamma, cset) =
blanchet@33192
   750
      let
blanchet@35385
   751
        val abs_M = mtype_for (domain_type (domain_type T))
blanchet@41012
   752
        val x = Unsynchronized.inc max_fresh
blanchet@35386
   753
        val body_M = mtype_for (body_type T)
blanchet@33192
   754
      in
blanchet@41012
   755
        (MFun (MFun (abs_M, V x, body_M), A Gen, body_M),
blanchet@41012
   756
         (gamma, cset |> add_mtype_is_complete [(x, (Plus, Tru))] abs_M))
blanchet@33192
   757
      end
blanchet@33192
   758
    fun do_equals T (gamma, cset) =
blanchet@40997
   759
      let
blanchet@40997
   760
        val M = mtype_for (domain_type T)
blanchet@41014
   761
        val x = Unsynchronized.inc max_fresh
blanchet@40997
   762
      in
blanchet@41014
   763
        (MFun (M, A Gen, MFun (M, V x, mtype_for (nth_range_type 2 T))),
blanchet@41000
   764
         (gamma, cset |> add_mtype_is_concrete [] M
blanchet@41014
   765
                      |> add_annotation_atom_comp Leq [] (A Fls) (V x)))
blanchet@33192
   766
      end
blanchet@33192
   767
    fun do_robust_set_operation T (gamma, cset) =
blanchet@33192
   768
      let
blanchet@33192
   769
        val set_T = domain_type T
blanchet@35385
   770
        val M1 = mtype_for set_T
blanchet@35385
   771
        val M2 = mtype_for set_T
blanchet@35385
   772
        val M3 = mtype_for set_T
blanchet@33192
   773
      in
blanchet@40985
   774
        (MFun (M1, A Gen, MFun (M2, A Gen, M3)),
blanchet@35385
   775
         (gamma, cset |> add_is_sub_mtype M1 M3 |> add_is_sub_mtype M2 M3))
blanchet@33192
   776
      end
blanchet@33192
   777
    fun do_fragile_set_operation T (gamma, cset) =
blanchet@33192
   778
      let
blanchet@33192
   779
        val set_T = domain_type T
blanchet@35385
   780
        val set_M = mtype_for set_T
blanchet@35665
   781
        fun custom_mtype_for (T as Type (@{type_name fun}, [T1, T2])) =
blanchet@35385
   782
            if T = set_T then set_M
blanchet@40985
   783
            else MFun (custom_mtype_for T1, A Gen, custom_mtype_for T2)
blanchet@46081
   784
          | custom_mtype_for (Type (@{type_name set}, [T'])) =
blanchet@46081
   785
            custom_mtype_for (T' --> bool_T)
blanchet@35385
   786
          | custom_mtype_for T = mtype_for T
blanchet@33192
   787
      in
blanchet@41000
   788
        (custom_mtype_for T, (gamma, cset |> add_mtype_is_concrete [] set_M))
blanchet@33192
   789
      end
blanchet@33192
   790
    fun do_pair_constr T accum =
blanchet@35385
   791
      case mtype_for (nth_range_type 2 T) of
blanchet@35385
   792
        M as MPair (a_M, b_M) =>
blanchet@40985
   793
        (MFun (a_M, A Gen, MFun (b_M, A Gen, M)), accum)
blanchet@35665
   794
      | M => raise MTYPE ("Nitpick_Mono.consider_term.do_pair_constr", [M], [])
blanchet@33192
   795
    fun do_nth_pair_sel n T =
blanchet@35385
   796
      case mtype_for (domain_type T) of
blanchet@35385
   797
        M as MPair (a_M, b_M) =>
blanchet@40985
   798
        pair (MFun (M, A Gen, if n = 0 then a_M else b_M))
blanchet@35665
   799
      | M => raise MTYPE ("Nitpick_Mono.consider_term.do_nth_pair_sel", [M], [])
blanchet@41054
   800
    and do_connect spec t1 t2 accum =
blanchet@41054
   801
      (bool_M, consider_connective mdata spec (snd o do_term t1)
blanchet@41054
   802
                                   (snd o do_term t2) accum)
blanchet@40998
   803
    and do_term t
blanchet@40998
   804
            (accum as (gamma as {bound_Ts, bound_Ms, frame, frees, consts},
blanchet@40998
   805
                       cset)) =
blanchet@40998
   806
      (trace_msg (fn () => "  " ^ string_for_mcontext ctxt t gamma ^
blanchet@40998
   807
                           " \<turnstile> " ^ Syntax.string_of_term ctxt t ^
blanchet@40998
   808
                           " : _?");
blanchet@40993
   809
       case t of
