src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
author blanchet
Wed Feb 12 08:35:56 2014 +0100 (2014-02-12)
changeset 55399 5c8e91f884af
parent 54742 7a86358a3c0b
child 55440 721b4561007a
permissions -rw-r--r--
ported predicate compiler to 'ctr_sugar'
* * *
ported predicate compiler to 'ctr_sugar', part 2
     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 get_constrs : theory -> (string * (int * string)) list
    51   val is_constrt : theory -> term -> bool
    52   val is_constr : Proof.context -> string -> bool
    53   val strip_ex : term -> (string * typ) list * term
    54   val focus_ex : term -> Name.context -> ((string * typ) list * term) * Name.context
    55   val strip_all : term -> (string * typ) list * term
    56   val strip_intro_concl : thm -> term * term list
    57   (* introduction rule combinators *)
    58   val map_atoms : (term -> term) -> term -> term
    59   val fold_atoms : (term -> 'a -> 'a) -> term -> 'a -> 'a
    60   val fold_map_atoms : (term -> 'a -> term * 'a) -> term -> 'a -> term * 'a
    61   val maps_premises : (term -> term list) -> term -> term
    62   val map_concl : (term -> term) -> term -> term
    63   val map_term : theory -> (term -> term) -> thm -> thm
    64   (* split theorems of case expressions *)
    65   val prepare_split_thm : Proof.context -> thm -> thm
    66   val find_split_thm : theory -> term -> thm option
    67   (* datastructures and setup for generic compilation *)
    68   datatype compilation_funs = CompilationFuns of {
    69     mk_monadT : typ -> typ,
    70     dest_monadT : typ -> typ,
    71     mk_empty : typ -> term,
    72     mk_single : term -> term,
    73     mk_bind : term * term -> term,
    74     mk_plus : term * term -> term,
    75     mk_if : term -> term,
    76     mk_iterate_upto : typ -> term * term * term -> term,
    77     mk_not : term -> term,
    78     mk_map : typ -> typ -> term -> term -> term
    79   };
    80   val mk_monadT : compilation_funs -> typ -> typ
    81   val dest_monadT : compilation_funs -> typ -> typ
    82   val mk_empty : compilation_funs -> typ -> term
    83   val mk_single : compilation_funs -> term -> term
    84   val mk_bind : compilation_funs -> term * term -> term
    85   val mk_plus : compilation_funs -> term * term -> term
    86   val mk_if : compilation_funs -> term -> term
    87   val mk_iterate_upto : compilation_funs -> typ -> term * term * term -> term
    88   val mk_not : compilation_funs -> term -> term
    89   val mk_map : compilation_funs -> typ -> typ -> term -> term -> term
    90   val funT_of : compilation_funs -> mode -> typ -> typ
    91   (* Different compilations *)
    92   datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
    93     | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq 
    94     | Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
    95   val negative_compilation_of : compilation -> compilation
    96   val compilation_for_polarity : bool -> compilation -> compilation
    97   val is_depth_limited_compilation : compilation -> bool 
    98   val string_of_compilation : compilation -> string
    99   val compilation_names : (string * compilation) list
   100   val non_random_compilations : compilation list
   101   val random_compilations : compilation list
   102   (* Different options for compiler *)
   103   datatype options = Options of {  
   104     expected_modes : (string * mode list) option,
   105     proposed_modes : (string * mode list) list,
   106     proposed_names : ((string * mode) * string) list,
   107     show_steps : bool,
   108     show_proof_trace : bool,
   109     show_intermediate_results : bool,
   110     show_mode_inference : bool,
   111     show_modes : bool,
   112     show_compilation : bool,
   113     show_caught_failures : bool,
   114     show_invalid_clauses : bool,
   115     skip_proof : bool,
   116     no_topmost_reordering : bool,
   117     function_flattening : bool,
   118     fail_safe_function_flattening : bool,
   119     specialise : bool,
   120     no_higher_order_predicate : string list,
   121     inductify : bool,
   122     detect_switches : bool,
   123     smart_depth_limiting : bool,
   124     compilation : compilation
   125   };
   126   val expected_modes : options -> (string * mode list) option
   127   val proposed_modes : options -> string -> mode list option
   128   val proposed_names : options -> string -> mode -> string option
   129   val show_steps : options -> bool
   130   val show_proof_trace : options -> bool
   131   val show_intermediate_results : options -> bool
   132   val show_mode_inference : options -> bool
   133   val show_modes : options -> bool
   134   val show_compilation : options -> bool
   135   val show_caught_failures : options -> bool
   136   val show_invalid_clauses : options -> bool
   137   val skip_proof : options -> bool
   138   val no_topmost_reordering : options -> bool
   139   val function_flattening : options -> bool
   140   val fail_safe_function_flattening : options -> bool
   141   val specialise : options -> bool
   142   val no_higher_order_predicate : options -> string list
   143   val is_inductify : options -> bool
   144   val detect_switches : options -> bool
   145   val smart_depth_limiting : options -> bool
   146   val compilation : options -> compilation
   147   val default_options : options
   148   val bool_options : string list
   149   val print_step : options -> string -> unit
   150   (* conversions *)
   151   val imp_prems_conv : conv -> conv
   152   (* simple transformations *)
   153   val split_conjuncts_in_assms : Proof.context -> thm -> thm
   154   val dest_conjunct_prem : thm -> thm list
   155   val expand_tuples : theory -> thm -> thm
   156   val case_betapply : theory -> term -> term
   157   val eta_contract_ho_arguments : theory -> thm -> thm
   158   val remove_equalities : theory -> thm -> thm
   159   val remove_pointless_clauses : thm -> thm list
