src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
author wenzelm
Wed Feb 12 13:33:05 2014 +0100 (2014-02-12)
changeset 55437 3fd63b92ea3b
parent 54742 7a86358a3c0b
child 55440 721b4561007a
permissions -rw-r--r--
tuned whitespace;
     1 (*  Title:      HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
     2     Author:     Lukas Bulwahn, TU Muenchen
     3 
     4 Auxilary functions for predicate compiler.
     5 *)
     6 
     7 signature PREDICATE_COMPILE_AUX =
     8 sig
     9   (* general functions *)
    10   val apfst3 : ('a -> 'd) -> 'a * 'b * 'c -> 'd * 'b * 'c
    11   val apsnd3 : ('b -> 'd) -> 'a * 'b * 'c -> 'a * 'd * 'c
    12   val aptrd3 : ('c -> 'd) -> 'a * 'b * 'c -> 'a * 'b * 'd
    13   val find_indices : ('a -> bool) -> 'a list -> int list
    14   (* mode *)
    15   datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
    16   val eq_mode : mode * mode -> bool
    17   val mode_ord: mode * mode -> order
    18   val list_fun_mode : mode list -> mode
    19   val strip_fun_mode : mode -> mode list
    20   val dest_fun_mode : mode -> mode list
    21   val dest_tuple_mode : mode -> mode list
    22   val all_modes_of_typ : typ -> mode list
    23   val all_smodes_of_typ : typ -> mode list
    24   val fold_map_aterms_prodT : ('a -> 'a -> 'a) -> (typ -> 'b -> 'a * 'b) -> typ -> 'b -> 'a * 'b
    25   val map_filter_prod : (term -> term option) -> term -> term option
    26   val replace_ho_args : mode -> term list -> term list -> term list
    27   val ho_arg_modes_of : mode -> mode list
    28   val ho_argsT_of : mode -> typ list -> typ list
    29   val ho_args_of : mode -> term list -> term list
    30   val ho_args_of_typ : typ -> term list -> term list
    31   val ho_argsT_of_typ : typ list -> typ list
    32   val split_map_mode : (mode -> term -> term option * term option)
    33     -> mode -> term list -> term list * term list
    34   val split_map_modeT : (mode -> typ -> typ option * typ option)
    35     -> mode -> typ list -> typ list * typ list
    36   val split_mode : mode -> term list -> term list * term list
    37   val split_modeT : mode -> typ list -> typ list * typ list
    38   val string_of_mode : mode -> string
    39   val ascii_string_of_mode : mode -> string
    40   (* premises *)
    41   datatype indprem = Prem of term | Negprem of term | Sidecond of term
    42     | Generator of (string * typ)
    43   val dest_indprem : indprem -> term
    44   val map_indprem : (term -> term) -> indprem -> indprem
    45   (* general syntactic functions *)
    46   val is_equationlike : thm -> bool
    47   val is_pred_equation : thm -> bool
    48   val is_intro : string -> thm -> bool
    49   val is_predT : typ -> bool
    50   val is_constrt : theory -> term -> bool
    51   val is_constr : Proof.context -> string -> bool
    52   val strip_ex : term -> (string * typ) list * term
    53   val focus_ex : term -> Name.context -> ((string * typ) list * term) * Name.context
    54   val strip_all : term -> (string * typ) list * term
    55   val strip_intro_concl : thm -> term * term list
    56   (* introduction rule combinators *)
    57   val map_atoms : (term -> term) -> term -> term
    58   val fold_atoms : (term -> 'a -> 'a) -> term -> 'a -> 'a
    59   val fold_map_atoms : (term -> 'a -> term * 'a) -> term -> 'a -> term * 'a
    60   val maps_premises : (term -> term list) -> term -> term
    61   val map_concl : (term -> term) -> term -> term
    62   val map_term : theory -> (term -> term) -> thm -> thm
    63   (* split theorems of case expressions *)
    64   val prepare_split_thm : Proof.context -> thm -> thm
    65   val find_split_thm : theory -> term -> thm option
    66   (* datastructures and setup for generic compilation *)
    67   datatype compilation_funs = CompilationFuns of {
    68     mk_monadT : typ -> typ,
    69     dest_monadT : typ -> typ,
    70     mk_empty : typ -> term,
    71     mk_single : term -> term,
    72     mk_bind : term * term -> term,
    73     mk_plus : term * term -> term,
    74     mk_if : term -> term,
    75     mk_iterate_upto : typ -> term * term * term -> term,
    76     mk_not : term -> term,
    77     mk_map : typ -> typ -> term -> term -> term
    78   };
    79   val mk_monadT : compilation_funs -> typ -> typ
    80   val dest_monadT : compilation_funs -> typ -> typ
    81   val mk_empty : compilation_funs -> typ -> term
    82   val mk_single : compilation_funs -> term -> term
    83   val mk_bind : compilation_funs -> term * term -> term
    84   val mk_plus : compilation_funs -> term * term -> term
    85   val mk_if : compilation_funs -> term -> term
    86   val mk_iterate_upto : compilation_funs -> typ -> term * term * term -> term
    87   val mk_not : compilation_funs -> term -> term
    88   val mk_map : compilation_funs -> typ -> typ -> term -> term -> term
    89   val funT_of : compilation_funs -> mode -> typ -> typ
    90   (* Different compilations *)
    91   datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
    92     | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq
    93     | Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
    94   val negative_compilation_of : compilation -> compilation
    95   val compilation_for_polarity : bool -> compilation -> compilation
    96   val is_depth_limited_compilation : compilation -> bool
    97   val string_of_compilation : compilation -> string
    98   val compilation_names : (string * compilation) list
    99   val non_random_compilations : compilation list
   100   val random_compilations : compilation list
   101   (* Different options for compiler *)
   102   datatype options = Options of {
   103     expected_modes : (string * mode list) option,
   104     proposed_modes : (string * mode list) list,
   105     proposed_names : ((string * mode) * string) list,
   106     show_steps : bool,
   107     show_proof_trace : bool,
   108     show_intermediate_results : bool,
   109     show_mode_inference : bool,
   110     show_modes : bool,
   111     show_compilation : bool,
   112     show_caught_failures : bool,
   113     show_invalid_clauses : bool,
   114     skip_proof : bool,
   115     no_topmost_reordering : bool,
   116     function_flattening : bool,
   117     fail_safe_function_flattening : bool,
   118     specialise : bool,
   119     no_higher_order_predicate : string list,
   120     inductify : bool,
   121     detect_switches : bool,
   122     smart_depth_limiting : bool,
   123     compilation : compilation
   124   };
   125   val expected_modes : options -> (string * mode list) option
   126   val proposed_modes : options -> string -> mode list option