blanchet@41054
   810
         @{const False} => (bool_M, accum ||> add_comp_frame (A Fls) Leq frame)
blanchet@41018
   811
       | Const (@{const_name None}, T) =>
blanchet@41054
   812
         (mtype_for T, accum ||> add_comp_frame (A Fls) Leq frame)
blanchet@41054
   813
       | @{const True} => (bool_M, accum ||> add_comp_frame (A Tru) Leq frame)
blanchet@41016
   814
       | (t0 as Const (@{const_name HOL.eq}, _)) $ Bound 0 $ t2 =>
blanchet@41016
   815
         (* hack to exploit symmetry of equality when typing "insert" *)
blanchet@41016
   816
         (if t2 = Bound 0 then do_term @{term True}
blanchet@41016
   817
          else do_term (t0 $ t2 $ Bound 0)) accum
blanchet@40994
   818
       | Const (x as (s, T)) =>
blanchet@40993
   819
         (case AList.lookup (op =) consts x of
blanchet@40993
   820
            SOME M => (M, accum)
blanchet@40993
   821
          | NONE =>
blanchet@40994
   822
            if not (could_exist_alpha_subtype alpha_T T) then
blanchet@40994
   823
              (mtype_for T, accum)
blanchet@40994
   824
            else case s of
blanchet@40994
   825
              @{const_name all} => do_all T accum
blanchet@40994
   826
            | @{const_name "=="} => do_equals T accum
blanchet@40994
   827
            | @{const_name All} => do_all T accum
blanchet@40994
   828
            | @{const_name Ex} =>
blanchet@40994
   829
              let val set_T = domain_type T in
blanchet@40994
   830
                do_term (Abs (Name.uu, set_T,
blanchet@40994
   831
                              @{const Not} $ (HOLogic.mk_eq
blanchet@40994
   832
                                  (Abs (Name.uu, domain_type set_T,
blanchet@40994
   833
                                        @{const False}),
blanchet@40994
   834
                                   Bound 0)))) accum
blanchet@40994
   835
              end
blanchet@40994
   836
            | @{const_name HOL.eq} => do_equals T accum
blanchet@40994
   837
            | @{const_name The} =>
blanchet@40994
   838
              (trace_msg (K "*** The"); raise UNSOLVABLE ())
blanchet@40994
   839
            | @{const_name Eps} =>
blanchet@40994
   840
              (trace_msg (K "*** Eps"); raise UNSOLVABLE ())
blanchet@40994
   841
            | @{const_name If} =>
blanchet@40994
   842
              do_robust_set_operation (range_type T) accum
blanchet@40994
   843
              |>> curry3 MFun bool_M (A Gen)
blanchet@40994
   844
            | @{const_name Pair} => do_pair_constr T accum
blanchet@40994
   845
            | @{const_name fst} => do_nth_pair_sel 0 T accum
blanchet@40994
   846
            | @{const_name snd} => do_nth_pair_sel 1 T accum
blanchet@40994
   847
            | @{const_name Id} =>
blanchet@40994
   848
              (MFun (mtype_for (domain_type T), A Gen, bool_M), accum)
blanchet@40994
   849
            | @{const_name converse} =>
blanchet@40994
   850
              let
blanchet@40994
   851
                val x = Unsynchronized.inc max_fresh
blanchet@46081
   852
                val ab_set_M = domain_type T |> mtype_for_set x
blanchet@46081
   853
                val ba_set_M = range_type T |> mtype_for_set x
blanchet@41011
   854
              in
blanchet@41011
   855
                (MFun (ab_set_M, A Gen, ba_set_M),
blanchet@41011
   856
                 accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
blanchet@41011
   857
              end
blanchet@40994
   858
            | @{const_name trancl} => do_fragile_set_operation T accum
blanchet@40994
   859
            | @{const_name rel_comp} =>
blanchet@40994
   860
              let
blanchet@40994
   861
                val x = Unsynchronized.inc max_fresh
blanchet@46081
   862
                val bc_set_M = domain_type T |> mtype_for_set x
blanchet@46081
   863
                val ab_set_M = domain_type (range_type T) |> mtype_for_set x