   160   val peephole_optimisation : theory -> thm -> thm option
   161   (* auxillary *)
   162   val unify_consts : theory -> term list -> term list -> (term list * term list)
   163   val mk_casesrule : Proof.context -> term -> thm list -> term
   164   val preprocess_intro : theory -> thm -> thm
   165   
   166   val define_quickcheck_predicate :
   167     term -> theory -> (((string * typ) * (string * typ) list) * thm) * theory
   168 end;
   169 
   170 structure Predicate_Compile_Aux : PREDICATE_COMPILE_AUX =
   171 struct
   172 
   173 (* general functions *)
   174 
   175 fun apfst3 f (x, y, z) = (f x, y, z)
   176 fun apsnd3 f (x, y, z) = (x, f y, z)
   177 fun aptrd3 f (x, y, z) = (x, y, f z)
   178 
   179 fun comb_option f (SOME x1, SOME x2) = SOME (f (x1, x2))
   180   | comb_option f (NONE, SOME x2) = SOME x2
   181   | comb_option f (SOME x1, NONE) = SOME x1
   182   | comb_option f (NONE, NONE) = NONE
   183 
   184 fun map2_optional f (x :: xs) (y :: ys) = f x (SOME y) :: (map2_optional f xs ys)
   185   | map2_optional f (x :: xs) [] = (f x NONE) :: (map2_optional f xs [])
   186   | map2_optional f [] [] = []
   187 
   188 fun find_indices f xs =
   189   map_filter (fn (i, true) => SOME i | (_, false) => NONE) (map_index (apsnd f) xs)
   190 
   191 (* mode *)
   192 
   193 datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
   194 
   195 (* equality of instantiatedness with respect to equivalences:
   196   Pair Input Input == Input and Pair Output Output == Output *)
   197 fun eq_mode (Fun (m1, m2), Fun (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
   198   | eq_mode (Pair (m1, m2), Pair (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
   199   | eq_mode (Pair (m1, m2), Input) = eq_mode (m1, Input) andalso eq_mode (m2, Input)
   200   | eq_mode (Pair (m1, m2), Output) = eq_mode (m1, Output) andalso eq_mode (m2, Output)
   201   | eq_mode (Input, Pair (m1, m2)) = eq_mode (Input, m1) andalso eq_mode (Input, m2)
   202   | eq_mode (Output, Pair (m1, m2)) = eq_mode (Output, m1) andalso eq_mode (Output, m2)
   203   | eq_mode (Input, Input) = true
   204   | eq_mode (Output, Output) = true
   205   | eq_mode (Bool, Bool) = true
   206   | eq_mode _ = false
   207 
   208 fun mode_ord (Input, Output) = LESS
   209   | mode_ord (Output, Input) = GREATER
   210   | mode_ord (Input, Input) = EQUAL
   211   | mode_ord (Output, Output) = EQUAL
   212   | mode_ord (Bool, Bool) = EQUAL
   213   | mode_ord (Pair (m1, m2), Pair (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
   214   | mode_ord (Fun (m1, m2), Fun (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
   215  
   216 fun list_fun_mode [] = Bool
   217   | list_fun_mode (m :: ms) = Fun (m, list_fun_mode ms)
   218 
   219 (* name: binder_modes? *)
   220 fun strip_fun_mode (Fun (mode, mode')) = mode :: strip_fun_mode mode'
   221   | strip_fun_mode Bool = []
   222   | strip_fun_mode _ = raise Fail "Bad mode for strip_fun_mode"
   223 
   224 (* name: strip_fun_mode? *)
   225 fun dest_fun_mode (Fun (mode, mode')) = mode :: dest_fun_mode mode'
   226   | dest_fun_mode mode = [mode]
   227 
   228 fun dest_tuple_mode (Pair (mode, mode')) = mode :: dest_tuple_mode mode'
   229   | dest_tuple_mode _ = []
   230 
   231 fun all_modes_of_typ' (T as Type ("fun", _)) = 
   232   let
   233     val (S, U) = strip_type T
   234   in
   235     if U = HOLogic.boolT then
   236       fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
   237         (map all_modes_of_typ' S) [Bool]
   238     else
   239       [Input, Output]
   240   end
   241   | all_modes_of_typ' (Type (@{type_name Product_Type.prod}, [T1, T2])) = 
   242     map_product (curry Pair) (all_modes_of_typ' T1) (all_modes_of_typ' T2)
   243   | all_modes_of_typ' _ = [Input, Output]
   244 
   245 fun all_modes_of_typ (T as Type ("fun", _)) =
   246     let
   247       val (S, U) = strip_type T
   248     in
   249       if U = @{typ bool} then
   250         fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
   251           (map all_modes_of_typ' S) [Bool]
   252       else
   253         raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
   254     end
   255   | all_modes_of_typ @{typ bool} = [Bool]
   256   | all_modes_of_typ _ =
   257     raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
   258 
   259 fun all_smodes_of_typ (T as Type ("fun", _)) =
   260   let
   261     val (S, U) = strip_type T
   262     fun all_smodes (Type (@{type_name Product_Type.prod}, [T1, T2])) = 
   263       map_product (curry Pair) (all_smodes T1) (all_smodes T2)
   264       | all_smodes _ = [Input, Output]
   265   in
   266     if U = HOLogic.boolT then
   267       fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2) (map all_smodes S) [Bool]
   268     else
   269       raise Fail "invalid type for predicate"
   270   end
   271 
   272 fun ho_arg_modes_of mode =
   273   let
   274     fun ho_arg_mode (m as Fun _) =  [m]
   275       | ho_arg_mode (Pair (m1, m2)) = ho_arg_mode m1 @ ho_arg_mode m2
   276       | ho_arg_mode _ = []
   277   in
   278     maps ho_arg_mode (strip_fun_mode mode)
   279   end
   280 
   281 fun ho_args_of mode ts =
   282   let
   283     fun ho_arg (Fun _) (SOME t) = [t]
   284       | ho_arg (Fun _) NONE = raise Fail "mode and term do not match"
   285       | ho_arg (Pair (m1, m2)) (SOME (Const (@{const_name Pair}, _) $ t1 $ t2)) =
   286           ho_arg m1 (SOME t1) @ ho_arg m2 (SOME t2)
   287       | ho_arg (Pair (m1, m2)) NONE = ho_arg m1 NONE @ ho_arg m2 NONE
   288       | ho_arg _ _ = []
   289   in
   290     flat (map2_optional ho_arg (strip_fun_mode mode) ts)
   291   end
   292 
   293 fun ho_args_of_typ T ts =
   294   let
   295     fun ho_arg (T as Type("fun", [_,_])) (SOME t) = 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])) = ho_arg m1 T1 @ ho_arg m2 T2
   338       | ho_arg _ _ = []
   339   in
   340     flat (map2 ho_arg (strip_fun_mode mode) Ts)
   341   end