   127   val proposed_names : options -> string -> mode -> string option
   128   val show_steps : options -> bool
   129   val show_proof_trace : options -> bool
   130   val show_intermediate_results : options -> bool
   131   val show_mode_inference : options -> bool
   132   val show_modes : options -> bool
   133   val show_compilation : options -> bool
   134   val show_caught_failures : options -> bool
   135   val show_invalid_clauses : options -> bool
   136   val skip_proof : options -> bool
   137   val no_topmost_reordering : options -> bool
   138   val function_flattening : options -> bool
   139   val fail_safe_function_flattening : options -> bool
   140   val specialise : options -> bool
   141   val no_higher_order_predicate : options -> string list
   142   val is_inductify : options -> bool
   143   val detect_switches : options -> bool
   144   val smart_depth_limiting : options -> bool
   145   val compilation : options -> compilation
   146   val default_options : options
   147   val bool_options : string list
   148   val print_step : options -> string -> unit
   149   (* conversions *)
   150   val imp_prems_conv : conv -> conv
   151   (* simple transformations *)
   152   val split_conjuncts_in_assms : Proof.context -> thm -> thm
   153   val dest_conjunct_prem : thm -> thm list
   154   val expand_tuples : theory -> thm -> thm
   155   val case_betapply : theory -> term -> term
   156   val eta_contract_ho_arguments : theory -> thm -> thm
   157   val remove_equalities : theory -> thm -> thm
   158   val remove_pointless_clauses : thm -> thm list
   159   val peephole_optimisation : theory -> thm -> thm option
   160   (* auxillary *)
   161   val unify_consts : theory -> term list -> term list -> (term list * term list)
   162   val mk_casesrule : Proof.context -> term -> thm list -> term
   163   val preprocess_intro : theory -> thm -> thm
   164 
   165   val define_quickcheck_predicate :
   166     term -> theory -> (((string * typ) * (string * typ) list) * thm) * theory
   167 end;
   168 
   169 structure Predicate_Compile_Aux : PREDICATE_COMPILE_AUX =
   170 struct
   171 
   172 (* general functions *)
   173 
   174 fun apfst3 f (x, y, z) = (f x, y, z)
   175 fun apsnd3 f (x, y, z) = (x, f y, z)
   176 fun aptrd3 f (x, y, z) = (x, y, f z)
   177 
   178 fun comb_option f (SOME x1, SOME x2) = SOME (f (x1, x2))
   179   | comb_option f (NONE, SOME x2) = SOME x2
   180   | comb_option f (SOME x1, NONE) = SOME x1
   181   | comb_option f (NONE, NONE) = NONE
   182 
   183 fun map2_optional f (x :: xs) (y :: ys) = f x (SOME y) :: (map2_optional f xs ys)
   184   | map2_optional f (x :: xs) [] = (f x NONE) :: (map2_optional f xs [])
   185   | map2_optional f [] [] = []
   186 
   187 fun find_indices f xs =
   188   map_filter (fn (i, true) => SOME i | (_, false) => NONE) (map_index (apsnd f) xs)
   189 
   190 (* mode *)
   191 
   192 datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
   193 
   194 (* equality of instantiatedness with respect to equivalences:
   195   Pair Input Input == Input and Pair Output Output == Output *)
   196 fun eq_mode (Fun (m1, m2), Fun (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
   197   | eq_mode (Pair (m1, m2), Pair (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
   198   | eq_mode (Pair (m1, m2), Input) = eq_mode (m1, Input) andalso eq_mode (m2, Input)
   199   | eq_mode (Pair (m1, m2), Output) = eq_mode (m1, Output) andalso eq_mode (m2, Output)
   200   | eq_mode (Input, Pair (m1, m2)) = eq_mode (Input, m1) andalso eq_mode (Input, m2)
   201   | eq_mode (Output, Pair (m1, m2)) = eq_mode (Output, m1) andalso eq_mode (Output, m2)
   202   | eq_mode (Input, Input) = true
   203   | eq_mode (Output, Output) = true
   204   | eq_mode (Bool, Bool) = true
   205   | eq_mode _ = false
   206 
   207 fun mode_ord (Input, Output) = LESS
   208   | mode_ord (Output, Input) = GREATER
   209   | mode_ord (Input, Input) = EQUAL
   210   | mode_ord (Output, Output) = EQUAL
   211   | mode_ord (Bool, Bool) = EQUAL
   212   | mode_ord (Pair (m1, m2), Pair (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
   213   | mode_ord (Fun (m1, m2), Fun (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
   214 
   215 fun list_fun_mode [] = Bool
   216   | list_fun_mode (m :: ms) = Fun (m, list_fun_mode ms)
   217 
   218 (* name: binder_modes? *)
   219 fun strip_fun_mode (Fun (mode, mode')) = mode :: strip_fun_mode mode'
   220   | strip_fun_mode Bool = []
   221   | strip_fun_mode _ = raise Fail "Bad mode for strip_fun_mode"
   222 
   223 (* name: strip_fun_mode? *)
   224 fun dest_fun_mode (Fun (mode, mode')) = mode :: dest_fun_mode mode'
   225   | dest_fun_mode mode = [mode]
   226 
   227 fun dest_tuple_mode (Pair (mode, mode')) = mode :: dest_tuple_mode mode'
   228   | dest_tuple_mode _ = []
   229 
   230 fun all_modes_of_typ' (T as Type ("fun", _)) =
   231   let
   232     val (S, U) = strip_type T
   233   in
   234     if U = HOLogic.boolT then
   235       fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
   236         (map all_modes_of_typ' S) [Bool]
   237     else
   238       [Input, Output]
   239   end
   240   | all_modes_of_typ' (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   241     map_product (curry Pair) (all_modes_of_typ' T1) (all_modes_of_typ' T2)
   242   | all_modes_of_typ' _ = [Input, Output]
   243 
   244 fun all_modes_of_typ (T as Type ("fun", _)) =
   245     let
   246       val (S, U) = strip_type T
   247     in
   248       if U = @{typ bool} then
   249         fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
   250           (map all_modes_of_typ' S) [Bool]
   251       else
   252         raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
   253     end
   254   | all_modes_of_typ @{typ bool} = [Bool]
   255   | all_modes_of_typ _ =
   256     raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
   257 
   258 fun all_smodes_of_typ (T as Type ("fun", _)) =
   259   let
   260     val (S, U) = strip_type T
   261     fun all_smodes (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   262       map_product (curry Pair) (all_smodes T1) (all_smodes T2)
   263       | all_smodes _ = [Input, Output]
   264   in
   265     if U = HOLogic.boolT then
   266       fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2) (map all_smodes S) [Bool]
   267     else
   268       raise Fail "invalid type for predicate"
   269   end
   270 
   271 fun ho_arg_modes_of mode =
   272   let
   273     fun ho_arg_mode (m as Fun _) =  [m]
   274       | ho_arg_mode (Pair (m1, m2)) = ho_arg_mode m1 @ ho_arg_mode m2