blanchet@46081
   864
                val ac_set_M = nth_range_type 2 T |> mtype_for_set x
blanchet@40994
   865
              in
blanchet@40994
   866
                (MFun (bc_set_M, A Gen, MFun (ab_set_M, A Gen, ac_set_M)),
blanchet@41011
   867
                 accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
blanchet@40994
   868
              end
blanchet@40994
   869
            | @{const_name finite} =>
blanchet@41011
   870
              let
blanchet@46081
   871
                val M1 = mtype_for (elem_type (domain_type T))
blanchet@41011
   872
                val a = if exists_alpha_sub_mtype M1 then Fls else Gen
blanchet@41011
   873
              in (MFun (MFun (M1, A a, bool_M), A Gen, bool_M), accum) end
blanchet@41050
   874
            | @{const_name prod} =>
blanchet@40994
   875
              let
blanchet@40994
   876
                val x = Unsynchronized.inc max_fresh
blanchet@46081
   877
                val a_set_M = domain_type T |> mtype_for_set x
blanchet@40994
   878
                val b_set_M =
blanchet@46081
   879
                  range_type (domain_type (range_type T)) |> mtype_for_set x
blanchet@46081
   880
                val ab_set_M = nth_range_type 2 T |> mtype_for_set x
blanchet@40994
   881
              in
blanchet@41050
   882
                (MFun (a_set_M, A Gen, MFun (b_set_M, A Gen, ab_set_M)),
blanchet@41011
   883
                 accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
blanchet@40994
   884
              end
blanchet@40993
   885
            | _ =>
blanchet@40994
   886
              if s = @{const_name safe_The} then
blanchet@33192
   887
                let
blanchet@40994
   888
                  val a_set_M = mtype_for (domain_type T)
blanchet@40994
   889
                  val a_M = dest_MFun a_set_M |> #1
blanchet@40994
   890
                in (MFun (a_set_M, A Gen, a_M), accum) end
blanchet@40994
   891
              else if s = @{const_name ord_class.less_eq} andalso
blanchet@46081
   892
                      is_set_like_type (domain_type T) then
blanchet@40994
   893
                do_fragile_set_operation T accum
blanchet@40994
   894
              else if is_sel s then
blanchet@40994
   895
                (mtype_for_sel mdata x, accum)
blanchet@40994
   896
              else if is_constr ctxt stds x then
blanchet@40994
   897
                (mtype_for_constr mdata x, accum)
blanchet@40994
   898
              else if is_built_in_const thy stds x then
blanchet@40994
   899
                (fresh_mtype_for_type mdata true T, accum)
blanchet@40994
   900
              else
blanchet@40994
   901
                let val M = mtype_for T in
blanchet@40998
   902
                  (M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame,
blanchet@40998
   903
                        frees = frees, consts = (x, M) :: consts}, cset))
blanchet@40994
   904
                end)
blanchet@40998
   905
           ||> apsnd (add_comp_frame (A Gen) Eq frame)
blanchet@33192
   906
         | Free (x as (_, T)) =>
blanchet@33192
   907
           (case AList.lookup (op =) frees x of
blanchet@35385
   908
              SOME M => (M, accum)
blanchet@33192
   909
            | NONE =>
blanchet@35385
   910
              let val M = mtype_for T in
blanchet@40998
   911
                (M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame,
blanchet@40998
   912
                      frees = (x, M) :: frees, consts = consts}, cset))
blanchet@40994
   913
              end)
blanchet@41054
   914
           ||> apsnd (add_comp_frame (A Gen) Eq frame)
blanchet@38179
   915
         | Var _ => (trace_msg (K "*** Var"); raise UNSOLVABLE ())
blanchet@40994
   916
         | Bound j =>
blanchet@41054
   917
           (nth bound_Ms j,
blanchet@40998
   918
            accum ||> add_bound_frame (length bound_Ts - j - 1) frame)