   342 
   343 (* splits mode and maps function to higher-order argument types *)
   344 fun split_map_mode f mode ts =
   345   let
   346     fun split_arg_mode' (m as Fun _) t = f m t
   347       | split_arg_mode' (Pair (m1, m2)) (Const (@{const_name Pair}, _) $ t1 $ t2) =
   348         let
   349           val (i1, o1) = split_arg_mode' m1 t1
   350           val (i2, o2) = split_arg_mode' m2 t2
   351         in
   352           (comb_option HOLogic.mk_prod (i1, i2), comb_option HOLogic.mk_prod (o1, o2))
   353         end
   354       | split_arg_mode' m t =
   355         if eq_mode (m, Input) then (SOME t, NONE)
   356         else if eq_mode (m, Output) then (NONE,  SOME t)
   357         else raise Fail "split_map_mode: mode and term do not match"
   358   in
   359     (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) ts)
   360   end
   361 
   362 (* splits mode and maps function to higher-order argument types *)
   363 fun split_map_modeT f mode Ts =
   364   let
   365     fun split_arg_mode' (m as Fun _) T = f m T
   366       | split_arg_mode' (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   367         let
   368           val (i1, o1) = split_arg_mode' m1 T1
   369           val (i2, o2) = split_arg_mode' m2 T2
   370         in
   371           (comb_option HOLogic.mk_prodT (i1, i2), comb_option HOLogic.mk_prodT (o1, o2))
   372         end
   373       | split_arg_mode' Input T = (SOME T, NONE)
   374       | split_arg_mode' Output T = (NONE,  SOME T)
   375       | split_arg_mode' _ _ = raise Fail "split_modeT': mode and type do not match"
   376   in
   377     (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
   378   end
   379 
   380 fun split_mode mode ts = split_map_mode (fn _ => fn _ => (NONE, NONE)) mode ts
   381 
   382 fun fold_map_aterms_prodT comb f (Type (@{type_name Product_Type.prod}, [T1, T2])) s =
   383   let
   384     val (x1, s') = fold_map_aterms_prodT comb f T1 s
   385     val (x2, s'') = fold_map_aterms_prodT comb f T2 s'
   386   in
   387     (comb x1 x2, s'')
   388   end
   389   | fold_map_aterms_prodT comb f T s = f T s
   390 
   391 fun map_filter_prod f (Const (@{const_name Pair}, _) $ t1 $ t2) =
   392   comb_option HOLogic.mk_prod (map_filter_prod f t1, map_filter_prod f t2)
   393   | map_filter_prod f t = f t
   394   
   395 fun split_modeT mode Ts =
   396   let
   397     fun split_arg_mode (Fun _) _ = ([], [])
   398       | split_arg_mode (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
   399         let
   400           val (i1, o1) = split_arg_mode m1 T1
   401           val (i2, o2) = split_arg_mode m2 T2
   402         in
   403           (i1 @ i2, o1 @ o2)
   404         end
   405       | split_arg_mode Input T = ([T], [])
   406       | split_arg_mode Output T = ([], [T])
   407       | split_arg_mode _ _ = raise Fail "split_modeT: mode and type do not match"
   408   in
   409     (pairself flat o split_list) (map2 split_arg_mode (strip_fun_mode mode) Ts)
   410   end
   411 
   412 fun string_of_mode mode =
   413   let
   414     fun string_of_mode1 Input = "i"
   415       | string_of_mode1 Output = "o"
   416       | string_of_mode1 Bool = "bool"
   417       | string_of_mode1 mode = "(" ^ (string_of_mode3 mode) ^ ")"
   418     and string_of_mode2 (Pair (m1, m2)) = string_of_mode3 m1 ^ " * " ^  string_of_mode2 m2
   419       | string_of_mode2 mode = string_of_mode1 mode
   420     and string_of_mode3 (Fun (m1, m2)) = string_of_mode2 m1 ^ " => " ^ string_of_mode3 m2
   421       | string_of_mode3 mode = string_of_mode2 mode
   422   in string_of_mode3 mode end
   423 
   424 fun ascii_string_of_mode mode' =
   425   let
   426     fun ascii_string_of_mode' Input = "i"
   427       | ascii_string_of_mode' Output = "o"
   428       | ascii_string_of_mode' Bool = "b"
   429       | ascii_string_of_mode' (Pair (m1, m2)) =
   430           "P" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
   431       | ascii_string_of_mode' (Fun (m1, m2)) = 
   432           "F" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Fun m2 ^ "B"
   433     and ascii_string_of_mode'_Fun (Fun (m1, m2)) =
   434           ascii_string_of_mode' m1 ^ (if m2 = Bool then "" else "_" ^ ascii_string_of_mode'_Fun m2)
   435       | ascii_string_of_mode'_Fun Bool = "B"
   436       | ascii_string_of_mode'_Fun m = ascii_string_of_mode' m
   437     and ascii_string_of_mode'_Pair (Pair (m1, m2)) =
   438           ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
   439       | ascii_string_of_mode'_Pair m = ascii_string_of_mode' m
   440   in ascii_string_of_mode'_Fun mode' end
   441 
   442 (* premises *)
   443 
   444 datatype indprem = Prem of term | Negprem of term | Sidecond of term
   445   | Generator of (string * typ);
   446 
   447 fun dest_indprem (Prem t) = t
   448   | dest_indprem (Negprem t) = t
   449   | dest_indprem (Sidecond t) = t
   450   | dest_indprem (Generator _) = raise Fail "cannot destruct generator"
   451 
   452 fun map_indprem f (Prem t) = Prem (f t)
   453   | map_indprem f (Negprem t) = Negprem (f t)
   454   | map_indprem f (Sidecond t) = Sidecond (f t)
   455   | map_indprem f (Generator (v, T)) = Generator (dest_Free (f (Free (v, T))))
   456 
   457 (* general syntactic functions *)
   458 
   459 fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
   460   | is_equationlike_term (Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) = true
   461   | is_equationlike_term _ = false
   462   
   463 val is_equationlike = is_equationlike_term o prop_of 
   464 
   465 fun is_pred_equation_term (Const ("==", _) $ u $ v) =
   466   (fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
   467   | is_pred_equation_term _ = false
   468   
   469 val is_pred_equation = is_pred_equation_term o prop_of 
   470 
   471 fun is_intro_term constname t =
   472   the_default false (try (fn t => case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
   473     Const (c, _) => c = constname