   275       | ho_arg_mode _ = []
   276   in
   277     maps ho_arg_mode (strip_fun_mode mode)
   278   end
   279 
   280 fun ho_args_of mode ts =
   281   let
   282     fun ho_arg (Fun _) (SOME t) = [t]
   283       | ho_arg (Fun _) NONE = raise Fail "mode and term do not match"
   284       | ho_arg (Pair (m1, m2)) (SOME (Const (@{const_name Pair}, _) $ t1 $ t2)) =
   285           ho_arg m1 (SOME t1) @ ho_arg m2 (SOME t2)
   286       | ho_arg (Pair (m1, m2)) NONE = ho_arg m1 NONE @ ho_arg m2 NONE
   287       | ho_arg _ _ = []
   288   in
   289     flat (map2_optional ho_arg (strip_fun_mode mode) ts)
   290   end
   291 
   292 fun ho_args_of_typ T ts =
   293   let
   294     fun ho_arg (T as Type ("fun", [_, _])) (SOME t) =
   295           if body_type T = @{typ bool} then [t] else []
   296       | ho_arg (Type ("fun", [_, _])) NONE = raise Fail "mode and term do not match"
   297       | ho_arg (Type(@{type_name "Product_Type.prod"}, [T1, T2]))
   298          (SOME (Const (@{const_name Pair}, _) $ t1 $ t2)) =
   299           ho_arg T1 (SOME t1) @ ho_arg T2 (SOME t2)
   300       | ho_arg (Type(@{type_name "Product_Type.prod"}, [T1, T2])) NONE =
   301           ho_arg T1 NONE @ ho_arg T2 NONE
   302       | ho_arg _ _ = []
   303   in
   304     flat (map2_optional ho_arg (binder_types T) ts)
   305   end
   306 
   307 fun ho_argsT_of_typ Ts =
   308   let
   309     fun ho_arg (T as Type("fun", [_,_])) = if body_type T = @{typ bool} then [T] else []
   310       | ho_arg (Type (@{type_name "Product_Type.prod"}, [T1, T2])) =
   311           ho_arg T1 @ ho_arg T2
   312       | ho_arg _ = []
   313   in
   314     maps ho_arg Ts
   315   end
   316 
   317 
   318 (* temporary function should be replaced by unsplit_input or so? *)
   319 fun replace_ho_args mode hoargs ts =
   320   let
   321     fun replace (Fun _, _) (arg' :: hoargs') = (arg', hoargs')
   322       | replace (Pair (m1, m2), Const (@{const_name Pair}, T) $ t1 $ t2) hoargs =
   323           let
   324             val (t1', hoargs') = replace (m1, t1) hoargs
   325             val (t2', hoargs'') = replace (m2, t2) hoargs'
   326           in
   327             (Const (@{const_name Pair}, T) $ t1' $ t2', hoargs'')
   328           end
   329       | replace (_, t) hoargs = (t, hoargs)
   330   in
   331     fst (fold_map replace (strip_fun_mode mode ~~ ts) hoargs)
   332   end
   333 
   334 fun ho_argsT_of mode Ts =
   335   let
   336     fun ho_arg (Fun _) T = [T]
   337       | ho_arg (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   338           ho_arg m1 T1 @ ho_arg m2 T2
   339       | ho_arg _ _ = []
   340   in
   341     flat (map2 ho_arg (strip_fun_mode mode) Ts)
   342   end
   343 
   344 (* splits mode and maps function to higher-order argument types *)
   345 fun split_map_mode f mode ts =
   346   let
   347     fun split_arg_mode' (m as Fun _) t = f m t
   348       | split_arg_mode' (Pair (m1, m2)) (Const (@{const_name Pair}, _) $ t1 $ t2) =
   349         let
   350           val (i1, o1) = split_arg_mode' m1 t1
   351           val (i2, o2) = split_arg_mode' m2 t2
   352         in
   353           (comb_option HOLogic.mk_prod (i1, i2), comb_option HOLogic.mk_prod (o1, o2))
   354         end
   355       | split_arg_mode' m t =
   356         if eq_mode (m, Input) then (SOME t, NONE)
   357         else if eq_mode (m, Output) then (NONE,  SOME t)
   358         else raise Fail "split_map_mode: mode and term do not match"
   359   in
   360     (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) ts)
   361   end
   362 
   363 (* splits mode and maps function to higher-order argument types *)
   364 fun split_map_modeT f mode Ts =
   365   let
   366     fun split_arg_mode' (m as Fun _) T = f m T
   367       | split_arg_mode' (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   368         let
   369           val (i1, o1) = split_arg_mode' m1 T1
   370           val (i2, o2) = split_arg_mode' m2 T2
   371         in
   372           (comb_option HOLogic.mk_prodT (i1, i2), comb_option HOLogic.mk_prodT (o1, o2))
   373         end
   374       | split_arg_mode' Input T = (SOME T, NONE)
   375       | split_arg_mode' Output T = (NONE,  SOME T)
   376       | split_arg_mode' _ _ = raise Fail "split_modeT': mode and type do not match"
   377   in
   378     (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
   379   end
   380 
   381 fun split_mode mode ts = split_map_mode (fn _ => fn _ => (NONE, NONE)) mode ts
   382 
   383 fun fold_map_aterms_prodT comb f (Type (@{type_name Product_Type.prod}, [T1, T2])) s =
   384       let
   385         val (x1, s') = fold_map_aterms_prodT comb f T1 s
   386         val (x2, s'') = fold_map_aterms_prodT comb f T2 s'
   387       in
   388         (comb x1 x2, s'')
   389       end
   390   | fold_map_aterms_prodT _ f T s = f T s
   391 
   392 fun map_filter_prod f (Const (@{const_name Pair}, _) $ t1 $ t2) =
   393       comb_option HOLogic.mk_prod (map_filter_prod f t1, map_filter_prod f t2)
   394   | map_filter_prod f t = f t
   395 
   396 fun split_modeT mode Ts =
   397   let
   398     fun split_arg_mode (Fun _) _ = ([], [])
   399       | split_arg_mode (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   400           let
   401             val (i1, o1) = split_arg_mode m1 T1
   402             val (i2, o2) = split_arg_mode m2 T2
   403           in
   404             (i1 @ i2, o1 @ o2)
   405           end
   406       | split_arg_mode Input T = ([T], [])
   407       | split_arg_mode Output T = ([], [T])
   408       | split_arg_mode _ _ = raise Fail "split_modeT: mode and type do not match"
   409   in
   410     (pairself flat o split_list) (map2 split_arg_mode (strip_fun_mode mode) Ts)
   411   end
   412 
   413 fun string_of_mode mode =
   414   let
   415     fun string_of_mode1 Input = "i"
   416       | string_of_mode1 Output = "o"
   417       | string_of_mode1 Bool = "bool"
   418       | string_of_mode1 mode = "(" ^ (string_of_mode3 mode) ^ ")"
   419     and string_of_mode2 (Pair (m1, m2)) = string_of_mode3 m1 ^ " * " ^  string_of_mode2 m2
   420       | string_of_mode2 mode = string_of_mode1 mode
   421     and string_of_mode3 (Fun (m1, m2)) = string_of_mode2 m1 ^ " => " ^ string_of_mode3 m2
   422       | string_of_mode3 mode = string_of_mode2 mode
   423   in string_of_mode3 mode end
   424 
   425 fun ascii_string_of_mode mode' =
   426   let
   427     fun ascii_string_of_mode' Input = "i"
   428       | ascii_string_of_mode' Output = "o"
   429       | ascii_string_of_mode' Bool = "b"
   430       | ascii_string_of_mode' (Pair (m1, m2)) =
