src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
author bulwahn
Thu Sep 30 15:37:11 2010 +0200 (2010-09-30)
changeset 39802 7cadad6a18cc
parent 39787 a44f6b11cdc4
child 40048 f3a46d524101
permissions -rw-r--r--
applying case beta reduction to case term before matching in predicate compile function flattening; moving case beta reduction function to Predicate_Compile_Aux
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(*  Title:      HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
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    Author:     Lukas Bulwahn, TU Muenchen
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Auxilary functions for predicate compiler.
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*)
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signature PREDICATE_COMPILE_AUX =
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sig
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  (* general functions *)
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  val apfst3 : ('a -> 'd) -> 'a * 'b * 'c -> 'd * 'b * 'c
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  val apsnd3 : ('b -> 'd) -> 'a * 'b * 'c -> 'a * 'd * 'c
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  val aptrd3 : ('c -> 'd) -> 'a * 'b * 'c -> 'a * 'b * 'd
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  val find_indices : ('a -> bool) -> 'a list -> int list
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  val assert : bool -> unit
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  (* mode *)
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  datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
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  val eq_mode : mode * mode -> bool
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  val mode_ord: mode * mode -> order
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  val list_fun_mode : mode list -> mode
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  val strip_fun_mode : mode -> mode list
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  val dest_fun_mode : mode -> mode list
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  val dest_tuple_mode : mode -> mode list
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  val all_modes_of_typ : typ -> mode list
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  val all_smodes_of_typ : typ -> mode list
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  val fold_map_aterms_prodT : ('a -> 'a -> 'a) -> (typ -> 'b -> 'a * 'b) -> typ -> 'b -> 'a * 'b
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  val map_filter_prod : (term -> term option) -> term -> term option
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  val replace_ho_args : mode -> term list -> term list -> term list
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  val ho_arg_modes_of : mode -> mode list
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  val ho_argsT_of : mode -> typ list -> typ list
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  val ho_args_of : mode -> term list -> term list
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  val ho_args_of_typ : typ -> term list -> term list
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  val ho_argsT_of_typ : typ list -> typ list
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  val split_map_mode : (mode -> term -> term option * term option)
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    -> mode -> term list -> term list * term list
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  val split_map_modeT : (mode -> typ -> typ option * typ option)
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    -> mode -> typ list -> typ list * typ list
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  val split_mode : mode -> term list -> term list * term list
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  val split_modeT' : mode -> typ list -> typ list * typ list
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  val string_of_mode : mode -> string
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  val ascii_string_of_mode : mode -> string
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  (* premises *)
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  datatype indprem = Prem of term | Negprem of term | Sidecond of term
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    | Generator of (string * typ)
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  val dest_indprem : indprem -> term
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  val map_indprem : (term -> term) -> indprem -> indprem
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  (* general syntactic functions *)
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  val conjuncts : term -> term list
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  val is_equationlike : thm -> bool
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  val is_pred_equation : thm -> bool
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  val is_intro : string -> thm -> bool
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  val is_predT : typ -> bool
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  val is_constrt : theory -> term -> bool
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  val is_constr : Proof.context -> string -> bool
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  val focus_ex : term -> Name.context -> ((string * typ) list * term) * Name.context
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  val strip_all : term -> (string * typ) list * term
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  (* introduction rule combinators *)
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  val map_atoms : (term -> term) -> term -> term
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  val fold_atoms : (term -> 'a -> 'a) -> term -> 'a -> 'a
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  val fold_map_atoms : (term -> 'a -> term * 'a) -> term -> 'a -> term * 'a
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  val maps_premises : (term -> term list) -> term -> term
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  val map_concl : (term -> term) -> term -> term
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  val map_term : theory -> (term -> term) -> thm -> thm
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  (* split theorems of case expressions *)
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  val prepare_split_thm : Proof.context -> thm -> thm
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  val find_split_thm : theory -> term -> thm option
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  (* datastructures and setup for generic compilation *)
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  datatype compilation_funs = CompilationFuns of {
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    mk_predT : typ -> typ,
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    dest_predT : typ -> typ,
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    mk_bot : typ -> term,
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    mk_single : term -> term,
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    mk_bind : term * term -> term,
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    mk_sup : term * term -> term,
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    mk_if : term -> term,
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    mk_iterate_upto : typ -> term * term * term -> term,
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    mk_not : term -> term,
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    mk_map : typ -> typ -> term -> term -> term
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  };
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  val mk_predT : compilation_funs -> typ -> typ
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  val dest_predT : compilation_funs -> typ -> typ
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  val mk_bot : compilation_funs -> typ -> term
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  val mk_single : compilation_funs -> term -> term
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  val mk_bind : compilation_funs -> term * term -> term
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  val mk_sup : compilation_funs -> term * term -> term
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  val mk_if : compilation_funs -> term -> term