   474   | _ => false) t)
   475   
   476 fun is_intro constname t = is_intro_term constname (prop_of t)
   477 
   478 fun is_predT (T as Type("fun", [_, _])) = (body_type T = @{typ bool})
   479   | is_predT _ = false
   480 
   481 fun get_constrs thy =
   482   let
   483     val ctxt = Proof_Context.init_global thy
   484   in
   485     Ctr_Sugar.ctr_sugars_of ctxt
   486     |> maps (map_filter (try dest_Const) o #ctrs)
   487     |> map (apsnd (fn T => (BNF_Util.num_binder_types T, fst (dest_Type (body_type T)))))
   488   end
   489 
   490 (*** check if a term contains only constructor functions ***)
   491 (* TODO: another copy in the core! *)
   492 (* FIXME: constructor terms are supposed to be seen in the way the code generator
   493   sees constructors.*)
   494 fun is_constrt thy =
   495   let
   496     val cnstrs = get_constrs thy
   497     fun check t = (case strip_comb t of
   498         (Var _, []) => true
   499       | (Free _, []) => true
   500       | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
   501             (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
   502           | _ => false)
   503       | _ => false)
   504   in check end;
   505 
   506 val is_constr = Code.is_constr o Proof_Context.theory_of;
   507 
   508 fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
   509 
   510 fun strip_ex (Const (@{const_name Ex}, _) $ Abs (x, T, t)) =
   511   let
   512     val (xTs, t') = strip_ex t
   513   in
   514     ((x, T) :: xTs, t')
   515   end
   516   | strip_ex t = ([], t)
   517 
   518 fun focus_ex t nctxt =
   519   let
   520     val ((xs, Ts), t') = apfst split_list (strip_ex t) 
   521     val (xs', nctxt') = fold_map Name.variant xs nctxt;
   522     val ps' = xs' ~~ Ts;
   523     val vs = map Free ps';
   524     val t'' = Term.subst_bounds (rev vs, t');
   525   in ((ps', t''), nctxt') end;
   526 
   527 val strip_intro_concl = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of)
   528   
   529 (* introduction rule combinators *)
   530 
   531 fun map_atoms f intro = 
   532   let
   533     val (literals, head) = Logic.strip_horn intro
   534     fun appl t = (case t of
   535         (@{term Not} $ t') => HOLogic.mk_not (f t')
   536       | _ => f t)
   537   in
   538     Logic.list_implies
   539       (map (HOLogic.mk_Trueprop o appl o HOLogic.dest_Trueprop) literals, head)
   540   end
   541 
   542 fun fold_atoms f intro s =
   543   let
   544     val (literals, _) = Logic.strip_horn intro
   545     fun appl t s = (case t of
   546       (@{term Not} $ t') => f t' s
   547       | _ => f t s)
   548   in fold appl (map HOLogic.dest_Trueprop literals) s end
   549 
   550 fun fold_map_atoms f intro s =
   551   let
   552     val (literals, head) = Logic.strip_horn intro
   553     fun appl t s = (case t of
   554       (@{term Not} $ t') => apfst HOLogic.mk_not (f t' s)
   555       | _ => f t s)
   556     val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
   557   in
   558     (Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
   559   end;
   560 
   561 fun map_filter_premises f intro =
   562   let
   563     val (premises, head) = Logic.strip_horn intro
   564   in
   565     Logic.list_implies (map_filter f premises, head)
   566   end
   567 
   568 fun maps_premises f intro =
   569   let
   570     val (premises, head) = Logic.strip_horn intro
   571   in
   572     Logic.list_implies (maps f premises, head)
   573   end
   574 
   575 fun map_concl f intro =
   576   let
   577     val (premises, head) = Logic.strip_horn intro
   578   in
   579     Logic.list_implies (premises, f head)
   580   end
   581 
   582 (* combinators to apply a function to all basic parts of nested products *)
   583 
   584 fun map_products f (Const (@{const_name Pair}, T) $ t1 $ t2) =
   585   Const (@{const_name Pair}, T) $ map_products f t1 $ map_products f t2
   586   | map_products f t = f t
   587 
   588 (* split theorems of case expressions *)
   589 
   590 fun prepare_split_thm ctxt split_thm =
   591     (split_thm RS @{thm iffD2})
   592     |> Local_Defs.unfold ctxt [@{thm atomize_conjL[symmetric]},
   593       @{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
   594 
   595 fun find_split_thm thy (Const (name, _)) =
   596     Option.map #split (Ctr_Sugar.ctr_sugar_of_case (Proof_Context.init_global thy) name)
   597   | find_split_thm thy _ = NONE
   598 
   599 (* lifting term operations to theorems *)
   600 
   601 fun map_term thy f th =
   602   Skip_Proof.make_thm thy (f (prop_of th))
   603 
   604 (*
   605 fun equals_conv lhs_cv rhs_cv ct =
   606   case Thm.term_of ct of
   607     Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct  
   608   | _ => error "equals_conv"  
   609 *)
   610 
   611 (* Different compilations *)
   612 
   613 datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
   614   | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq |
   615     Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
   616 
   617 fun negative_compilation_of Pos_Random_DSeq = Neg_Random_DSeq
   618   | negative_compilation_of Neg_Random_DSeq = Pos_Random_DSeq
   619   | negative_compilation_of New_Pos_Random_DSeq = New_Neg_Random_DSeq
   620   | negative_compilation_of New_Neg_Random_DSeq = New_Pos_Random_DSeq
   621   | negative_compilation_of Pos_Generator_DSeq = Neg_Generator_DSeq
   622   | negative_compilation_of Neg_Generator_DSeq = Pos_Generator_DSeq
   623   | negative_compilation_of Pos_Generator_CPS = Neg_Generator_CPS
   624   | negative_compilation_of Neg_Generator_CPS = Pos_Generator_CPS  
   625   | negative_compilation_of c = c
   626   
   627 fun compilation_for_polarity false Pos_Random_DSeq = Neg_Random_DSeq
   628   | compilation_for_polarity false New_Pos_Random_DSeq = New_Neg_Random_DSeq
   629   | compilation_for_polarity _ c = c
   630 
   631 fun is_depth_limited_compilation c =