   431           "P" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
   432       | ascii_string_of_mode' (Fun (m1, m2)) =
   433           "F" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Fun m2 ^ "B"
   434     and ascii_string_of_mode'_Fun (Fun (m1, m2)) =
   435           ascii_string_of_mode' m1 ^ (if m2 = Bool then "" else "_" ^ ascii_string_of_mode'_Fun m2)
   436       | ascii_string_of_mode'_Fun Bool = "B"
   437       | ascii_string_of_mode'_Fun m = ascii_string_of_mode' m
   438     and ascii_string_of_mode'_Pair (Pair (m1, m2)) =
   439           ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
   440       | ascii_string_of_mode'_Pair m = ascii_string_of_mode' m
   441   in ascii_string_of_mode'_Fun mode' end
   442 
   443 
   444 (* premises *)
   445 
   446 datatype indprem =
   447   Prem of term | Negprem of term | Sidecond of term | Generator of (string * typ)
   448 
   449 fun dest_indprem (Prem t) = t
   450   | dest_indprem (Negprem t) = t
   451   | dest_indprem (Sidecond t) = t
   452   | dest_indprem (Generator _) = raise Fail "cannot destruct generator"
   453 
   454 fun map_indprem f (Prem t) = Prem (f t)
   455   | map_indprem f (Negprem t) = Negprem (f t)
   456   | map_indprem f (Sidecond t) = Sidecond (f t)
   457   | map_indprem f (Generator (v, T)) = Generator (dest_Free (f (Free (v, T))))
   458 
   459 
   460 (* general syntactic functions *)
   461 
   462 fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
   463   | is_equationlike_term
   464       (Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) = true
   465   | is_equationlike_term _ = false
   466 
   467 val is_equationlike = is_equationlike_term o prop_of
   468 
   469 fun is_pred_equation_term (Const ("==", _) $ u $ v) =
   470       (fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
   471   | is_pred_equation_term _ = false
   472 
   473 val is_pred_equation = is_pred_equation_term o prop_of
   474 
   475 fun is_intro_term constname t =
   476   the_default false (try (fn t =>
   477     case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
   478       Const (c, _) => c = constname
   479     | _ => false) t)
   480 
   481 fun is_intro constname t = is_intro_term constname (prop_of t)
   482 
   483 fun is_predT (T as Type("fun", [_, _])) = (body_type T = @{typ bool})
   484   | is_predT _ = false
   485 
   486 (*** check if a term contains only constructor functions ***)
   487 (* TODO: another copy in the core! *)
   488 (* FIXME: constructor terms are supposed to be seen in the way the code generator
   489   sees constructors.*)
   490 fun is_constrt thy =
   491   let
   492     val cnstrs = flat (maps
   493       (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
   494       (Symtab.dest (Datatype.get_all thy)));
   495     fun check t =
   496       (case strip_comb t of
   497         (Var _, []) => true
   498       | (Free _, []) => true
   499       | (Const (s, T), ts) =>
   500           (case (AList.lookup (op =) cnstrs s, body_type T) of
   501             (SOME (i, Tname), Type (Tname', _)) =>
   502               length ts = i andalso Tname = Tname' andalso forall check ts
   503           | _ => false)
   504       | _ => false)
   505   in check end
   506 
   507 (* returns true if t is an application of an datatype constructor *)
   508 (* which then consequently would be splitted *)
   509 (* else false *)
   510 (*
   511 fun is_constructor thy t =
   512   if (is_Type (fastype_of t)) then
   513     (case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
   514       NONE => false
   515     | SOME info => (let
   516       val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
   517       val (c, _) = strip_comb t
   518       in (case c of
   519         Const (name, _) => name mem_string constr_consts
   520         | _ => false) end))
   521   else false
   522 *)
   523 
   524 val is_constr = Code.is_constr o Proof_Context.theory_of
   525 
   526 fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
   527 
   528 fun strip_ex (Const (@{const_name Ex}, _) $ Abs (x, T, t)) =
   529       let
   530         val (xTs, t') = strip_ex t
   531       in
   532         ((x, T) :: xTs, t')
   533       end
   534   | strip_ex t = ([], t)
   535 
   536 fun focus_ex t nctxt =
   537   let
   538     val ((xs, Ts), t') = apfst split_list (strip_ex t)
   539     val (xs', nctxt') = fold_map Name.variant xs nctxt;
   540     val ps' = xs' ~~ Ts;
   541     val vs = map Free ps';
   542     val t'' = Term.subst_bounds (rev vs, t');
   543   in ((ps', t''), nctxt') end
   544 
   545 val strip_intro_concl = strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of
   546 
   547 
   548 (* introduction rule combinators *)
   549 
   550 fun map_atoms f intro =
   551   let
   552     val (literals, head) = Logic.strip_horn intro
   553     fun appl t =
   554       (case t of
   555         (@{term Not} $ t') => HOLogic.mk_not (f t')
   556       | _ => f t)
   557   in
   558     Logic.list_implies
   559       (map (HOLogic.mk_Trueprop o appl o HOLogic.dest_Trueprop) literals, head)
   560   end
   561 
   562 fun fold_atoms f intro s =
   563   let
   564     val (literals, _) = Logic.strip_horn intro
   565     fun appl t s =
   566       (case t of
   567         (@{term Not} $ t') => f t' s
   568       | _ => f t s)
   569   in fold appl (map HOLogic.dest_Trueprop literals) s end
   570 
   571 fun fold_map_atoms f intro s =
   572   let
   573     val (literals, head) = Logic.strip_horn intro
   574     fun appl t s =
   575       (case t of
   576         (@{term Not} $ t') => apfst HOLogic.mk_not (f t' s)
   577       | _ => f t s)
   578     val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
   579   in
   580     (Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
   581   end;
   582 
   583 fun map_filter_premises f intro =
   584   let
   585     val (premises, head) = Logic.strip_horn intro
   586   in
   587     Logic.list_implies (map_filter f premises, head)
   588   end
   589 
   590 fun maps_premises f intro =
   591   let
   592     val (premises, head) = Logic.strip_horn intro
   593   in
   594     Logic.list_implies (maps f premises, head)
   595   end
   596 
   597 fun map_concl f intro =
   598   let
   599     val (premises, head) = Logic.strip_horn intro
   600   in
   601     Logic.list_implies (premises, f head)
   602   end
   603 
   604 
   605 (* combinators to apply a function to all basic parts of nested products *)
   606 
   607 fun map_products f (Const (@{const_name Pair}, T) $ t1 $ t2) =
   608   Const (@{const_name Pair}, T) $ map_products f t1 $ map_products f t2
