src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
author haftmann
Mon Nov 12 23:24:40 2012 +0100 (2012-11-12)
changeset 50056 72efd6b4038d
parent 48221 e0ed7fab0d09
child 51314 eac4bb5adbf9
permissions -rw-r--r--
dropped dead code
     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 conjuncts : term -> term list
    47   val is_equationlike : thm -> bool
    48   val is_pred_equation : thm -> bool
    49   val is_intro : string -> thm -> bool
    50   val is_predT : typ -> bool
    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 (*Like dest_conj, but flattens conjunctions however nested*)
   460 fun conjuncts_aux (Const (@{const_name HOL.conj}, _) $ t $ t') conjs = conjuncts_aux t (conjuncts_aux t' conjs)
   461   | conjuncts_aux t conjs = t::conjs;
   462 
   463 fun conjuncts t = conjuncts_aux t [];
   464 
   465 fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
   466   | is_equationlike_term (Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) = true
   467   | is_equationlike_term _ = false
   468   
   469 val is_equationlike = is_equationlike_term o prop_of 
   470 
   471 fun is_pred_equation_term (Const ("==", _) $ u $ v) =
   472   (fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
   473   | is_pred_equation_term _ = false
   474   
   475 val is_pred_equation = is_pred_equation_term o prop_of 
   476 
   477 fun is_intro_term constname t =
   478   the_default false (try (fn t => case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
   479     Const (c, _) => c = constname
   480   | _ => false) t)
   481   
   482 fun is_intro constname t = is_intro_term constname (prop_of t)
   483 
   484 fun is_predT (T as Type("fun", [_, _])) = (body_type T = @{typ bool})
   485   | is_predT _ = false
   486 
   487 (*** check if a term contains only constructor functions ***)
   488 (* TODO: another copy in the core! *)
   489 (* FIXME: constructor terms are supposed to be seen in the way the code generator
   490   sees constructors.*)
   491 fun is_constrt thy =
   492   let
   493     val cnstrs = flat (maps
   494       (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
   495       (Symtab.dest (Datatype.get_all thy)));
   496     fun check t = (case strip_comb t of
   497         (Var _, []) => true
   498       | (Free _, []) => true
   499       | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
   500             (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
   501           | _ => false)
   502       | _ => false)
   503   in check end;
   504 
   505 (* returns true if t is an application of an datatype constructor *)
   506 (* which then consequently would be splitted *)
   507 (* else false *)
   508 (*
   509 fun is_constructor thy t =
   510   if (is_Type (fastype_of t)) then
   511     (case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
   512       NONE => false
   513     | SOME info => (let
   514       val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
   515       val (c, _) = strip_comb t
   516       in (case c of
   517         Const (name, _) => name mem_string constr_consts
   518         | _ => false) end))
   519   else false
   520 *)
   521 
   522 val is_constr = Code.is_constr o Proof_Context.theory_of;
   523 
   524 fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
   525 
   526 fun strip_ex (Const (@{const_name Ex}, _) $ Abs (x, T, t)) =
   527   let
   528     val (xTs, t') = strip_ex t
   529   in
   530     ((x, T) :: xTs, t')
   531   end
   532   | strip_ex t = ([], t)
   533 
   534 fun focus_ex t nctxt =
   535   let
   536     val ((xs, Ts), t') = apfst split_list (strip_ex t) 
   537     val (xs', nctxt') = fold_map Name.variant xs nctxt;
   538     val ps' = xs' ~~ Ts;
   539     val vs = map Free ps';
   540     val t'' = Term.subst_bounds (rev vs, t');
   541   in ((ps', t''), nctxt') end;
   542 
   543 val strip_intro_concl = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of)
   544   