   632   (c = New_Pos_Random_DSeq) orelse (c = New_Neg_Random_DSeq) orelse
   633   (c = Pos_Generator_DSeq) orelse (c = Pos_Generator_DSeq)
   634 
   635 fun string_of_compilation c =
   636   case c of
   637     Pred => ""
   638   | Random => "random"
   639   | Depth_Limited => "depth limited"
   640   | Depth_Limited_Random => "depth limited random"
   641   | DSeq => "dseq"
   642   | Annotated => "annotated"
   643   | Pos_Random_DSeq => "pos_random dseq"
   644   | Neg_Random_DSeq => "neg_random_dseq"
   645   | New_Pos_Random_DSeq => "new_pos_random dseq"
   646   | New_Neg_Random_DSeq => "new_neg_random_dseq"
   647   | Pos_Generator_DSeq => "pos_generator_dseq"
   648   | Neg_Generator_DSeq => "neg_generator_dseq"
   649   | Pos_Generator_CPS => "pos_generator_cps"
   650   | Neg_Generator_CPS => "neg_generator_cps"
   651   
   652 val compilation_names = [("pred", Pred),
   653   ("random", Random),
   654   ("depth_limited", Depth_Limited),
   655   ("depth_limited_random", Depth_Limited_Random),
   656   (*("annotated", Annotated),*)
   657   ("dseq", DSeq),
   658   ("random_dseq", Pos_Random_DSeq),
   659   ("new_random_dseq", New_Pos_Random_DSeq),
   660   ("generator_dseq", Pos_Generator_DSeq),
   661   ("generator_cps", Pos_Generator_CPS)]
   662 
   663 val non_random_compilations = [Pred, Depth_Limited, DSeq, Annotated]
   664 
   665 
   666 val random_compilations = [Random, Depth_Limited_Random,
   667   Pos_Random_DSeq, Neg_Random_DSeq, New_Pos_Random_DSeq, New_Neg_Random_DSeq,
   668   Pos_Generator_CPS, Neg_Generator_CPS]
   669 
   670 (* datastructures and setup for generic compilation *)
   671 
   672 datatype compilation_funs = CompilationFuns of {
   673   mk_monadT : typ -> typ,
   674   dest_monadT : typ -> typ,
   675   mk_empty : typ -> term,
   676   mk_single : term -> term,
   677   mk_bind : term * term -> term,
   678   mk_plus : term * term -> term,
   679   mk_if : term -> term,
   680   mk_iterate_upto : typ -> term * term * term -> term,
   681   mk_not : term -> term,
   682   mk_map : typ -> typ -> term -> term -> term
   683 };
   684 
   685 fun mk_monadT (CompilationFuns funs) = #mk_monadT funs
   686 fun dest_monadT (CompilationFuns funs) = #dest_monadT funs
   687 fun mk_empty (CompilationFuns funs) = #mk_empty funs
   688 fun mk_single (CompilationFuns funs) = #mk_single funs
   689 fun mk_bind (CompilationFuns funs) = #mk_bind funs
   690 fun mk_plus (CompilationFuns funs) = #mk_plus funs
   691 fun mk_if (CompilationFuns funs) = #mk_if funs
   692 fun mk_iterate_upto (CompilationFuns funs) = #mk_iterate_upto funs
   693 fun mk_not (CompilationFuns funs) = #mk_not funs
   694 fun mk_map (CompilationFuns funs) = #mk_map funs
   695 
   696 (** function types and names of different compilations **)
   697 
   698 fun funT_of compfuns mode T =
   699   let
   700     val Ts = binder_types T
   701     val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
   702   in
   703     inTs ---> (mk_monadT compfuns (HOLogic.mk_tupleT outTs))
   704   end;
   705 
   706 (* Different options for compiler *)
   707 
   708 datatype options = Options of {  
   709   expected_modes : (string * mode list) option,
   710   proposed_modes : (string * mode list) list,
   711   proposed_names : ((string * mode) * string) list,
   712   show_steps : bool,
   713   show_proof_trace : bool,
   714   show_intermediate_results : bool,
   715   show_mode_inference : bool,
   716   show_modes : bool,
   717   show_compilation : bool,
   718   show_caught_failures : bool,
   719   show_invalid_clauses : bool,
   720   skip_proof : bool,
   721   no_topmost_reordering : bool,
   722   function_flattening : bool,
   723   specialise : bool,
   724   fail_safe_function_flattening : bool,
   725   no_higher_order_predicate : string list,
   726   inductify : bool,
   727   detect_switches : bool,
   728   smart_depth_limiting : bool,
   729   compilation : compilation
   730 };
   731 
   732 fun expected_modes (Options opt) = #expected_modes opt
   733 fun proposed_modes (Options opt) = AList.lookup (op =) (#proposed_modes opt)
   734 fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode)
   735   (#proposed_names opt) (name, mode)
   736 
   737 fun show_steps (Options opt) = #show_steps opt
   738 fun show_intermediate_results (Options opt) = #show_intermediate_results opt
   739 fun show_proof_trace (Options opt) = #show_proof_trace opt
   740 fun show_modes (Options opt) = #show_modes opt
   741 fun show_mode_inference (Options opt) = #show_mode_inference opt
   742 fun show_compilation (Options opt) = #show_compilation opt
   743 fun show_caught_failures (Options opt) = #show_caught_failures opt
   744 fun show_invalid_clauses (Options opt) = #show_invalid_clauses opt
   745 fun skip_proof (Options opt) = #skip_proof opt
   746 
   747 fun function_flattening (Options opt) = #function_flattening opt
   748 fun fail_safe_function_flattening (Options opt) = #fail_safe_function_flattening opt
   749 fun specialise (Options opt) = #specialise opt
   750 fun no_topmost_reordering (Options opt) = #no_topmost_reordering opt
   751 fun no_higher_order_predicate (Options opt) = #no_higher_order_predicate opt
   752 
   753 fun is_inductify (Options opt) = #inductify opt
   754 
   755 fun compilation (Options opt) = #compilation opt
   756 
   757 fun detect_switches (Options opt) = #detect_switches opt
   758 
   759 fun smart_depth_limiting (Options opt) = #smart_depth_limiting opt
   760 
   761 val default_options = Options {
   762   expected_modes = NONE,
   763   proposed_modes = [],
   764   proposed_names = [],
   765   show_steps = false,
   766   show_intermediate_results = false,
   767   show_proof_trace = false,
   768   show_modes = false,
   769   show_mode_inference = false,
   770   show_compilation = false,
   771   show_caught_failures = false,
   772   show_invalid_clauses = false,
   773   skip_proof = true,
   774   no_topmost_reordering = false,
   775   function_flattening = false,