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  val mk_iterate_upto : compilation_funs -> typ -> term * term * term -> term
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  val mk_not : compilation_funs -> term -> term
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  val mk_map : compilation_funs -> typ -> typ -> term -> term -> term
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  val funT_of : compilation_funs -> mode -> typ -> typ
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  (* Different compilations *)
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  datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
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    | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq
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  val negative_compilation_of : compilation -> compilation
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  val compilation_for_polarity : bool -> compilation -> compilation
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  val string_of_compilation : compilation -> string
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  val compilation_names : (string * compilation) list
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  val non_random_compilations : compilation list
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  val random_compilations : compilation list
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  (* Different options for compiler *)
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  datatype options = Options of {  
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    expected_modes : (string * mode list) option,
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    proposed_modes : (string * mode list) list,
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    proposed_names : ((string * mode) * string) list,
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    show_steps : bool,
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    show_proof_trace : bool,
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    show_intermediate_results : bool,
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    show_mode_inference : bool,
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    show_modes : bool,
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    show_compilation : bool,
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    show_caught_failures : bool,
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    show_invalid_clauses : bool,
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    skip_proof : bool,
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    no_topmost_reordering : bool,
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    function_flattening : bool,
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    fail_safe_function_flattening : bool,
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    specialise : bool,
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    no_higher_order_predicate : string list,
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    inductify : bool,
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    detect_switches : bool,
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    compilation : compilation
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  };
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  val expected_modes : options -> (string * mode list) option
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  val proposed_modes : options -> string -> mode list option
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  val proposed_names : options -> string -> mode -> string option
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  val show_steps : options -> bool
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  val show_proof_trace : options -> bool
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  val show_intermediate_results : options -> bool
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  val show_mode_inference : options -> bool
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  val show_modes : options -> bool
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  val show_compilation : options -> bool
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  val show_caught_failures : options -> bool
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  val show_invalid_clauses : options -> bool
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  val skip_proof : options -> bool
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  val no_topmost_reordering : options -> bool
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  val function_flattening : options -> bool
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  val fail_safe_function_flattening : options -> bool
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  val specialise : options -> bool
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  val no_higher_order_predicate : options -> string list
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  val is_inductify : options -> bool
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  val detect_switches : options -> bool
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  val compilation : options -> compilation
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  val default_options : options
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  val bool_options : string list
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  val print_step : options -> string -> unit
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  (* conversions *)
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  val imp_prems_conv : conv -> conv
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  (* simple transformations *)
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  val split_conjuncts_in_assms : Proof.context -> thm -> thm
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  val expand_tuples : theory -> thm -> thm
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  val case_betapply : theory -> term -> term
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  val eta_contract_ho_arguments : theory -> thm -> thm
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  val remove_equalities : theory -> thm -> thm
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  val remove_pointless_clauses : thm -> thm list
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  val peephole_optimisation : theory -> thm -> thm option
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  val define_quickcheck_predicate :
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    term -> theory -> (((string * typ) * (string * typ) list) * thm) * theory 
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end;
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structure Predicate_Compile_Aux : PREDICATE_COMPILE_AUX =
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struct
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(* general functions *)
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fun apfst3 f (x, y, z) = (f x, y, z)
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fun apsnd3 f (x, y, z) = (x, f y, z)
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fun aptrd3 f (x, y, z) = (x, y, f z)
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fun comb_option f (SOME x1, SOME x2) = SOME (f (x1, x2))
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  | comb_option f (NONE, SOME x2) = SOME x2
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  | comb_option f (SOME x1, NONE) = SOME x1
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  | comb_option f (NONE, NONE) = NONE
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fun map2_optional f (x :: xs) (y :: ys) = f x (SOME y) :: (map2_optional f xs ys)
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  | map2_optional f (x :: xs) [] = (f x NONE) :: (map2_optional f xs [])
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  | map2_optional f [] [] = []
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fun find_indices f xs =
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  map_filter (fn (i, true) => SOME i | (i, false) => NONE) (map_index (apsnd f) xs)
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fun assert check = if check then () else raise Fail "Assertion failed!"