blanchet@41054
   919
         | Abs (_, T, t') =>
blanchet@35665
   920
           (case fin_fun_body T (fastype_of1 (T :: bound_Ts, t')) t' of
blanchet@35665
   921
              SOME t' =>
blanchet@35665
   922
              let
blanchet@35665
   923
                val M = mtype_for T
blanchet@41014
   924
                val x = Unsynchronized.inc max_fresh
blanchet@41054
   925
                val (M', accum) = do_term t' (accum |>> push_bound (V x) T M)
blanchet@41014
   926
              in
blanchet@41054
   927
                (MFun (M, V x, M'),
blanchet@41014
   928
                 accum |>> pop_bound
blanchet@41014
   929
                       ||> add_annotation_atom_comp Leq [] (A Fls) (V x))
blanchet@41014
   930
              end
blanchet@35665
   931
            | NONE =>
blanchet@35665
   932
              ((case t' of
blanchet@35665
   933
                  t1' $ Bound 0 =>
blanchet@37476
   934
                  if not (loose_bvar1 (t1', 0)) andalso
blanchet@37476
   935
                     is_enough_eta_expanded t1' then
blanchet@35665
   936
                    do_term (incr_boundvars ~1 t1') accum
blanchet@35665
   937
                  else
blanchet@35665
   938
                    raise SAME ()
haftmann@38864
   939
                | (t11 as Const (@{const_name HOL.eq}, _)) $ Bound 0 $ t13 =>
blanchet@37476
   940
                  if not (loose_bvar1 (t13, 0)) then
blanchet@37476
   941
                    do_term (incr_boundvars ~1 (t11 $ t13)) accum
blanchet@37476
   942
                  else
blanchet@37476
   943
                    raise SAME ()
blanchet@35665
   944
                | _ => raise SAME ())
blanchet@35665
   945
               handle SAME () =>
blanchet@35665
   946
                      let
blanchet@35665
   947
                        val M = mtype_for T
blanchet@41014
   948
                        val x = Unsynchronized.inc max_fresh
blanchet@41054
   949
                        val (M', accum) =
blanchet@41014
   950
                          do_term t' (accum |>> push_bound (V x) T M)
blanchet@41054
   951
                      in (MFun (M, V x, M'), accum |>> pop_bound) end))
blanchet@41054
   952
         | @{const Not} $ t1 => do_connect imp_spec t1 @{const False} accum
blanchet@41054
   953
         | @{const conj} $ t1 $ t2 => do_connect conj_spec t1 t2 accum
blanchet@41054
   954
         | @{const disj} $ t1 $ t2 => do_connect disj_spec t1 t2 accum
blanchet@41054
   955
         | @{const implies} $ t1 $ t2 => do_connect imp_spec t1 t2 accum
blanchet@33192
   956
         | Const (@{const_name Let}, _) $ t1 $ t2 =>
blanchet@33192
   957
           do_term (betapply (t2, t1)) accum
blanchet@33192
   958
         | t1 $ t2 =>
blanchet@33192
   959
           let
blanchet@40998
   960
             fun is_in t (j, _) = loose_bvar1 (t, length bound_Ts - j - 1)
blanchet@40998
   961
             val accum as ({frame, ...}, _) =
blanchet@40998
   962
               accum |> kill_unused_in_frame (is_in t)
blanchet@40998
   963
             val ((frame1a, frame1b), accum) = accum |> split_frame (is_in t1)
blanchet@40998
   964
             val frame2a = frame1a |> map (apsnd (K (A Gen)))
blanchet@40998
   965
             val frame2b =
blanchet@40998
   966
               frame1b |> map (apsnd (fn _ => V (Unsynchronized.inc max_fresh)))
blanchet@40998
   967
             val frame2 = frame2a @ frame2b
blanchet@41054
   968
             val (M1, accum) = accum |>> set_frame frame1a |> do_term t1
blanchet@41054
   969
             val (M2, accum) = accum |>> set_frame frame2 |> do_term t2
blanchet@33192
   970
           in
blanchet@35812
   971
             let
blanchet@41054
   972
               val (M11, aa, M12) = M1 |> dest_MFun
blanchet@40998
   973
             in
blanchet@41054
   974
               (M12, accum |>> set_frame frame