   776   specialise = false,
   777   fail_safe_function_flattening = false,
   778   no_higher_order_predicate = [],
   779   inductify = false,
   780   detect_switches = true,
   781   smart_depth_limiting = false,
   782   compilation = Pred
   783 }
   784 
   785 val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
   786   "show_mode_inference", "show_compilation", "show_invalid_clauses", "skip_proof", "inductify",
   787   "no_function_flattening", "detect_switches", "specialise", "no_topmost_reordering",
   788   "smart_depth_limiting"]
   789 
   790 fun print_step options s =
   791   if show_steps options then tracing s else ()
   792 
   793 (* simple transformations *)
   794 
   795 (** tuple processing **)
   796 
   797 fun rewrite_args [] (pats, intro_t, ctxt) = (pats, intro_t, ctxt)
   798   | rewrite_args (arg::args) (pats, intro_t, ctxt) = 
   799     (case HOLogic.strip_tupleT (fastype_of arg) of
   800       (_ :: _ :: _) =>
   801       let
   802         fun rewrite_arg' (Const (@{const_name Pair}, _) $ _ $ t2, Type (@{type_name Product_Type.prod}, [_, T2]))
   803           (args, (pats, intro_t, ctxt)) = rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
   804           | rewrite_arg' (t, Type (@{type_name Product_Type.prod}, [T1, T2])) (args, (pats, intro_t, ctxt)) =
   805             let
   806               val thy = Proof_Context.theory_of ctxt
   807               val ([x, y], ctxt') = Variable.variant_fixes ["x", "y"] ctxt
   808               val pat = (t, HOLogic.mk_prod (Free (x, T1), Free (y, T2)))
   809               val intro_t' = Pattern.rewrite_term thy [pat] [] intro_t
   810               val args' = map (Pattern.rewrite_term thy [pat] []) args
   811             in
   812               rewrite_arg' (Free (y, T2), T2) (args', (pat::pats, intro_t', ctxt'))
   813             end
   814           | rewrite_arg' _ (args, (pats, intro_t, ctxt)) = (args, (pats, intro_t, ctxt))
   815         val (args', (pats, intro_t', ctxt')) = rewrite_arg' (arg, fastype_of arg)
   816           (args, (pats, intro_t, ctxt))
   817       in
   818         rewrite_args args' (pats, intro_t', ctxt')
   819       end
   820   | _ => rewrite_args args (pats, intro_t, ctxt))
   821 
   822 fun rewrite_prem atom =
   823   let
   824     val (_, args) = strip_comb atom
   825   in rewrite_args args end
   826 
   827 fun split_conjuncts_in_assms ctxt th =
   828   let
   829     val ((_, [fixed_th]), ctxt') = Variable.import false [th] ctxt 
   830     fun split_conjs i nprems th =
   831       if i > nprems then th
   832       else
   833         case try Drule.RSN (@{thm conjI}, (i, th)) of
   834           SOME th' => split_conjs i (nprems+1) th'
   835         | NONE => split_conjs (i+1) nprems th
   836   in
   837     singleton (Variable.export ctxt' ctxt) (split_conjs 1 (Thm.nprems_of fixed_th) fixed_th)
   838   end
   839 
   840 fun dest_conjunct_prem th =
   841   case HOLogic.dest_Trueprop (prop_of th) of
   842     (Const (@{const_name HOL.conj}, _) $ _ $ _) =>
   843       dest_conjunct_prem (th RS @{thm conjunct1})
   844         @ dest_conjunct_prem (th RS @{thm conjunct2})
   845     | _ => [th]
   846 
   847 fun expand_tuples thy intro =
   848   let
   849     val ctxt = Proof_Context.init_global thy
   850     val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
   851     val intro_t = prop_of intro'
   852     val concl = Logic.strip_imp_concl intro_t
   853     val (_, args) = strip_comb (HOLogic.dest_Trueprop concl)
   854     val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
   855     val (pats', _, ctxt3) = fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
   856     fun rewrite_pat (ct1, ct2) =
   857       (ct1, cterm_of thy (Pattern.rewrite_term thy pats' [] (term_of ct2)))
   858     val t_insts' = map rewrite_pat t_insts
   859     val intro'' = Thm.instantiate (T_insts, t_insts') intro
   860     val [intro'''] = Variable.export ctxt3 ctxt [intro'']
   861     val intro'''' =
   862       Simplifier.full_simplify
   863         (put_simpset HOL_basic_ss ctxt
   864           addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}])
   865       intro'''
   866     (* splitting conjunctions introduced by Pair_eq*)
   867     val intro''''' = split_conjuncts_in_assms ctxt intro''''
   868   in
   869     intro'''''
   870   end
   871 
   872 (** making case distributivity rules **)
   873 (*** this should be part of the datatype package ***)
   874 
   875 fun datatype_name_of_case_name thy =
   876   Ctr_Sugar.ctr_sugar_of_case (Proof_Context.init_global thy)
   877   #> the #> #ctrs #> hd #> fastype_of #> body_type #> dest_Type #> fst
   878 
   879 fun make_case_comb thy Tcon =
   880   let
   881     val ctxt = Proof_Context.init_global thy
   882     val SOME {casex, ...} = Ctr_Sugar.ctr_sugar_of ctxt Tcon
   883     val casex' = Type.legacy_freeze casex
   884     val Ts = BNF_Util.binder_fun_types (fastype_of casex')
   885   in
   886     list_comb (casex', map_index (fn (j, T) => Free ("f" ^ string_of_int j,  T)) Ts)
   887   end
   888 
   889 fun make_case_distrib thy Tcon =
   890   let
   891     val comb = make_case_comb thy Tcon;
   892     val Type ("fun", [T, T']) = fastype_of comb;
   893     val (Const (case_name, _), fs) = strip_comb comb
   894     val used = Term.add_tfree_names comb []
   895     val U = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS)
   896     val x = Free ("x", T)
   897     val f = Free ("f", T' --> U)
   898     fun apply_f f' =
   899       let
   900         val Ts = binder_types (fastype_of f')
   901         val bs = map Bound ((length Ts - 1) downto 0)
   902       in
   903         fold_rev absdummy Ts (f $ (list_comb (f', bs)))
   904       end
   905     val fs' = map apply_f fs
   906     val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U)
   907   in
   908     HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x)
   909   end