   545 (* introduction rule combinators *)
   546 
   547 fun map_atoms f intro = 
   548   let
   549     val (literals, head) = Logic.strip_horn intro
   550     fun appl t = (case t of
   551         (@{term Not} $ t') => HOLogic.mk_not (f t')
   552       | _ => f t)
   553   in
   554     Logic.list_implies
   555       (map (HOLogic.mk_Trueprop o appl o HOLogic.dest_Trueprop) literals, head)
   556   end
   557 
   558 fun fold_atoms f intro s =
   559   let
   560     val (literals, _) = Logic.strip_horn intro
   561     fun appl t s = (case t of
   562       (@{term Not} $ t') => f t' s
   563       | _ => f t s)
   564   in fold appl (map HOLogic.dest_Trueprop literals) s end
   565 
   566 fun fold_map_atoms f intro s =
   567   let
   568     val (literals, head) = Logic.strip_horn intro
   569     fun appl t s = (case t of
   570       (@{term Not} $ t') => apfst HOLogic.mk_not (f t' s)
   571       | _ => f t s)
   572     val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
   573   in
   574     (Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
   575   end;
   576 
   577 fun map_filter_premises f intro =
   578   let
   579     val (premises, head) = Logic.strip_horn intro
   580   in
   581     Logic.list_implies (map_filter f premises, head)
   582   end
   583 
   584 fun maps_premises f intro =
   585   let
   586     val (premises, head) = Logic.strip_horn intro
   587   in
   588     Logic.list_implies (maps f premises, head)
   589   end
   590 
   591 fun map_concl f intro =
   592   let
   593     val (premises, head) = Logic.strip_horn intro
   594   in
   595     Logic.list_implies (premises, f head)
   596   end
   597 
   598 (* combinators to apply a function to all basic parts of nested products *)
   599 
   600 fun map_products f (Const (@{const_name Pair}, T) $ t1 $ t2) =
   601   Const (@{const_name Pair}, T) $ map_products f t1 $ map_products f t2
   602   | map_products f t = f t
   603 
   604 (* split theorems of case expressions *)
   605 
   606 fun prepare_split_thm ctxt split_thm =
   607     (split_thm RS @{thm iffD2})
   608     |> Local_Defs.unfold ctxt [@{thm atomize_conjL[symmetric]},
   609       @{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
   610 
   611 fun find_split_thm thy (Const (name, _)) = Option.map #split (Datatype.info_of_case thy name)
   612   | find_split_thm thy _ = NONE
   613 
   614 (* lifting term operations to theorems *)
   615 
   616 fun map_term thy f th =
   617   Skip_Proof.make_thm thy (f (prop_of th))
   618 
   619 (*
   620 fun equals_conv lhs_cv rhs_cv ct =
   621   case Thm.term_of ct of
   622     Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct  
   623   | _ => error "equals_conv"  
   624 *)
   625 
   626 (* Different compilations *)
   627 
   628 datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
   629   | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq |
   630     Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
   631 
   632 fun negative_compilation_of Pos_Random_DSeq = Neg_Random_DSeq
   633   | negative_compilation_of Neg_Random_DSeq = Pos_Random_DSeq
   634   | negative_compilation_of New_Pos_Random_DSeq = New_Neg_Random_DSeq
   635   | negative_compilation_of New_Neg_Random_DSeq = New_Pos_Random_DSeq
   636   | negative_compilation_of Pos_Generator_DSeq = Neg_Generator_DSeq
   637   | negative_compilation_of Neg_Generator_DSeq = Pos_Generator_DSeq
   638   | negative_compilation_of Pos_Generator_CPS = Neg_Generator_CPS
   639   | negative_compilation_of Neg_Generator_CPS = Pos_Generator_CPS  
   640   | negative_compilation_of c = c
   641   
   642 fun compilation_for_polarity false Pos_Random_DSeq = Neg_Random_DSeq
   643   | compilation_for_polarity false New_Pos_Random_DSeq = New_Neg_Random_DSeq
   644   | compilation_for_polarity _ c = c
   645 
   646 fun is_depth_limited_compilation c =
   647   (c = New_Pos_Random_DSeq) orelse (c = New_Neg_Random_DSeq) orelse
   648   (c = Pos_Generator_DSeq) orelse (c = Pos_Generator_DSeq)