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(* mode *)
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datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
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(* equality of instantiatedness with respect to equivalences:
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  Pair Input Input == Input and Pair Output Output == Output *)
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fun eq_mode (Fun (m1, m2), Fun (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
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  | eq_mode (Pair (m1, m2), Pair (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
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  | eq_mode (Pair (m1, m2), Input) = eq_mode (m1, Input) andalso eq_mode (m2, Input)
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  | eq_mode (Pair (m1, m2), Output) = eq_mode (m1, Output) andalso eq_mode (m2, Output)
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  | eq_mode (Input, Pair (m1, m2)) = eq_mode (Input, m1) andalso eq_mode (Input, m2)
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  | eq_mode (Output, Pair (m1, m2)) = eq_mode (Output, m1) andalso eq_mode (Output, m2)
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  | eq_mode (Input, Input) = true
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  | eq_mode (Output, Output) = true
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  | eq_mode (Bool, Bool) = true
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  | eq_mode _ = false
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fun mode_ord (Input, Output) = LESS
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  | mode_ord (Output, Input) = GREATER
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  | mode_ord (Input, Input) = EQUAL
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  | mode_ord (Output, Output) = EQUAL
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  | mode_ord (Bool, Bool) = EQUAL
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  | mode_ord (Pair (m1, m2), Pair (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
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  | mode_ord (Fun (m1, m2), Fun (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
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fun list_fun_mode [] = Bool
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  | list_fun_mode (m :: ms) = Fun (m, list_fun_mode ms)
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(* name: binder_modes? *)
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fun strip_fun_mode (Fun (mode, mode')) = mode :: strip_fun_mode mode'
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  | strip_fun_mode Bool = []
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  | strip_fun_mode _ = raise Fail "Bad mode for strip_fun_mode"
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(* name: strip_fun_mode? *)
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fun dest_fun_mode (Fun (mode, mode')) = mode :: dest_fun_mode mode'
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  | dest_fun_mode mode = [mode]
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fun dest_tuple_mode (Pair (mode, mode')) = mode :: dest_tuple_mode mode'
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  | dest_tuple_mode _ = []
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fun all_modes_of_typ' (T as Type ("fun", _)) = 
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  let
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    val (S, U) = strip_type T
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  in
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    if U = HOLogic.boolT then
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      fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
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        (map all_modes_of_typ' S) [Bool]
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    else
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      [Input, Output]
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  end
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  | all_modes_of_typ' (Type (@{type_name Product_Type.prod}, [T1, T2])) = 
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    map_product (curry Pair) (all_modes_of_typ' T1) (all_modes_of_typ' T2)
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  | all_modes_of_typ' _ = [Input, Output]
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fun all_modes_of_typ (T as Type ("fun", _)) =
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    let
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      val (S, U) = strip_type T
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    in