   609   | map_products f t = f t
   610 
   611 
   612 (* split theorems of case expressions *)
   613 
   614 fun prepare_split_thm ctxt split_thm =
   615     (split_thm RS @{thm iffD2})
   616     |> Local_Defs.unfold ctxt [@{thm atomize_conjL[symmetric]},
   617       @{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
   618 
   619 fun find_split_thm thy (Const (name, _)) = Option.map #split (Datatype.info_of_case thy name)
   620   | find_split_thm _ _ = NONE
   621 
   622 
   623 (* lifting term operations to theorems *)
   624 
   625 fun map_term thy f th =
   626   Skip_Proof.make_thm thy (f (prop_of th))
   627 
   628 (*
   629 fun equals_conv lhs_cv rhs_cv ct =
   630   case Thm.term_of ct of
   631     Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct
   632   | _ => error "equals_conv"
   633 *)
   634 
   635 
   636 (* Different compilations *)
   637 
   638 datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
   639   | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq |
   640     Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
   641 
   642 fun negative_compilation_of Pos_Random_DSeq = Neg_Random_DSeq
   643   | negative_compilation_of Neg_Random_DSeq = Pos_Random_DSeq
   644   | negative_compilation_of New_Pos_Random_DSeq = New_Neg_Random_DSeq
   645   | negative_compilation_of New_Neg_Random_DSeq = New_Pos_Random_DSeq
   646   | negative_compilation_of Pos_Generator_DSeq = Neg_Generator_DSeq
   647   | negative_compilation_of Neg_Generator_DSeq = Pos_Generator_DSeq
   648   | negative_compilation_of Pos_Generator_CPS = Neg_Generator_CPS
   649   | negative_compilation_of Neg_Generator_CPS = Pos_Generator_CPS
   650   | negative_compilation_of c = c
   651 
   652 fun compilation_for_polarity false Pos_Random_DSeq = Neg_Random_DSeq
   653   | compilation_for_polarity false New_Pos_Random_DSeq = New_Neg_Random_DSeq
   654   | compilation_for_polarity _ c = c
   655 
   656 fun is_depth_limited_compilation c =
   657   (c = New_Pos_Random_DSeq) orelse (c = New_Neg_Random_DSeq) orelse
   658   (c = Pos_Generator_DSeq) orelse (c = Pos_Generator_DSeq)
   659 
   660 fun string_of_compilation c =
   661   (case c of
   662     Pred => ""
   663   | Random => "random"
   664   | Depth_Limited => "depth limited"
   665   | Depth_Limited_Random => "depth limited random"
   666   | DSeq => "dseq"
   667   | Annotated => "annotated"
   668   | Pos_Random_DSeq => "pos_random dseq"
   669   | Neg_Random_DSeq => "neg_random_dseq"
   670   | New_Pos_Random_DSeq => "new_pos_random dseq"
   671   | New_Neg_Random_DSeq => "new_neg_random_dseq"
   672   | Pos_Generator_DSeq => "pos_generator_dseq"
   673   | Neg_Generator_DSeq => "neg_generator_dseq"
   674   | Pos_Generator_CPS => "pos_generator_cps"
   675   | Neg_Generator_CPS => "neg_generator_cps")
   676 
   677 val compilation_names =
   678  [("pred", Pred),
   679   ("random", Random),
   680   ("depth_limited", Depth_Limited),
   681   ("depth_limited_random", Depth_Limited_Random),
   682   (*("annotated", Annotated),*)
   683   ("dseq", DSeq),
   684   ("random_dseq", Pos_Random_DSeq),
   685   ("new_random_dseq", New_Pos_Random_DSeq),
   686   ("generator_dseq", Pos_Generator_DSeq),
   687   ("generator_cps", Pos_Generator_CPS)]
   688 
   689 val non_random_compilations = [Pred, Depth_Limited, DSeq, Annotated]
   690 
   691 
   692 val random_compilations = [Random, Depth_Limited_Random,
   693   Pos_Random_DSeq, Neg_Random_DSeq, New_Pos_Random_DSeq, New_Neg_Random_DSeq,
   694   Pos_Generator_CPS, Neg_Generator_CPS]
   695 
   696 
   697 (* datastructures and setup for generic compilation *)
   698 
   699 datatype compilation_funs = CompilationFuns of {
   700   mk_monadT : typ -> typ,
   701   dest_monadT : typ -> typ,
   702   mk_empty : typ -> term,
   703   mk_single : term -> term,
   704   mk_bind : term * term -> term,
   705   mk_plus : term * term -> term,
   706   mk_if : term -> term,
   707   mk_iterate_upto : typ -> term * term * term -> term,
   708   mk_not : term -> term,
   709   mk_map : typ -> typ -> term -> term -> term
   710 }
   711 
   712 fun mk_monadT (CompilationFuns funs) = #mk_monadT funs
   713 fun dest_monadT (CompilationFuns funs) = #dest_monadT funs
   714 fun mk_empty (CompilationFuns funs) = #mk_empty funs
   715 fun mk_single (CompilationFuns funs) = #mk_single funs
   716 fun mk_bind (CompilationFuns funs) = #mk_bind funs
   717 fun mk_plus (CompilationFuns funs) = #mk_plus funs
   718 fun mk_if (CompilationFuns funs) = #mk_if funs
   719 fun mk_iterate_upto (CompilationFuns funs) = #mk_iterate_upto funs
   720 fun mk_not (CompilationFuns funs) = #mk_not funs
   721 fun mk_map (CompilationFuns funs) = #mk_map funs
   722 
   723 
   724 (** function types and names of different compilations **)
   725 
   726 fun funT_of compfuns mode T =
   727   let
   728     val Ts = binder_types T
   729     val (inTs, outTs) =
   730       split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
   731   in
   732     inTs ---> (mk_monadT compfuns (HOLogic.mk_tupleT outTs))
   733   end
   734 
   735 
   736 (* Different options for compiler *)
   737 
   738 datatype options = Options of {
   739   expected_modes : (string * mode list) option,
   740   proposed_modes : (string * mode list) list,
   741   proposed_names : ((string * mode) * string) list,
   742   show_steps : bool,
   743   show_proof_trace : bool,
   744   show_intermediate_results : bool,
   745   show_mode_inference : bool,
   746   show_modes : bool,
   747   show_compilation : bool,
   748   show_caught_failures : bool,
   749   show_invalid_clauses : bool,
   750   skip_proof : bool,
   751   no_topmost_reordering : bool,
   752   function_flattening : bool,
   753   specialise : bool,
   754   fail_safe_function_flattening : bool,
   755   no_higher_order_predicate : string list,
   756   inductify : bool,
   757   detect_switches : bool,
   758   smart_depth_limiting : bool,
   759   compilation : compilation
   760 }
   761 
   762 fun expected_modes (Options opt) = #expected_modes opt
   763 fun proposed_modes (Options opt) = AList.lookup (op =) (#proposed_modes opt)
   764 fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode)
   765   (#proposed_names opt) (name, mode)
   766 
   767 fun show_steps (Options opt) = #show_steps opt
   768 fun show_intermediate_results (Options opt) = #show_intermediate_results opt
   769 fun show_proof_trace (Options opt) = #show_proof_trace opt
   770 fun show_modes (Options opt) = #show_modes opt
   771 fun show_mode_inference (Options opt) = #show_mode_inference opt