   649 
   650 fun string_of_compilation c =
   651   case c of
   652     Pred => ""
   653   | Random => "random"
   654   | Depth_Limited => "depth limited"
   655   | Depth_Limited_Random => "depth limited random"
   656   | DSeq => "dseq"
   657   | Annotated => "annotated"
   658   | Pos_Random_DSeq => "pos_random dseq"
   659   | Neg_Random_DSeq => "neg_random_dseq"
   660   | New_Pos_Random_DSeq => "new_pos_random dseq"
   661   | New_Neg_Random_DSeq => "new_neg_random_dseq"
   662   | Pos_Generator_DSeq => "pos_generator_dseq"
   663   | Neg_Generator_DSeq => "neg_generator_dseq"
   664   | Pos_Generator_CPS => "pos_generator_cps"
   665   | Neg_Generator_CPS => "neg_generator_cps"
   666   
   667 val compilation_names = [("pred", Pred),
   668   ("random", Random),
   669   ("depth_limited", Depth_Limited),
   670   ("depth_limited_random", Depth_Limited_Random),
   671   (*("annotated", Annotated),*)
   672   ("dseq", DSeq),
   673   ("random_dseq", Pos_Random_DSeq),
   674   ("new_random_dseq", New_Pos_Random_DSeq),
   675   ("generator_dseq", Pos_Generator_DSeq),
   676   ("generator_cps", Pos_Generator_CPS)]
   677 
   678 val non_random_compilations = [Pred, Depth_Limited, DSeq, Annotated]
   679 
   680 
   681 val random_compilations = [Random, Depth_Limited_Random,
   682   Pos_Random_DSeq, Neg_Random_DSeq, New_Pos_Random_DSeq, New_Neg_Random_DSeq,
   683   Pos_Generator_CPS, Neg_Generator_CPS]
   684 
   685 (* datastructures and setup for generic compilation *)
   686 
   687 datatype compilation_funs = CompilationFuns of {
   688   mk_monadT : typ -> typ,
   689   dest_monadT : typ -> typ,
   690   mk_empty : typ -> term,
   691   mk_single : term -> term,
   692   mk_bind : term * term -> term,
   693   mk_plus : term * term -> term,
   694   mk_if : term -> term,
   695   mk_iterate_upto : typ -> term * term * term -> term,
   696   mk_not : term -> term,
   697   mk_map : typ -> typ -> term -> term -> term
   698 };
   699 
   700 fun mk_monadT (CompilationFuns funs) = #mk_monadT funs
   701 fun dest_monadT (CompilationFuns funs) = #dest_monadT funs
   702 fun mk_empty (CompilationFuns funs) = #mk_empty funs
   703 fun mk_single (CompilationFuns funs) = #mk_single funs
   704 fun mk_bind (CompilationFuns funs) = #mk_bind funs
   705 fun mk_plus (CompilationFuns funs) = #mk_plus funs
   706 fun mk_if (CompilationFuns funs) = #mk_if funs
   707 fun mk_iterate_upto (CompilationFuns funs) = #mk_iterate_upto funs
   708 fun mk_not (CompilationFuns funs) = #mk_not funs
   709 fun mk_map (CompilationFuns funs) = #mk_map funs
   710 
   711 (** function types and names of different compilations **)
   712 
   713 fun funT_of compfuns mode T =
   714   let
   715     val Ts = binder_types T
   716     val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
   717   in
   718     inTs ---> (mk_monadT compfuns (HOLogic.mk_tupleT outTs))
   719   end;
   720 
   721 (* Different options for compiler *)
   722 
   723 datatype options = Options of {  
   724   expected_modes : (string * mode list) option,
   725   proposed_modes : (string * mode list) list,
   726   proposed_names : ((string * mode) * string) list,
   727   show_steps : bool,
   728   show_proof_trace : bool,
   729   show_intermediate_results : bool,
   730   show_mode_inference : bool,
   731   show_modes : bool,
   732   show_compilation : bool,
   733   show_caught_failures : bool,
   734   show_invalid_clauses : bool,
   735   skip_proof : bool,
   736   no_topmost_reordering : bool,
   737   function_flattening : bool,
   738   specialise : bool,
   739   fail_safe_function_flattening : bool,
   740   no_higher_order_predicate : string list,
   741   inductify : bool,
   742   detect_switches : bool,
   743   smart_depth_limiting : bool,
   744   compilation : compilation
   745 };
   746 
   747 fun expected_modes (Options opt) = #expected_modes opt
   748 fun proposed_modes (Options opt) = AList.lookup (op =) (#proposed_modes opt)