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      if U = @{typ bool} then
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        fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
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          (map all_modes_of_typ' S) [Bool]
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      else
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        raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
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    end
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  | all_modes_of_typ @{typ bool} = [Bool]
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  | all_modes_of_typ T =
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    raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
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fun all_smodes_of_typ (T as Type ("fun", _)) =
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  let
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    val (S, U) = strip_type T
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    fun all_smodes (Type (@{type_name Product_Type.prod}, [T1, T2])) = 
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      map_product (curry Pair) (all_smodes T1) (all_smodes T2)
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      | all_smodes _ = [Input, Output]
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  in
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    if U = HOLogic.boolT then
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      fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2) (map all_smodes S) [Bool]
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    else
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      raise Fail "invalid type for predicate"
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  end
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fun ho_arg_modes_of mode =
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  let
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    fun ho_arg_mode (m as Fun _) =  [m]
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      | ho_arg_mode (Pair (m1, m2)) = ho_arg_mode m1 @ ho_arg_mode m2
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      | ho_arg_mode _ = []
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  in
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    maps ho_arg_mode (strip_fun_mode mode)
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  end
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fun ho_args_of mode ts =
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  let
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    fun ho_arg (Fun _) (SOME t) = [t]
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      | ho_arg (Fun _) NONE = raise Fail "mode and term do not match"
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      | ho_arg (Pair (m1, m2)) (SOME (Const (@{const_name Pair}, _) $ t1 $ t2)) =
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          ho_arg m1 (SOME t1) @ ho_arg m2 (SOME t2)
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      | ho_arg (Pair (m1, m2)) NONE = ho_arg m1 NONE @ ho_arg m2 NONE
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      | ho_arg _ _ = []
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  in
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    flat (map2_optional ho_arg (strip_fun_mode mode) ts)
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  end
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fun ho_args_of_typ T ts =
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  let
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    fun ho_arg (T as Type("fun", [_,_])) (SOME t) = if body_type T = @{typ bool} then [t] else []
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      | ho_arg (Type("fun", [_,_])) NONE = raise Fail "mode and term do not match"
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      | ho_arg (Type(@{type_name "Product_Type.prod"}, [T1, T2]))
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         (SOME (Const (@{const_name Pair}, _) $ t1 $ t2)) =
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          ho_arg T1 (SOME t1) @ ho_arg T2 (SOME t2)
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      | ho_arg (Type(@{type_name "Product_Type.prod"}, [T1, T2])) NONE =
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          ho_arg T1 NONE @ ho_arg T2 NONE
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      | ho_arg _ _ = []
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   294
  in
bulwahn@39299
   295
    flat (map2_optional ho_arg (binder_types T) ts)
bulwahn@39299
   296
  end
bulwahn@39299
   297
bulwahn@39299
   298
fun ho_argsT_of_typ Ts =
bulwahn@39299
   299
  let
bulwahn@39312