blanchet@41054
   975
                           ||> add_is_sub_mtype M2 M11
blanchet@41054
   976
                           ||> add_app aa frame1b frame2b)
blanchet@40998
   977
             end
blanchet@33192
   978
           end)
blanchet@41054
   979
        |> tap (fn (M, (gamma, _)) =>
blanchet@40998
   980
                   trace_msg (fn () => "  " ^ string_for_mcontext ctxt t gamma ^
blanchet@40998
   981
                                       " \<turnstile> " ^
blanchet@41054
   982
                                       Syntax.string_of_term ctxt t ^ " : " ^
blanchet@41054
   983
                                       string_for_mtype M))
blanchet@33192
   984
  in do_term end
blanchet@33192
   985
blanchet@41001
   986
fun force_gen_funs 0 _ = I
blanchet@41001
   987
  | force_gen_funs n (M as MFun (M1, _, M2)) =
blanchet@41001
   988
    add_mtypes_equal M (MFun (M1, A Gen, M2)) #> force_gen_funs (n - 1) M2
blanchet@41001
   989
  | force_gen_funs _ M = raise MTYPE ("Nitpick_Mono.force_gen_funs", [M], [])
blanchet@41054
   990
fun consider_general_equals mdata def t1 t2 accum =
blanchet@35386
   991
  let
blanchet@41054
   992
    val (M1, accum) = consider_term mdata t1 accum
blanchet@41054
   993
    val (M2, accum) = consider_term mdata t2 accum
blanchet@35665
   994
    val accum = accum ||> add_mtypes_equal M1 M2
blanchet@35386
   995
  in
blanchet@41054
   996
    if def then
blanchet@41054
   997
      let
blanchet@41054
   998
        val (head1, args1) = strip_comb t1
blanchet@41054
   999
        val (head_M1, accum) = consider_term mdata head1 accum
blanchet@41054
  1000
      in accum ||> force_gen_funs (length args1) head_M1 end
blanchet@41054
  1001
    else
blanchet@41054
  1002
      accum
blanchet@35386
  1003
  end
blanchet@35386
  1004
blanchet@41000
  1005
fun consider_general_formula (mdata as {hol_ctxt = {ctxt, ...}, max_fresh,
blanchet@41000
  1006
                                        ...}) =
blanchet@33192
  1007
  let
blanchet@35672
  1008
    val mtype_for = fresh_mtype_for_type mdata false
blanchet@41054
  1009
    val do_term = snd oo consider_term mdata
blanchet@40998
  1010
    fun do_formula sn t (accum as (gamma, _)) =
blanchet@41000
  1011
      let
blanchet@41054
  1012
        fun do_quantifier quant_s abs_T body_t =
blanchet@41000
  1013
          let
blanchet@41000
  1014
            val abs_M = mtype_for abs_T
blanchet@41000
  1015
            val x = Unsynchronized.inc max_fresh
blanchet@41000
  1016
            val side_cond = ((sn = Minus) = (quant_s = @{const_name Ex}))
blanchet@41001
  1017
            fun ann () = if quant_s = @{const_name Ex} then Fls else Tru
blanchet@41000
  1018
          in
blanchet@41054
  1019
            accum ||> side_cond
blanchet@41054
  1020
                      ? add_mtype_is_complete [(x, (Plus, ann ()))] abs_M
blanchet@41054
  1021
                  |>> push_bound (V x) abs_T abs_M
blanchet@41054
  1022
                  |> do_formula sn body_t
blanchet@41054
  1023
                  |>> pop_bound
blanchet@41000
  1024
          end
blanchet@41054
  1025
        fun do_connect spec neg1 t1 t2 =
blanchet@41054
  1026
          consider_connective mdata spec
blanchet@41003
  1027
              (do_formula (sn |> neg1 ? negate_sign) t1) (do_formula sn t2)
blanchet@41054
  1028
        fun do_equals t1 t2 =
blanchet@41000
  1029
          case sn of
blanchet@41000
  1030
            Plus => do_term t accum
blanchet@41054
  1031
          | Minus => consider_general_equals mdata false t1 t2 accum
blanchet@41000
  1032
      in
blanchet@41004
  1033
        trace_msg (fn () => "  " ^ string_for_mcontext ctxt t gamma ^
blanchet@41004
  1034
                            " \<turnstile> " ^ Syntax.string_of_term ctxt t ^
blanchet@41004
  1035
                            " : o\<^sup>" ^ string_for_sign sn ^ "?");