   749 fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode)
   750   (#proposed_names opt) (name, mode)
   751 
   752 fun show_steps (Options opt) = #show_steps opt
   753 fun show_intermediate_results (Options opt) = #show_intermediate_results opt
   754 fun show_proof_trace (Options opt) = #show_proof_trace opt
   755 fun show_modes (Options opt) = #show_modes opt
   756 fun show_mode_inference (Options opt) = #show_mode_inference opt
   757 fun show_compilation (Options opt) = #show_compilation opt
   758 fun show_caught_failures (Options opt) = #show_caught_failures opt
   759 fun show_invalid_clauses (Options opt) = #show_invalid_clauses opt
   760 fun skip_proof (Options opt) = #skip_proof opt
   761 
   762 fun function_flattening (Options opt) = #function_flattening opt
   763 fun fail_safe_function_flattening (Options opt) = #fail_safe_function_flattening opt
   764 fun specialise (Options opt) = #specialise opt
   765 fun no_topmost_reordering (Options opt) = #no_topmost_reordering opt
   766 fun no_higher_order_predicate (Options opt) = #no_higher_order_predicate opt
   767 
   768 fun is_inductify (Options opt) = #inductify opt
   769 
   770 fun compilation (Options opt) = #compilation opt
   771 
   772 fun detect_switches (Options opt) = #detect_switches opt
   773 
   774 fun smart_depth_limiting (Options opt) = #smart_depth_limiting opt
   775 
   776 val default_options = Options {
   777   expected_modes = NONE,
   778   proposed_modes = [],
   779   proposed_names = [],
   780   show_steps = false,
   781   show_intermediate_results = false,
   782   show_proof_trace = false,
   783   show_modes = false,
   784   show_mode_inference = false,
   785   show_compilation = false,
   786   show_caught_failures = false,
   787   show_invalid_clauses = false,
   788   skip_proof = true,
   789   no_topmost_reordering = false,
   790   function_flattening = false,
   791   specialise = false,
   792   fail_safe_function_flattening = false,
   793   no_higher_order_predicate = [],
   794   inductify = false,
   795   detect_switches = true,
   796   smart_depth_limiting = false,
   797   compilation = Pred
   798 }
   799 
   800 val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
   801   "show_mode_inference", "show_compilation", "show_invalid_clauses", "skip_proof", "inductify",
   802   "no_function_flattening", "detect_switches", "specialise", "no_topmost_reordering",
   803   "smart_depth_limiting"]
   804 
   805 fun print_step options s =
   806   if show_steps options then tracing s else ()
   807 
   808 (* simple transformations *)
   809 
   810 (** tuple processing **)
   811 
   812 fun rewrite_args [] (pats, intro_t, ctxt) = (pats, intro_t, ctxt)
   813   | rewrite_args (arg::args) (pats, intro_t, ctxt) = 
   814     (case HOLogic.strip_tupleT (fastype_of arg) of
   815       (_ :: _ :: _) =>
   816       let
   817         fun rewrite_arg' (Const (@{const_name Pair}, _) $ _ $ t2, Type (@{type_name Product_Type.prod}, [_, T2]))
   818           (args, (pats, intro_t, ctxt)) = rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
   819           | rewrite_arg' (t, Type (@{type_name Product_Type.prod}, [T1, T2])) (args, (pats, intro_t, ctxt)) =
   820             let
   821               val thy = Proof_Context.theory_of ctxt
   822               val ([x, y], ctxt') = Variable.variant_fixes ["x", "y"] ctxt
   823               val pat = (t, HOLogic.mk_prod (Free (x, T1), Free (y, T2)))
   824               val intro_t' = Pattern.rewrite_term thy [pat] [] intro_t
   825               val args' = map (Pattern.rewrite_term thy [pat] []) args
   826             in
   827               rewrite_arg' (Free (y, T2), T2) (args', (pat::pats, intro_t', ctxt'))
   828             end
   829           | rewrite_arg' _ (args, (pats, intro_t, ctxt)) = (args, (pats, intro_t, ctxt))
   830         val (args', (pats, intro_t', ctxt')) = rewrite_arg' (arg, fastype_of arg)