   772 fun show_compilation (Options opt) = #show_compilation opt
   773 fun show_caught_failures (Options opt) = #show_caught_failures opt
   774 fun show_invalid_clauses (Options opt) = #show_invalid_clauses opt
   775 fun skip_proof (Options opt) = #skip_proof opt
   776 
   777 fun function_flattening (Options opt) = #function_flattening opt
   778 fun fail_safe_function_flattening (Options opt) = #fail_safe_function_flattening opt
   779 fun specialise (Options opt) = #specialise opt
   780 fun no_topmost_reordering (Options opt) = #no_topmost_reordering opt
   781 fun no_higher_order_predicate (Options opt) = #no_higher_order_predicate opt
   782 
   783 fun is_inductify (Options opt) = #inductify opt
   784 
   785 fun compilation (Options opt) = #compilation opt
   786 
   787 fun detect_switches (Options opt) = #detect_switches opt
   788 
   789 fun smart_depth_limiting (Options opt) = #smart_depth_limiting opt
   790 
   791 val default_options = Options {
   792   expected_modes = NONE,
   793   proposed_modes = [],
   794   proposed_names = [],
   795   show_steps = false,
   796   show_intermediate_results = false,
   797   show_proof_trace = false,
   798   show_modes = false,
   799   show_mode_inference = false,
   800   show_compilation = false,
   801   show_caught_failures = false,
   802   show_invalid_clauses = false,
   803   skip_proof = true,
   804   no_topmost_reordering = false,
   805   function_flattening = false,
   806   specialise = false,
   807   fail_safe_function_flattening = false,
   808   no_higher_order_predicate = [],
   809   inductify = false,
   810   detect_switches = true,
   811   smart_depth_limiting = false,
   812   compilation = Pred
   813 }
   814 
   815 val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
   816   "show_mode_inference", "show_compilation", "show_invalid_clauses", "skip_proof", "inductify",
   817   "no_function_flattening", "detect_switches", "specialise", "no_topmost_reordering",
   818   "smart_depth_limiting"]
   819 
   820 fun print_step options s =
   821   if show_steps options then tracing s else ()
   822 
   823 
   824 (* simple transformations *)
   825 
   826 (** tuple processing **)
   827 
   828 fun rewrite_args [] (pats, intro_t, ctxt) = (pats, intro_t, ctxt)
   829   | rewrite_args (arg::args) (pats, intro_t, ctxt) =
   830       (case HOLogic.strip_tupleT (fastype_of arg) of
   831         (_ :: _ :: _) =>
   832         let
   833           fun rewrite_arg'
   834                 (Const (@{const_name Pair}, _) $ _ $ t2, Type (@{type_name Product_Type.prod}, [_, T2]))
   835                 (args, (pats, intro_t, ctxt)) =
   836                 rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
   837             | rewrite_arg'
   838                 (t, Type (@{type_name Product_Type.prod}, [T1, T2])) (args, (pats, intro_t, ctxt)) =
   839                 let
   840                   val thy = Proof_Context.theory_of ctxt
   841                   val ([x, y], ctxt') = Variable.variant_fixes ["x", "y"] ctxt
   842                   val pat = (t, HOLogic.mk_prod (Free (x, T1), Free (y, T2)))
   843                   val intro_t' = Pattern.rewrite_term thy [pat] [] intro_t
   844                   val args' = map (Pattern.rewrite_term thy [pat] []) args
   845                 in
   846                   rewrite_arg' (Free (y, T2), T2) (args', (pat::pats, intro_t', ctxt'))
   847                 end
   848             | rewrite_arg' _ (args, (pats, intro_t, ctxt)) = (args, (pats, intro_t, ctxt))
   849           val (args', (pats, intro_t', ctxt')) =
   850             rewrite_arg' (arg, fastype_of arg) (args, (pats, intro_t, ctxt))
   851         in
   852           rewrite_args args' (pats, intro_t', ctxt')
   853         end
   854   | _ => rewrite_args args (pats, intro_t, ctxt))
   855 
   856 fun rewrite_prem atom =
   857   let
   858     val (_, args) = strip_comb atom
   859   in rewrite_args args end
   860 
   861 fun split_conjuncts_in_assms ctxt th =
   862   let
   863     val ((_, [fixed_th]), ctxt') = Variable.import false [th] ctxt
   864     fun split_conjs i nprems th =
   865       if i > nprems then th
   866       else
   867         (case try Drule.RSN (@{thm conjI}, (i, th)) of
   868           SOME th' => split_conjs i (nprems + 1) th'
   869         | NONE => split_conjs (i + 1) nprems th)
   870   in
   871     singleton (Variable.export ctxt' ctxt)
   872       (split_conjs 1 (Thm.nprems_of fixed_th) fixed_th)
   873   end
   874 
   875 fun dest_conjunct_prem th =
   876   (case HOLogic.dest_Trueprop (prop_of th) of
   877     (Const (@{const_name HOL.conj}, _) $ _ $ _) =>
   878       dest_conjunct_prem (th RS @{thm conjunct1})
   879         @ dest_conjunct_prem (th RS @{thm conjunct2})
   880    | _ => [th])
   881 
   882 fun expand_tuples thy intro =
   883   let
   884     val ctxt = Proof_Context.init_global thy
   885     val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
   886     val intro_t = prop_of intro'
   887     val concl = Logic.strip_imp_concl intro_t
   888     val (_, args) = strip_comb (HOLogic.dest_Trueprop concl)
   889     val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
   890     val (pats', _, ctxt3) = fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
   891     fun rewrite_pat (ct1, ct2) =
   892       (ct1, cterm_of thy (Pattern.rewrite_term thy pats' [] (term_of ct2)))
   893     val t_insts' = map rewrite_pat t_insts
   894     val intro'' = Thm.instantiate (T_insts, t_insts') intro
   895     val [intro'''] = Variable.export ctxt3 ctxt [intro'']
   896     val intro'''' =
   897       Simplifier.full_simplify
   898         (put_simpset HOL_basic_ss ctxt
   899           addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}])
   900       intro'''
   901     (* splitting conjunctions introduced by Pair_eq*)
   902     val intro''''' = split_conjuncts_in_assms ctxt intro''''
   903   in
   904     intro'''''
   905   end
   906 
   907 
   908 (** making case distributivity rules **)
   909 (*** this should be part of the datatype package ***)
   910 
   911 fun datatype_names_of_case_name thy case_name =
   912   map (#1 o #2) (#descr (the (Datatype.info_of_case thy case_name)))
   913 
   914 fun make_case_distribs case_names descr thy =
   915   let
   916     val case_combs = Datatype_Prop.make_case_combs case_names descr thy "f";
   917     fun make comb =
   918       let
   919         val Type ("fun", [T, T']) = fastype_of comb
   920         val (Const (case_name, _), fs) = strip_comb comb
   921         val used = Term.add_tfree_names comb []
   922         val U = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS)