   910 
   911 fun case_rewrite thy Tcon =
   912   (Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop)
   913     (make_case_distrib thy Tcon)
   914 
   915 fun instantiated_case_rewrite thy Tcon =
   916   let
   917     val th = case_rewrite thy Tcon
   918     val ctxt = Proof_Context.init_global thy
   919     val f = (fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th))))))
   920     val Type ("fun", [uninst_T, uninst_T']) = fastype_of f
   921     val ([_, tname', uname, yname], ctxt') = Variable.add_fixes ["'t", "'t'", "'u", "y"] ctxt
   922     val T' = TFree (tname', HOLogic.typeS)
   923     val U = TFree (uname, HOLogic.typeS)
   924     val y = Free (yname, U)
   925     val f' = absdummy (U --> T') (Bound 0 $ y)
   926     val th' = Thm.certify_instantiate
   927       ([(dest_TVar uninst_T, U --> T'), (dest_TVar uninst_T', T')],
   928        [((fst (dest_Var f), (U --> T') --> T'), f')]) th
   929     val [th'] = Variable.export ctxt' ctxt [th']
   930   in
   931     th'
   932   end
   933 
   934 fun case_betapply thy t =
   935   let
   936     val case_name = fst (dest_Const (fst (strip_comb t)))
   937     val Tcon = datatype_name_of_case_name thy case_name
   938     val th = instantiated_case_rewrite thy Tcon
   939   in
   940     Raw_Simplifier.rewrite_term thy [th RS @{thm eq_reflection}] [] t
   941   end
   942 
   943 (*** conversions ***)
   944 
   945 fun imp_prems_conv cv ct =
   946   case Thm.term_of ct of
   947     Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
   948   | _ => Conv.all_conv ct
   949 
   950 (** eta contract higher-order arguments **)
   951 
   952 fun eta_contract_ho_arguments thy intro =
   953   let
   954     fun f atom = list_comb (apsnd ((map o map_products) Envir.eta_contract) (strip_comb atom))
   955   in
   956     map_term thy (map_concl f o map_atoms f) intro
   957   end
   958 
   959 (** remove equalities **)
   960 
   961 fun remove_equalities thy intro =
   962   let
   963     fun remove_eqs intro_t =
   964       let
   965         val (prems, concl) = Logic.strip_horn intro_t
   966         fun remove_eq (prems, concl) =
   967           let
   968             fun removable_eq prem =
   969               case try (HOLogic.dest_eq o HOLogic.dest_Trueprop) prem of
   970                 SOME (lhs, rhs) => (case lhs of
   971                   Var _ => true
   972                   | _ => (case rhs of Var _ => true | _ => false))
   973               | NONE => false
   974           in
   975             case find_first removable_eq prems of
   976               NONE => (prems, concl)
   977             | SOME eq =>
   978               let
   979                 val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
   980                 val prems' = remove (op =) eq prems
   981                 val subst = (case lhs of
   982                   (v as Var _) =>
   983                     (fn t => if t = v then rhs else t)
   984                 | _ => (case rhs of
   985                    (v as Var _) => (fn t => if t = v then lhs else t)))
   986               in
   987                 remove_eq (map (map_aterms subst) prems', map_aterms subst concl)
   988               end
   989           end
   990       in
   991         Logic.list_implies (remove_eq (prems, concl))
   992       end
   993   in
   994     map_term thy remove_eqs intro
   995   end
   996 
   997 (* Some last processing *)
   998 
   999 fun remove_pointless_clauses intro =
  1000   if Logic.strip_imp_prems (prop_of intro) = [@{prop "False"}] then
  1001     []
  1002   else [intro]
  1003 
  1004 (* some peephole optimisations *)
  1005 
  1006 fun peephole_optimisation thy intro =
  1007   let
  1008     val ctxt = Proof_Context.init_global thy  (* FIXME proper context!? *)
  1009     val process =
  1010       rewrite_rule ctxt (Predicate_Compile_Simps.get ctxt)
  1011     fun process_False intro_t =
  1012       if member (op =) (Logic.strip_imp_prems intro_t) @{prop "False"} then NONE else SOME intro_t
  1013     fun process_True intro_t =
  1014       map_filter_premises (fn p => if p = @{prop True} then NONE else SOME p) intro_t
  1015   in
  1016     Option.map (Skip_Proof.make_thm thy)
  1017       (process_False (process_True (prop_of (process intro))))
  1018   end
  1019 
  1020 
  1021 (* importing introduction rules *)
  1022 
  1023 fun import_intros inp_pred [] ctxt =
  1024   let
  1025     val ([outp_pred], ctxt') = Variable.import_terms true [inp_pred] ctxt
  1026     val T = fastype_of outp_pred
  1027     val paramTs = ho_argsT_of_typ (binder_types T)
  1028     val (param_names, _) = Variable.variant_fixes
  1029       (map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'
  1030     val params = map2 (curry Free) param_names paramTs
  1031   in
  1032     (((outp_pred, params), []), ctxt')
  1033   end
  1034   | import_intros inp_pred (th :: ths) ctxt =
  1035     let
  1036       val ((_, [th']), ctxt') = Variable.import true [th] ctxt
  1037       val thy = Proof_Context.theory_of ctxt'
  1038       val (pred, args) = strip_intro_concl th'
  1039       val T = fastype_of pred
  1040       val ho_args = ho_args_of_typ T args
  1041       fun subst_of (pred', pred) =
  1042         let
  1043           val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty
  1044             handle Type.TYPE_MATCH => error ("Type mismatch of predicate " ^ fst (dest_Const pred)
  1045             ^ " (trying to match " ^ Syntax.string_of_typ ctxt (fastype_of pred')
  1046             ^ " and " ^ Syntax.string_of_typ ctxt (fastype_of pred) ^ ")"
  1047             ^ " in " ^ Display.string_of_thm ctxt th)
  1048         in map (fn (indexname, (s, T)) => ((indexname, s), T)) (Vartab.dest subst) end
  1049       fun instantiate_typ th =
  1050         let
  1051           val (pred', _) = strip_intro_concl th
  1052           val _ = if not (fst (dest_Const pred) = fst (dest_Const pred')) then