   300
    fun ho_arg (T as Type("fun", [_,_])) = if body_type T = @{typ bool} then [T] else []
bulwahn@39299
   301
      | ho_arg (Type(@{type_name "Product_Type.prod"}, [T1, T2])) =
bulwahn@39299
   302
          ho_arg T1 @ ho_arg T2
bulwahn@39299
   303
      | ho_arg _ = []
bulwahn@39299
   304
  in
bulwahn@39299
   305
    maps ho_arg Ts
bulwahn@39299
   306
  end
bulwahn@39299
   307
  
bulwahn@39299
   308
bulwahn@34948
   309
(* temporary function should be replaced by unsplit_input or so? *)
bulwahn@34948
   310
fun replace_ho_args mode hoargs ts =
bulwahn@34948
   311
  let
bulwahn@34948
   312
    fun replace (Fun _, _) (arg' :: hoargs') = (arg', hoargs')
haftmann@37391
   313
      | replace (Pair (m1, m2), Const (@{const_name Pair}, T) $ t1 $ t2) hoargs =
bulwahn@34948
   314
        let
bulwahn@34948
   315
          val (t1', hoargs') = replace (m1, t1) hoargs
bulwahn@34948
   316
          val (t2', hoargs'') = replace (m2, t2) hoargs'
bulwahn@34948
   317
        in
haftmann@37391
   318
          (Const (@{const_name Pair}, T) $ t1' $ t2', hoargs'')
bulwahn@34948
   319
        end
bulwahn@34948
   320
      | replace (_, t) hoargs = (t, hoargs)
bulwahn@34948
   321
  in
bulwahn@35885
   322
    fst (fold_map replace (strip_fun_mode mode ~~ ts) hoargs)
bulwahn@34948
   323
  end
bulwahn@34948
   324
bulwahn@34948
   325
fun ho_argsT_of mode Ts =
bulwahn@34948
   326
  let
bulwahn@34948
   327
    fun ho_arg (Fun _) T = [T]
haftmann@37678
   328
      | ho_arg (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) = ho_arg m1 T1 @ ho_arg m2 T2
bulwahn@34948
   329
      | ho_arg _ _ = []
bulwahn@34948
   330
  in
bulwahn@34948
   331
    flat (map2 ho_arg (strip_fun_mode mode) Ts)
bulwahn@34948
   332
  end
bulwahn@34948
   333
bulwahn@34948
   334
(* splits mode and maps function to higher-order argument types *)
bulwahn@34948
   335
fun split_map_mode f mode ts =
bulwahn@34948
   336
  let
bulwahn@34948
   337
    fun split_arg_mode' (m as Fun _) t = f m t
haftmann@37391
   338
      | split_arg_mode' (Pair (m1, m2)) (Const (@{const_name Pair}, _) $ t1 $ t2) =
bulwahn@34948
   339
        let
bulwahn@34948
   340
          val (i1, o1) = split_arg_mode' m1 t1
bulwahn@34948
   341
          val (i2, o2) = split_arg_mode' m2 t2
bulwahn@34948
   342
        in
bulwahn@34948
   343
          (comb_option HOLogic.mk_prod (i1, i2), comb_option HOLogic.mk_prod (o1, o2))
bulwahn@34948
   344
        end
bulwahn@35324
   345
      | split_arg_mode' m t =
bulwahn@35324
   346
        if eq_mode (m, Input) then (SOME t, NONE)
bulwahn@35324
   347
        else if eq_mode (m, Output) then (NONE,  SOME t)
bulwahn@35885
   348
        else raise Fail "split_map_mode: mode and term do not match"
bulwahn@34948
   349
  in
bulwahn@34948
   350
    (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) ts)
bulwahn@34948
   351
  end
bulwahn@34948
   352
bulwahn@34948
   353
(* splits mode and maps function to higher-order argument types *)
bulwahn@34948
   354
fun split_map_modeT f mode Ts =
bulwahn@34948
   355
  let
bulwahn@34948
   356
    fun split_arg_mode' (m as Fun _) T = f m T
haftmann@37678
   357
      | split_arg_mode' (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
bulwahn@34948
   358
        let
bulwahn@34948
   359
          val (i1, o1) = split_arg_mode' m1 T1
bulwahn@34948
   360
          val (i2, o2) = split_arg_mode' m2 T2
bulwahn@34948
   361
        in
bulwahn@34948
   362
          (comb_option HOLogic.mk_prodT (i1, i2), comb_option HOLogic.mk_prodT (o1, o2))
bulwahn@34948
   363
        end
bulwahn@34948
   364
      | split_arg_mode' Input T = (SOME T, NONE)
bulwahn@34948
   365
      | split_arg_mode' Output T = (NONE,  SOME T)
bulwahn@35885
   366
      | split_arg_mode' _ _ = raise Fail "split_modeT': mode and type do not match"
bulwahn@34948
   367
  in
bulwahn@34948
   368
    (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
bulwahn@34948
   369
  end
bulwahn@34948
   370
bulwahn@34948
   371
fun split_mode mode ts = split_map_mode (fn _ => fn _ => (NONE, NONE)) mode ts
bulwahn@34948
   372
haftmann@37678
   373
fun fold_map_aterms_prodT comb f (Type (@{type_name Product_Type.prod}, [T1, T2])) s =
bulwahn@34948
   374
  let
bulwahn@34948
   375
    val (x1, s') = fold_map_aterms_prodT comb f T1 s
bulwahn@34948
   376
    val (x2, s'') = fold_map_aterms_prodT comb f T2 s'
bulwahn@34948
   377
  in
bulwahn@34948
   378
    (comb x1 x2, s'')
bulwahn@34948
   379
  end
bulwahn@34948
   380
  | fold_map_aterms_prodT comb f T s = f T s
bulwahn@34948
   381
haftmann@37391
   382
fun map_filter_prod f (Const (@{const_name Pair}, _) $ t1 $ t2) =
bulwahn@34948
   383
  comb_option HOLogic.mk_prod (map_filter_prod f t1, map_filter_prod f t2)
bulwahn@34948
   384
  | map_filter_prod f t = f t
bulwahn@34948
   385
bulwahn@34948
   386