blanchet@41004
  1036
        case t of
blanchet@41054
  1037
          Const (s as @{const_name all}, _) $ Abs (_, T1, t1) =>
blanchet@41054
  1038
          do_quantifier s T1 t1
blanchet@41054
  1039
        | Const (@{const_name "=="}, _) $ t1 $ t2 => do_equals t1 t2
blanchet@41054
  1040
        | @{const Trueprop} $ t1 => do_formula sn t1 accum
blanchet@41054
  1041
        | Const (s as @{const_name All}, _) $ Abs (_, T1, t1) =>
blanchet@41054
  1042
          do_quantifier s T1 t1
blanchet@41054
  1043
        | Const (s as @{const_name Ex}, T0) $ (t1 as Abs (_, T1, t1')) =>
blanchet@41004
  1044
          (case sn of
blanchet@41054
  1045
             Plus => do_quantifier s T1 t1'
blanchet@41004
  1046
           | Minus =>
blanchet@41054
  1047
             (* FIXME: Needed? *)
blanchet@41004
  1048
             do_term (@{const Not}
blanchet@41004
  1049
                      $ (HOLogic.eq_const (domain_type T0) $ t1
blanchet@41004
  1050
                         $ Abs (Name.uu, T1, @{const False}))) accum)
blanchet@41054
  1051
        | Const (@{const_name HOL.eq}, _) $ t1 $ t2 => do_equals t1 t2
blanchet@41004
  1052
        | Const (@{const_name Let}, _) $ t1 $ t2 =>
blanchet@41004
  1053
          do_formula sn (betapply (t2, t1)) accum
blanchet@41004
  1054
        | @{const Pure.conjunction} $ t1 $ t2 =>
blanchet@41054
  1055
          do_connect meta_conj_spec false t1 t2 accum
blanchet@41054
  1056
        | @{const "==>"} $ t1 $ t2 => do_connect meta_imp_spec true t1 t2 accum
blanchet@41054
  1057
        | @{const Not} $ t1 => do_connect imp_spec true t1 @{const False} accum
blanchet@41054
  1058
        | @{const conj} $ t1 $ t2 => do_connect conj_spec false t1 t2 accum
blanchet@41054
  1059
        | @{const disj} $ t1 $ t2 => do_connect disj_spec false t1 t2 accum
blanchet@41054
  1060
        | @{const implies} $ t1 $ t2 => do_connect imp_spec true t1 t2 accum
blanchet@41004
  1061
        | _ => do_term t accum
blanchet@41000
  1062
      end
blanchet@41054
  1063
      |> tap (fn (gamma, _) =>
blanchet@41000
  1064
                 trace_msg (fn () => string_for_mcontext ctxt t gamma ^
blanchet@41000
  1065
                                     " \<turnstile> " ^
blanchet@41054
  1066
                                     Syntax.string_of_term ctxt t ^
blanchet@41054
  1067
                                     " : o\<^sup>" ^ string_for_sign sn))
blanchet@33192
  1068
  in do_formula end
blanchet@33192
  1069
blanchet@33192
  1070
(* The harmless axiom optimization below is somewhat too aggressive in the face
blanchet@33192
  1071
   of (rather peculiar) user-defined axioms. *)
blanchet@33192
  1072
val harmless_consts =
blanchet@33192
  1073
  [@{const_name ord_class.less}, @{const_name ord_class.less_eq}]
blanchet@33192
  1074
val bounteous_consts = [@{const_name bisim}]
blanchet@33192
  1075
krauss@41109
  1076
fun is_harmless_axiom ({hol_ctxt = {thy, stds, ...}, ...} : mdata) t =
blanchet@35665
  1077
    Term.add_consts t []
blanchet@39359
  1078
    |> filter_out (is_built_in_const thy stds)
blanchet@35665
  1079
    |> (forall (member (op =) harmless_consts o original_name o fst) orf
blanchet@35665
  1080
        exists (member (op =) bounteous_consts o fst))
blanchet@33192
  1081
blanchet@35665
  1082
fun consider_nondefinitional_axiom mdata t =
blanchet@41054
  1083
  if is_harmless_axiom mdata t then I
blanchet@35386
  1084
  else consider_general_formula mdata Plus t
blanchet@33192
  1085
krauss@41109
  1086
fun consider_definitional_axiom (mdata as {hol_ctxt = {ctxt, ...}, ...} : mdata) t =
blanchet@37256
  1087
  if not (is_constr_pattern_formula ctxt t) then
blanchet@35386
  1088
    consider_nondefinitional_axiom mdata t
blanchet@35665
  1089
  else if is_harmless_axiom mdata t then
blanchet@41054
  1090
    I
blanchet@33192
  1091
  else
blanchet@33192