  1053             raise Fail "Trying to instantiate another predicate" else ()
  1054         in Thm.certify_instantiate (subst_of (pred', pred), []) th end;
  1055       fun instantiate_ho_args th =
  1056         let
  1057           val (_, args') = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of) th
  1058           val ho_args' = map dest_Var (ho_args_of_typ T args')
  1059         in Thm.certify_instantiate ([], ho_args' ~~ ho_args) th end
  1060       val outp_pred =
  1061         Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred
  1062       val ((_, ths'), ctxt1) =
  1063         Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'
  1064     in
  1065       (((outp_pred, ho_args), th' :: ths'), ctxt1)
  1066     end
  1067   
  1068 (* generation of case rules from user-given introduction rules *)
  1069 
  1070 fun mk_args2 (Type (@{type_name Product_Type.prod}, [T1, T2])) st =
  1071     let
  1072       val (t1, st') = mk_args2 T1 st
  1073       val (t2, st'') = mk_args2 T2 st'
  1074     in
  1075       (HOLogic.mk_prod (t1, t2), st'')
  1076     end
  1077   (*| mk_args2 (T as Type ("fun", _)) (params, ctxt) = 
  1078     let
  1079       val (S, U) = strip_type T
  1080     in
  1081       if U = HOLogic.boolT then
  1082         (hd params, (tl params, ctxt))
  1083       else
  1084         let
  1085           val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
  1086         in
  1087           (Free (x, T), (params, ctxt'))
  1088         end
  1089     end*)
  1090   | mk_args2 T (params, ctxt) =
  1091     let
  1092       val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
  1093     in
  1094       (Free (x, T), (params, ctxt'))
  1095     end
  1096 
  1097 fun mk_casesrule ctxt pred introrules =
  1098   let
  1099     (* TODO: can be simplified if parameters are not treated specially ? *)
  1100     val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt
  1101     (* TODO: distinct required ? -- test case with more than one parameter! *)
  1102     val params = distinct (op aconv) params
  1103     val intros = map prop_of intros_th
  1104     val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
  1105     val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
  1106     val argsT = binder_types (fastype_of pred)
  1107     (* TODO: can be simplified if parameters are not treated specially ? <-- see uncommented code! *)
  1108     val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)
  1109     fun mk_case intro =
  1110       let
  1111         val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) intro
  1112         val prems = Logic.strip_imp_prems intro
  1113         val eqprems =
  1114           map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) argvs args
  1115         val frees = map Free (fold Term.add_frees (args @ prems) [])
  1116       in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
  1117     val assm = HOLogic.mk_Trueprop (list_comb (pred, argvs))
  1118     val cases = map mk_case intros
  1119   in Logic.list_implies (assm :: cases, prop) end;
  1120   
  1121 
  1122 (* unifying constants to have the same type variables *)
  1123 
  1124 fun unify_consts thy cs intr_ts =
  1125   (let
  1126      val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
  1127      fun varify (t, (i, ts)) =
  1128        let val t' = map_types (Logic.incr_tvar (i + 1)) (#2 (Type.varify_global [] t))
  1129        in (maxidx_of_term t', t'::ts) end;
  1130      val (i, cs') = List.foldr varify (~1, []) cs;
  1131      val (i', intr_ts') = List.foldr varify (i, []) intr_ts;
  1132      val rec_consts = fold add_term_consts_2 cs' [];
  1133      val intr_consts = fold add_term_consts_2 intr_ts' [];
  1134      fun unify (cname, cT) =
  1135        let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
  1136        in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
  1137      val (env, _) = fold unify rec_consts (Vartab.empty, i');
  1138      val subst = map_types (Envir.norm_type env)
  1139    in (map subst cs', map subst intr_ts')
  1140    end) handle Type.TUNIFY =>
  1141      (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
  1142 
  1143 (* preprocessing rules *)
  1144 
  1145 fun preprocess_equality thy rule =
  1146   Conv.fconv_rule
  1147     (imp_prems_conv
  1148       (HOLogic.Trueprop_conv
  1149         (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
  1150     (Thm.transfer thy rule)
  1151 
  1152 fun preprocess_intro thy = expand_tuples thy #> preprocess_equality thy
  1153 
  1154 (* defining a quickcheck predicate *)
  1155 
  1156 fun strip_imp_prems (Const(@{const_name HOL.implies}, _) $ A $ B) = A :: strip_imp_prems B
  1157   | strip_imp_prems _ = [];
  1158 
  1159 fun strip_imp_concl (Const(@{const_name HOL.implies}, _) $ _ $ B) = strip_imp_concl B
  1160   | strip_imp_concl A = A;
  1161 
  1162 fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);
  1163 
  1164 fun define_quickcheck_predicate t thy =
  1165   let
  1166     val (vs, t') = strip_abs t
  1167     val vs' = Variable.variant_frees (Proof_Context.init_global thy) [] vs (* FIXME proper context!? *)
  1168     val t'' = subst_bounds (map Free (rev vs'), t')
  1169     val (prems, concl) = strip_horn t''
  1170     val constname = "quickcheck"
  1171     val full_constname = Sign.full_bname thy constname
  1172     val constT = map snd vs' ---> @{typ bool}
  1173     val thy1 = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
  1174     val const = Const (full_constname, constT)
  1175     val t = Logic.list_implies
  1176       (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
  1177        HOLogic.mk_Trueprop (list_comb (const, map Free vs')))
  1178     val intro =
  1179       Goal.prove (Proof_Context.init_global thy1) (map fst vs') [] t
  1180         (fn _ => ALLGOALS Skip_Proof.cheat_tac)
  1181   in
  1182     ((((full_constname, constT), vs'), intro), thy1)
  1183   end
  1184 
  1185 end;