   831           (args, (pats, intro_t, ctxt))
   832       in
   833         rewrite_args args' (pats, intro_t', ctxt')
   834       end
   835   | _ => rewrite_args args (pats, intro_t, ctxt))
   836 
   837 fun rewrite_prem atom =
   838   let
   839     val (_, args) = strip_comb atom
   840   in rewrite_args args end
   841 
   842 fun split_conjuncts_in_assms ctxt th =
   843   let
   844     val ((_, [fixed_th]), ctxt') = Variable.import false [th] ctxt 
   845     fun split_conjs i nprems th =
   846       if i > nprems then th
   847       else
   848         case try Drule.RSN (@{thm conjI}, (i, th)) of
   849           SOME th' => split_conjs i (nprems+1) th'
   850         | NONE => split_conjs (i+1) nprems th
   851   in
   852     singleton (Variable.export ctxt' ctxt) (split_conjs 1 (Thm.nprems_of fixed_th) fixed_th)
   853   end
   854 
   855 fun dest_conjunct_prem th =
   856   case HOLogic.dest_Trueprop (prop_of th) of
   857     (Const (@{const_name HOL.conj}, _) $ _ $ _) =>
   858       dest_conjunct_prem (th RS @{thm conjunct1})
   859         @ dest_conjunct_prem (th RS @{thm conjunct2})
   860     | _ => [th]
   861 
   862 fun expand_tuples thy intro =
   863   let
   864     val ctxt = Proof_Context.init_global thy
   865     val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
   866     val intro_t = prop_of intro'
   867     val concl = Logic.strip_imp_concl intro_t
   868     val (_, args) = strip_comb (HOLogic.dest_Trueprop concl)
   869     val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
   870     val (pats', _, ctxt3) = fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
   871     fun rewrite_pat (ct1, ct2) =
   872       (ct1, cterm_of thy (Pattern.rewrite_term thy pats' [] (term_of ct2)))
   873     val t_insts' = map rewrite_pat t_insts
   874     val intro'' = Thm.instantiate (T_insts, t_insts') intro
   875     val [intro'''] = Variable.export ctxt3 ctxt [intro'']
   876     val intro'''' = Simplifier.full_simplify
   877       (HOL_basic_ss addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}])
   878       intro'''
   879     (* splitting conjunctions introduced by Pair_eq*)
   880     val intro''''' = split_conjuncts_in_assms ctxt intro''''
   881   in
   882     intro'''''
   883   end
   884 
   885 (** making case distributivity rules **)
   886 (*** this should be part of the datatype package ***)
   887 
   888 fun datatype_names_of_case_name thy case_name =
   889   map (#1 o #2) (#descr (the (Datatype.info_of_case thy case_name)))
   890 
   891 fun make_case_distribs case_names descr thy =
   892   let
   893     val case_combs = Datatype_Prop.make_case_combs case_names descr thy "f";
   894     fun make comb =
   895       let
   896         val Type ("fun", [T, T']) = fastype_of comb;
   897         val (Const (case_name, _), fs) = strip_comb comb
   898         val used = Term.add_tfree_names comb []
   899         val U = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS)
   900         val x = Free ("x", T)
   901         val f = Free ("f", T' --> U)
   902         fun apply_f f' =
   903           let
   904             val Ts = binder_types (fastype_of f')
   905             val bs = map Bound ((length Ts - 1) downto 0)
   906           in
   907             fold_rev absdummy Ts (f $ (list_comb (f', bs)))
   908           end
   909         val fs' = map apply_f fs
   910         val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U)
   911       in
   912         HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x)
   913       end
   914   in
   915     map make case_combs
   916   end
   917 
   918 fun case_rewrites thy Tcon =
   919   let
   920     val {descr, case_name, ...} = Datatype.the_info thy Tcon
   921   in
   922     map (Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop)
   923       (make_case_distribs [case_name] [descr] thy)
   924   end
   925 
   926 fun instantiated_case_rewrites thy Tcon =
   927   let
   928     val rew_ths = case_rewrites thy Tcon