  1092
    let
blanchet@35672
  1093
      val mtype_for = fresh_mtype_for_type mdata false
blanchet@41054
  1094
      val do_term = snd oo consider_term mdata
blanchet@41054
  1095
      fun do_all abs_T body_t accum =
blanchet@41054
  1096
        accum |>> push_bound (A Gen) abs_T (mtype_for abs_T)
blanchet@41054
  1097
              |> do_formula body_t
blanchet@41054
  1098
              |>> pop_bound
blanchet@41054
  1099
      and do_implies t1 t2 = do_term t1 #> do_formula t2
blanchet@35812
  1100
      and do_formula t accum =
blanchet@41002
  1101
        case t of
blanchet@41054
  1102
          Const (@{const_name all}, _) $ Abs (_, T1, t1) => do_all T1 t1 accum
blanchet@41054
  1103
        | @{const Trueprop} $ t1 => do_formula t1 accum
blanchet@41054
  1104
        | Const (@{const_name "=="}, _) $ t1 $ t2 =>
blanchet@41054
  1105
          consider_general_equals mdata true t1 t2 accum
blanchet@41054
  1106
        | @{const "==>"} $ t1 $ t2 => do_implies t1 t2 accum
blanchet@41054
  1107
        | @{const Pure.conjunction} $ t1 $ t2 =>
blanchet@41054
  1108
          fold (do_formula) [t1, t2] accum
blanchet@41054
  1109
        | Const (@{const_name All}, _) $ Abs (_, T1, t1) => do_all T1 t1 accum
blanchet@41054
  1110
        | Const (@{const_name HOL.eq}, _) $ t1 $ t2 =>
blanchet@41054
  1111
          consider_general_equals mdata true t1 t2 accum
blanchet@41054
  1112
        | @{const conj} $ t1 $ t2 => fold (do_formula) [t1, t2] accum
blanchet@41054
  1113
        | @{const implies} $ t1 $ t2 => do_implies t1 t2 accum
blanchet@41002
  1114
        | _ => raise TERM ("Nitpick_Mono.consider_definitional_axiom.\
blanchet@41002
  1115
                           \do_formula", [t])
blanchet@33192
  1116
    in do_formula t end
blanchet@33192
  1117
blanchet@40989
  1118
fun string_for_mtype_of_term ctxt asgs t M =
blanchet@40989
  1119
  Syntax.string_of_term ctxt t ^ " : " ^ string_for_mtype (resolve_mtype asgs M)
blanchet@33192
  1120
blanchet@40998
  1121
fun print_mcontext ctxt asgs ({frees, consts, ...} : mcontext) =
blanchet@38179
  1122
  trace_msg (fn () =>
blanchet@40989
  1123
      map (fn (x, M) => string_for_mtype_of_term ctxt asgs (Free x) M) frees @
blanchet@40989
  1124
      map (fn (x, M) => string_for_mtype_of_term ctxt asgs (Const x) M) consts
blanchet@37476
  1125
      |> cat_lines)
blanchet@33192
  1126
blanchet@41054
  1127
fun formulas_monotonic (hol_ctxt as {ctxt, tac_timeout, ...}) binarize alpha_T
blanchet@41054
  1128
                       (nondef_ts, def_ts) =
blanchet@33192
  1129
  let
blanchet@41054
  1130
    val _ = trace_msg (fn () => "****** Monotonicity analysis: " ^
blanchet@38179
  1131
                                string_for_mtype MAlpha ^ " is " ^
blanchet@38179
  1132
                                Syntax.string_of_typ ctxt alpha_T)
blanchet@41054
  1133
    val mdata as {max_fresh, ...} = initial_mdata hol_ctxt binarize alpha_T
blanchet@41054
  1134
    val (gamma, cset) =
blanchet@41054
  1135
      (initial_gamma, ([], []))
blanchet@41054
  1136
      |> consider_general_formula mdata Plus (hd nondef_ts)
blanchet@41054
  1137
      |> fold (consider_nondefinitional_axiom mdata) (tl nondef_ts)
blanchet@41054
  1138
      |> fold (consider_definitional_axiom mdata) def_ts
blanchet@33192
  1139
  in
blanchet@41007
  1140
    case solve tac_timeout (!max_fresh) cset of
blanchet@41054
  1141
      SOME asgs => (print_mcontext ctxt asgs gamma; true)
blanchet@41054
  1142
    | _ => false
blanchet@33192
  1143
  end
blanchet@41054
  1144
  handle UNSOLVABLE () => false
blanchet@35812
  1145
       | MTYPE (loc, Ms, Ts) =>
blanchet@35665
  1146
         raise BAD (loc, commas (map string_for_mtype Ms @
blanchet@35665
  1147
                                 map (Syntax.string_of_typ ctxt) Ts))
blanchet@35665
  1148
blanchet@33192
  1149
end;