   923         val x = Free ("x", T)
   924         val f = Free ("f", T' --> U)
   925         fun apply_f f' =
   926           let
   927             val Ts = binder_types (fastype_of f')
   928             val bs = map Bound ((length Ts - 1) downto 0)
   929           in
   930             fold_rev absdummy Ts (f $ (list_comb (f', bs)))
   931           end
   932         val fs' = map apply_f fs
   933         val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U)
   934       in
   935         HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x)
   936       end
   937   in
   938     map make case_combs
   939   end
   940 
   941 fun case_rewrites thy Tcon =
   942   let
   943     val {descr, case_name, ...} = Datatype.the_info thy Tcon
   944   in
   945     map (Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop)
   946       (make_case_distribs [case_name] [descr] thy)
   947   end
   948 
   949 fun instantiated_case_rewrites thy Tcon =
   950   let
   951     val rew_ths = case_rewrites thy Tcon
   952     val ctxt = Proof_Context.init_global thy
   953     fun instantiate th =
   954     let
   955       val f = (fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th))))))
   956       val Type ("fun", [uninst_T, uninst_T']) = fastype_of f
   957       val ([_, tname', uname, yname], ctxt') = Variable.add_fixes ["'t", "'t'", "'u", "y"] ctxt
   958       val T' = TFree (tname', HOLogic.typeS)
   959       val U = TFree (uname, HOLogic.typeS)
   960       val y = Free (yname, U)
   961       val f' = absdummy (U --> T') (Bound 0 $ y)
   962       val th' = Thm.certify_instantiate
   963         ([(dest_TVar uninst_T, U --> T'), (dest_TVar uninst_T', T')],
   964          [((fst (dest_Var f), (U --> T') --> T'), f')]) th
   965       val [th'] = Variable.export ctxt' ctxt [th']
   966    in
   967      th'
   968    end
   969  in
   970    map instantiate rew_ths
   971  end
   972 
   973 fun case_betapply thy t =
   974   let
   975     val case_name = fst (dest_Const (fst (strip_comb t)))
   976     val Tcons = datatype_names_of_case_name thy case_name
   977     val ths = maps (instantiated_case_rewrites thy) Tcons
   978   in
   979     Raw_Simplifier.rewrite_term thy
   980       (map (fn th => th RS @{thm eq_reflection}) ths) [] t
   981   end
   982 
   983 
   984 (*** conversions ***)
   985 
   986 fun imp_prems_conv cv ct =
   987   (case Thm.term_of ct of
   988     Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
   989   | _ => Conv.all_conv ct)
   990 
   991 
   992 (** eta contract higher-order arguments **)
   993 
   994 fun eta_contract_ho_arguments thy intro =
   995   let
   996     fun f atom = list_comb (apsnd ((map o map_products) Envir.eta_contract) (strip_comb atom))
   997   in
   998     map_term thy (map_concl f o map_atoms f) intro
   999   end
  1000 
  1001 
  1002 (** remove equalities **)
  1003 
  1004 fun remove_equalities thy intro =
  1005   let
  1006     fun remove_eqs intro_t =
  1007       let
  1008         val (prems, concl) = Logic.strip_horn intro_t
  1009         fun remove_eq (prems, concl) =
  1010           let
  1011             fun removable_eq prem =
  1012               (case try (HOLogic.dest_eq o HOLogic.dest_Trueprop) prem of
  1013                 SOME (lhs, rhs) =>
  1014                   (case lhs of
  1015                     Var _ => true
  1016                   | _ => (case rhs of Var _ => true | _ => false))
  1017               | NONE => false)
  1018           in
  1019             (case find_first removable_eq prems of
  1020               NONE => (prems, concl)
  1021             | SOME eq =>
  1022                 let
  1023                   val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
  1024                   val prems' = remove (op =) eq prems
  1025                   val subst =
  1026                     (case lhs of
  1027                       (v as Var _) =>
  1028                         (fn t => if t = v then rhs else t)
  1029                     | _ => (case rhs of (v as Var _) => (fn t => if t = v then lhs else t)))
  1030                 in
  1031                   remove_eq (map (map_aterms subst) prems', map_aterms subst concl)
  1032                 end)
  1033           end
  1034       in
  1035         Logic.list_implies (remove_eq (prems, concl))
  1036       end
  1037   in
  1038     map_term thy remove_eqs intro
  1039   end
  1040 
  1041 
  1042 (* Some last processing *)
  1043 
  1044 fun remove_pointless_clauses intro =
  1045   if Logic.strip_imp_prems (prop_of intro) = [@{prop "False"}] then
  1046     []
  1047   else [intro]
  1048 
  1049 
  1050 (* some peephole optimisations *)
  1051 
  1052 fun peephole_optimisation thy intro =
  1053   let
  1054     val ctxt = Proof_Context.init_global thy  (* FIXME proper context!? *)
  1055     val process =
  1056       rewrite_rule ctxt (Predicate_Compile_Simps.get ctxt)
  1057     fun process_False intro_t =
  1058       if member (op =) (Logic.strip_imp_prems intro_t) @{prop "False"}
  1059       then NONE else SOME intro_t
  1060     fun process_True intro_t =
  1061       map_filter_premises (fn p => if p = @{prop True} then NONE else SOME p) intro_t
  1062   in
  1063     Option.map (Skip_Proof.make_thm thy)
  1064       (process_False (process_True (prop_of (process intro))))
  1065   end
  1066 
  1067 
  1068 (* importing introduction rules *)
  1069 
  1070 fun import_intros inp_pred [] ctxt =
  1071       let
  1072         val ([outp_pred], ctxt') = Variable.import_terms true [inp_pred] ctxt
  1073         val T = fastype_of outp_pred
  1074         val paramTs = ho_argsT_of_typ (binder_types T)
  1075         val (param_names, _) = Variable.variant_fixes
  1076           (map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'
  1077         val params = map2 (curry Free) param_names paramTs
  1078       in
  1079         (((outp_pred, params), []), ctxt')
  1080       end
  1081   | import_intros inp_pred (th :: ths) ctxt =
  1082       let
  1083         val ((_, [th']), ctxt') = Variable.import true [th] ctxt
  1084         val thy = Proof_Context.theory_of ctxt'
  1085         val (pred, args) = strip_intro_concl th'
  1086         val T = fastype_of pred
  1087         val ho_args = ho_args_of_typ T args
  1088         fun subst_of (pred', pred) =
  1089           let
  1090             val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty
  1091               handle Type.TYPE_MATCH =>
  1092                 error ("Type mismatch of predicate " ^ fst (dest_Const pred) ^