   929     val ctxt = Proof_Context.init_global thy
   930     fun instantiate th =
   931     let
   932       val f = (fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th))))))
   933       val Type ("fun", [uninst_T, uninst_T']) = fastype_of f
   934       val ([_, tname', uname, yname], ctxt') = Variable.add_fixes ["'t", "'t'", "'u", "y"] ctxt
   935       val T' = TFree (tname', HOLogic.typeS)
   936       val U = TFree (uname, HOLogic.typeS)
   937       val y = Free (yname, U)
   938       val f' = absdummy (U --> T') (Bound 0 $ y)
   939       val th' = Thm.certify_instantiate
   940         ([(dest_TVar uninst_T, U --> T'), (dest_TVar uninst_T', T')],
   941          [((fst (dest_Var f), (U --> T') --> T'), f')]) th
   942       val [th'] = Variable.export ctxt' ctxt [th']
   943    in
   944      th'
   945    end
   946  in
   947    map instantiate rew_ths
   948  end
   949 
   950 fun case_betapply thy t =
   951   let
   952     val case_name = fst (dest_Const (fst (strip_comb t)))
   953     val Tcons = datatype_names_of_case_name thy case_name
   954     val ths = maps (instantiated_case_rewrites thy) Tcons
   955   in
   956     Raw_Simplifier.rewrite_term thy
   957       (map (fn th => th RS @{thm eq_reflection}) ths) [] t
   958   end
   959 
   960 (*** conversions ***)
   961 
   962 fun imp_prems_conv cv ct =
   963   case Thm.term_of ct of
   964     Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
   965   | _ => Conv.all_conv ct
   966 
   967 (** eta contract higher-order arguments **)
   968 
   969 fun eta_contract_ho_arguments thy intro =
   970   let
   971     fun f atom = list_comb (apsnd ((map o map_products) Envir.eta_contract) (strip_comb atom))
   972   in
   973     map_term thy (map_concl f o map_atoms f) intro
   974   end
   975 
   976 (** remove equalities **)
   977 
   978 fun remove_equalities thy intro =
   979   let
   980     fun remove_eqs intro_t =
   981       let
   982         val (prems, concl) = Logic.strip_horn intro_t
   983         fun remove_eq (prems, concl) =
   984           let
   985             fun removable_eq prem =
   986               case try (HOLogic.dest_eq o HOLogic.dest_Trueprop) prem of
   987                 SOME (lhs, rhs) => (case lhs of
   988                   Var _ => true
   989                   | _ => (case rhs of Var _ => true | _ => false))
   990               | NONE => false
   991           in
   992             case find_first removable_eq prems of
   993               NONE => (prems, concl)
   994             | SOME eq =>
   995               let
   996                 val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
   997                 val prems' = remove (op =) eq prems
   998                 val subst = (case lhs of
   999                   (v as Var _) =>
  1000                     (fn t => if t = v then rhs else t)
  1001                 | _ => (case rhs of
  1002                    (v as Var _) => (fn t => if t = v then lhs else t)))
  1003               in
  1004                 remove_eq (map (map_aterms subst) prems', map_aterms subst concl)
  1005               end
  1006           end
  1007       in
  1008         Logic.list_implies (remove_eq (prems, concl))
  1009       end
  1010   in
  1011     map_term thy remove_eqs intro
  1012   end
  1013 
  1014 (* Some last processing *)
  1015 
  1016 fun remove_pointless_clauses intro =
  1017   if Logic.strip_imp_prems (prop_of intro) = [@{prop "False"}] then
  1018     []
  1019   else [intro]
  1020 
  1021 (* some peephole optimisations *)
  1022 
  1023 fun peephole_optimisation thy intro =
  1024   let
  1025     val process =
  1026       Raw_Simplifier.rewrite_rule (Predicate_Compile_Simps.get (Proof_Context.init_global thy))
  1027     fun process_False intro_t =
  1028       if member (op =) (Logic.strip_imp_prems intro_t) @{prop "False"} then NONE else SOME intro_t
  1029     fun process_True intro_t =
  1030       map_filter_premises (fn p => if p = @{prop True} then NONE else SOME p) intro_t
  1031   in
  1032     Option.map (Skip_Proof.make_thm thy)
  1033       (process_False (process_True (prop_of (process intro))))
  1034   end
  1035 
  1036 
  1037 (* importing introduction rules *)
  1038 
  1039 fun import_intros inp_pred [] ctxt =
  1040   let
  1041     val ([outp_pred], ctxt') = Variable.import_terms true [inp_pred] ctxt
  1042     val T = fastype_of outp_pred
  1043     val paramTs = ho_argsT_of_typ (binder_types T)
  1044     val (param_names, _) = Variable.variant_fixes
  1045       (map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'
  1046     val params = map2 (curry Free) param_names paramTs
  1047   in
  1048     (((outp_pred, params), []), ctxt')
  1049   end
  1050   | import_intros inp_pred (th :: ths) ctxt =
  1051     let
  1052       val ((_, [th']), ctxt') = Variable.import true [th] ctxt
  1053       val thy = Proof_Context.theory_of ctxt'
  1054       val (pred, args) = strip_intro_concl th'
  1055       val T = fastype_of pred
  1056       val ho_args = ho_args_of_typ T args
  1057       fun subst_of (pred', pred) =
  1058         let
  1059           val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty
  1060             handle Type.TYPE_MATCH => error ("Type mismatch of predicate " ^ fst (dest_Const pred)
  1061             ^ " (trying to match " ^ Syntax.string_of_typ ctxt (fastype_of pred')
  1062             ^ " and " ^ Syntax.string_of_typ ctxt (fastype_of pred) ^ ")"
  1063             ^ " in " ^ Display.string_of_thm ctxt th)
  1064         in map (fn (indexname, (s, T)) => ((indexname, s), T)) (Vartab.dest subst) end
  1065       fun instantiate_typ th =
  1066         let
  1067           val (pred', _) = strip_intro_concl th
  1068           val _ = if not (fst (dest_Const pred) = fst (dest_Const pred')) then
  1069             raise Fail "Trying to instantiate another predicate" else ()
  1070         in Thm.certify_instantiate (subst_of (pred', pred), []) th end;
  1071       fun instantiate_ho_args th =
  1072         let
  1073           val (_, args') = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of) th
  1074           val ho_args' = map dest_Var (ho_args_of_typ T args')
  1075         in Thm.certify_instantiate ([], ho_args' ~~ ho_args) th end
  1076       val outp_pred =
  1077         Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred
  1078       val ((_, ths'), ctxt1) =
  1079         Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'
  1080     in
  1081       (((outp_pred, ho_args), th' :: ths'), ctxt1)
  1082     end
  1083   
  1084 (* generation of case rules from user-given introduction rules *)
  1085 
  1086 fun mk_args2 (Type (@{type_name Product_Type.prod}, [T1, T2])) st =
  1087     let
  1088       val (t1, st') = mk_args2 T1 st
  1089       val (t2, st'') = mk_args2 T2 st'
  1090     in
  1091       (HOLogic.mk_prod (t1, t2), st'')
  1092     end
  1093   (*| mk_args2 (T as Type ("fun", _)) (params, ctxt) = 
  1094     let
  1095       val (S, U) = strip_type T
  1096     in
  1097       if U = HOLogic.boolT then
  1098         (hd params, (tl params, ctxt))
  1099       else
  1100         let
  1101           val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
  1102         in
  1103           (Free (x, T), (params, ctxt'))
  1104         end
  1105     end*)
  1106   | mk_args2 T (params, ctxt) =
  1107     let
  1108       val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
  1109     in
  1110       (Free (x, T), (params, ctxt'))
  1111     end
  1112 
  1113 fun mk_casesrule ctxt pred introrules =
  1114   let
  1115     (* TODO: can be simplified if parameters are not treated specially ? *)
  1116     val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt
  1117     (* TODO: distinct required ? -- test case with more than one parameter! *)
  1118     val params = distinct (op aconv) params
  1119     val intros = map prop_of intros_th