  1093                   " (trying to match " ^ Syntax.string_of_typ ctxt (fastype_of pred') ^
  1094                   " and " ^ Syntax.string_of_typ ctxt (fastype_of pred) ^ ")" ^
  1095                   " in " ^ Display.string_of_thm ctxt th)
  1096           in map (fn (indexname, (s, T)) => ((indexname, s), T)) (Vartab.dest subst) end
  1097         fun instantiate_typ th =
  1098           let
  1099             val (pred', _) = strip_intro_concl th
  1100             val _ =
  1101               if not (fst (dest_Const pred) = fst (dest_Const pred')) then
  1102                 raise Fail "Trying to instantiate another predicate"
  1103               else ()
  1104           in Thm.certify_instantiate (subst_of (pred', pred), []) th end
  1105         fun instantiate_ho_args th =
  1106           let
  1107             val (_, args') =
  1108               (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of) th
  1109             val ho_args' = map dest_Var (ho_args_of_typ T args')
  1110           in Thm.certify_instantiate ([], ho_args' ~~ ho_args) th end
  1111         val outp_pred =
  1112           Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred
  1113         val ((_, ths'), ctxt1) =
  1114           Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'
  1115       in
  1116         (((outp_pred, ho_args), th' :: ths'), ctxt1)
  1117       end
  1118 
  1119 
  1120 (* generation of case rules from user-given introduction rules *)
  1121 
  1122 fun mk_args2 (Type (@{type_name Product_Type.prod}, [T1, T2])) st =
  1123       let
  1124         val (t1, st') = mk_args2 T1 st
  1125         val (t2, st'') = mk_args2 T2 st'
  1126       in
  1127         (HOLogic.mk_prod (t1, t2), st'')
  1128       end
  1129   (*| mk_args2 (T as Type ("fun", _)) (params, ctxt) =
  1130     let
  1131       val (S, U) = strip_type T
  1132     in
  1133       if U = HOLogic.boolT then
  1134         (hd params, (tl params, ctxt))
  1135       else
  1136         let
  1137           val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
  1138         in
  1139           (Free (x, T), (params, ctxt'))
  1140         end
  1141     end*)
  1142   | mk_args2 T (params, ctxt) =
  1143       let
  1144         val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
  1145       in
  1146         (Free (x, T), (params, ctxt'))
  1147       end
  1148 
  1149 fun mk_casesrule ctxt pred introrules =
  1150   let
  1151     (* TODO: can be simplified if parameters are not treated specially ? *)
  1152     val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt
  1153     (* TODO: distinct required ? -- test case with more than one parameter! *)
  1154     val params = distinct (op aconv) params
  1155     val intros = map prop_of intros_th
  1156     val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
  1157     val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
  1158     val argsT = binder_types (fastype_of pred)
  1159     (* TODO: can be simplified if parameters are not treated specially ? <-- see uncommented code! *)
  1160     val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)
  1161     fun mk_case intro =
  1162       let
  1163         val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) intro
  1164         val prems = Logic.strip_imp_prems intro
  1165         val eqprems =
  1166           map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) argvs args
  1167         val frees = map Free (fold Term.add_frees (args @ prems) [])
  1168       in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
  1169     val assm = HOLogic.mk_Trueprop (list_comb (pred, argvs))
  1170     val cases = map mk_case intros
  1171   in Logic.list_implies (assm :: cases, prop) end;
  1172 
  1173 
  1174 (* unifying constants to have the same type variables *)
  1175 
  1176 fun unify_consts thy cs intr_ts =
  1177   let
  1178      val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
  1179      fun varify (t, (i, ts)) =
  1180        let val t' = map_types (Logic.incr_tvar (i + 1)) (#2 (Type.varify_global [] t))
  1181        in (maxidx_of_term t', t' :: ts) end
  1182      val (i, cs') = List.foldr varify (~1, []) cs
  1183      val (i', intr_ts') = List.foldr varify (i, []) intr_ts
  1184      val rec_consts = fold add_term_consts_2 cs' []
  1185      val intr_consts = fold add_term_consts_2 intr_ts' []
  1186      fun unify (cname, cT) =
  1187        let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
  1188        in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end
  1189      val (env, _) = fold unify rec_consts (Vartab.empty, i')
  1190      val subst = map_types (Envir.norm_type env)
  1191    in (map subst cs', map subst intr_ts')
  1192    end handle Type.TUNIFY =>
  1193      (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts))
  1194 
  1195 
  1196 (* preprocessing rules *)
  1197 
  1198 fun preprocess_equality thy rule =
  1199   Conv.fconv_rule
  1200     (imp_prems_conv
  1201       (HOLogic.Trueprop_conv
  1202         (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
  1203     (Thm.transfer thy rule)
  1204 
  1205 fun preprocess_intro thy = expand_tuples thy #> preprocess_equality thy
  1206 
  1207 
  1208 (* defining a quickcheck predicate *)
  1209 
  1210 fun strip_imp_prems (Const(@{const_name HOL.implies}, _) $ A $ B) = A :: strip_imp_prems B
  1211   | strip_imp_prems _ = [];
  1212 
  1213 fun strip_imp_concl (Const(@{const_name HOL.implies}, _) $ _ $ B) = strip_imp_concl B
  1214   | strip_imp_concl A = A;
  1215 
  1216 fun strip_horn A = (strip_imp_prems A, strip_imp_concl A)
  1217 
  1218 fun define_quickcheck_predicate t thy =
  1219   let
  1220     val (vs, t') = strip_abs t
  1221     val vs' = Variable.variant_frees (Proof_Context.init_global thy) [] vs (* FIXME proper context!? *)
  1222     val t'' = subst_bounds (map Free (rev vs'), t')
  1223     val (prems, concl) = strip_horn t''
  1224     val constname = "quickcheck"
  1225     val full_constname = Sign.full_bname thy constname
  1226     val constT = map snd vs' ---> @{typ bool}
  1227     val thy1 = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
  1228     val const = Const (full_constname, constT)
  1229     val t =
  1230       Logic.list_implies
  1231         (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
  1232           HOLogic.mk_Trueprop (list_comb (const, map Free vs')))
  1233     val intro =
  1234       Goal.prove (Proof_Context.init_global thy1) (map fst vs') [] t
  1235         (fn _ => ALLGOALS Skip_Proof.cheat_tac)
  1236   in
  1237     ((((full_constname, constT), vs'), intro), thy1)
  1238   end
  1239 
  1240 end