  1120     val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
  1121     val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
  1122     val argsT = binder_types (fastype_of pred)
  1123     (* TODO: can be simplified if parameters are not treated specially ? <-- see uncommented code! *)
  1124     val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)
  1125     fun mk_case intro =
  1126       let
  1127         val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) intro
  1128         val prems = Logic.strip_imp_prems intro
  1129         val eqprems =
  1130           map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) argvs args
  1131         val frees = map Free (fold Term.add_frees (args @ prems) [])
  1132       in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
  1133     val assm = HOLogic.mk_Trueprop (list_comb (pred, argvs))
  1134     val cases = map mk_case intros
  1135   in Logic.list_implies (assm :: cases, prop) end;
  1136   
  1137 
  1138 (* unifying constants to have the same type variables *)
  1139 
  1140 fun unify_consts thy cs intr_ts =
  1141   (let
  1142      val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
  1143      fun varify (t, (i, ts)) =
  1144        let val t' = map_types (Logic.incr_tvar (i + 1)) (#2 (Type.varify_global [] t))
  1145        in (maxidx_of_term t', t'::ts) end;
  1146      val (i, cs') = List.foldr varify (~1, []) cs;
  1147      val (i', intr_ts') = List.foldr varify (i, []) intr_ts;
  1148      val rec_consts = fold add_term_consts_2 cs' [];
  1149      val intr_consts = fold add_term_consts_2 intr_ts' [];
  1150      fun unify (cname, cT) =
  1151        let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
  1152        in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
  1153      val (env, _) = fold unify rec_consts (Vartab.empty, i');
  1154      val subst = map_types (Envir.norm_type env)
  1155    in (map subst cs', map subst intr_ts')
  1156    end) handle Type.TUNIFY =>
  1157      (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
  1158 
  1159 (* preprocessing rules *)
  1160 
  1161 fun Trueprop_conv cv ct =
  1162   case Thm.term_of ct of
  1163     Const (@{const_name Trueprop}, _) $ _ => Conv.arg_conv cv ct  
  1164   | _ => raise Fail "Trueprop_conv"
  1165 
  1166 fun preprocess_equality thy rule =
  1167   Conv.fconv_rule
  1168     (imp_prems_conv
  1169       (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
  1170     (Thm.transfer thy rule)
  1171 
  1172 fun preprocess_intro thy = expand_tuples thy #> preprocess_equality thy
  1173 
  1174 (* defining a quickcheck predicate *)
  1175 
  1176 fun strip_imp_prems (Const(@{const_name HOL.implies}, _) $ A $ B) = A :: strip_imp_prems B
  1177   | strip_imp_prems _ = [];
  1178 
  1179 fun strip_imp_concl (Const(@{const_name HOL.implies}, _) $ _ $ B) = strip_imp_concl B
  1180   | strip_imp_concl A = A;
  1181 
  1182 fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);
  1183 
  1184 fun define_quickcheck_predicate t thy =
  1185   let
  1186     val (vs, t') = strip_abs t
  1187     val vs' = Variable.variant_frees (Proof_Context.init_global thy) [] vs
  1188     val t'' = subst_bounds (map Free (rev vs'), t')
  1189     val (prems, concl) = strip_horn t''
  1190     val constname = "quickcheck"
  1191     val full_constname = Sign.full_bname thy constname
  1192     val constT = map snd vs' ---> @{typ bool}
  1193     val thy1 = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
  1194     val const = Const (full_constname, constT)
  1195     val t = Logic.list_implies
  1196       (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
  1197        HOLogic.mk_Trueprop (list_comb (const, map Free vs')))
  1198     val tac = fn _ => Skip_Proof.cheat_tac thy1
  1199     val intro = Goal.prove (Proof_Context.init_global thy1) (map fst vs') [] t tac
  1200   in
  1201     ((((full_constname, constT), vs'), intro), thy1)
  1202   end
  1203 
  1204 end;