(* obviously, split_mode' and split_modeT' do not match? where does that cause problems? *)
bulwahn@34948
   387
  
bulwahn@34948
   388
fun split_modeT' mode Ts =
bulwahn@34948
   389
  let
bulwahn@34948
   390
    fun split_arg_mode' (Fun _) T = ([], [])
haftmann@37678
   391
      | split_arg_mode' (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =
bulwahn@34948
   392
        let
bulwahn@34948
   393
          val (i1, o1) = split_arg_mode' m1 T1
bulwahn@34948
   394
          val (i2, o2) = split_arg_mode' m2 T2
bulwahn@34948
   395
        in
bulwahn@34948
   396
          (i1 @ i2, o1 @ o2)
bulwahn@34948
   397
        end
bulwahn@34948
   398
      | split_arg_mode' Input T = ([T], [])
bulwahn@34948
   399
      | split_arg_mode' Output T = ([], [T])
bulwahn@35885
   400
      | split_arg_mode' _ _ = raise Fail "split_modeT': mode and type do not match"
bulwahn@34948
   401
  in
bulwahn@34948
   402
    (pairself flat o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
bulwahn@34948
   403
  end
bulwahn@34948
   404
bulwahn@34948
   405
fun string_of_mode mode =
bulwahn@33619
   406
  let
bulwahn@33619
   407
    fun string_of_mode1 Input = "i"
bulwahn@33619
   408
      | string_of_mode1 Output = "o"
bulwahn@33619
   409
      | string_of_mode1 Bool = "bool"
bulwahn@33619
   410
      | string_of_mode1 mode = "(" ^ (string_of_mode3 mode) ^ ")"
bulwahn@33626
   411
    and string_of_mode2 (Pair (m1, m2)) = string_of_mode3 m1 ^ " * " ^  string_of_mode2 m2
bulwahn@33619
   412
      | string_of_mode2 mode = string_of_mode1 mode
bulwahn@33619
   413
    and string_of_mode3 (Fun (m1, m2)) = string_of_mode2 m1 ^ " => " ^ string_of_mode3 m2
bulwahn@33619
   414
      | string_of_mode3 mode = string_of_mode2 mode
bulwahn@34948
   415
  in string_of_mode3 mode end
bulwahn@33619
   416
bulwahn@34948
   417
fun ascii_string_of_mode mode' =
bulwahn@33626
   418
  let
bulwahn@33626
   419
    fun ascii_string_of_mode' Input = "i"
bulwahn@33626
   420
      | ascii_string_of_mode' Output = "o"
bulwahn@33626
   421
      | ascii_string_of_mode' Bool = "b"
bulwahn@33626
   422
      | ascii_string_of_mode' (Pair (m1, m2)) =
bulwahn@33626
   423
          "P" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
bulwahn@33626
   424
      | ascii_string_of_mode' (Fun (m1, m2)) = 
bulwahn@33626
   425
          "F" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Fun m2 ^ "B"
bulwahn@33626
   426
    and ascii_string_of_mode'_Fun (Fun (m1, m2)) =
bulwahn@33626
   427
          ascii_string_of_mode' m1 ^ (if m2 = Bool then "" else "_" ^ ascii_string_of_mode'_Fun m2)
bulwahn@33626
   428
      | ascii_string_of_mode'_Fun Bool = "B"
bulwahn@33626
   429
      | ascii_string_of_mode'_Fun m = ascii_string_of_mode' m
bulwahn@33626
   430
    and ascii_string_of_mode'_Pair (Pair (m1, m2)) =
bulwahn@33626
   431
          ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
bulwahn@33626
   432
      | ascii_string_of_mode'_Pair m = ascii_string_of_mode' m
bulwahn@33626
   433
  in ascii_string_of_mode'_Fun mode' end
bulwahn@33626
   434
bulwahn@34948
   435
(* premises *)
bulwahn@33619
   436
bulwahn@34948
   437
datatype indprem = Prem of term | Negprem of term | Sidecond of term
bulwahn@34948
   438
  | Generator of (string * typ);
bulwahn@33619
   439
bulwahn@36251
   440
fun dest_indprem (Prem t) = t
bulwahn@36251
   441
  | dest_indprem (Negprem t) = t
bulwahn@36251
   442
  | dest_indprem (Sidecond t) = t
bulwahn@36251
   443
  | dest_indprem (Generator _) = raise Fail "cannot destruct generator"
bulwahn@36251
   444
bulwahn@36254
   445
fun map_indprem f (Prem t) = Prem (f t)
bulwahn@36254
   446
  | map_indprem f (Negprem t) = Negprem (f t)
bulwahn@36254
   447
  | map_indprem f (Sidecond t) = Sidecond (f t)
bulwahn@36254
   448
  | map_indprem f (Generator (v, T)) = Generator (dest_Free (f (Free (v, T))))
bulwahn@36254
   449
bulwahn@33250
   450
(* general syntactic functions *)
bulwahn@33250
   451
bulwahn@33250
   452
(*Like dest_conj, but flattens conjunctions however nested*)
haftmann@38795
   453
fun conjuncts_aux (Const (@{const_name HOL.conj}, _) $ t $ t') conjs = conjuncts_aux t (conjuncts_aux t' conjs)
bulwahn@33250
   454
  | conjuncts_aux t conjs = t::conjs;
bulwahn@33250
   455
bulwahn@33250
   456
fun conjuncts t = conjuncts_aux t [];
bulwahn@33250
   457
bulwahn@33250
   458
fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
haftmann@38864
   459
  | is_equationlike_term (Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) = true
bulwahn@33250
   460
  | is_equationlike_term _ = false
bulwahn@33250
   461
  
bulwahn@33250
   462
val is_equationlike = is_equationlike_term o prop_of 
bulwahn@33250
   463
bulwahn@33250
   464
fun is_pred_equation_term (Const ("==", _) $ u $ v) =
bulwahn@33250
   465
  (fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
bulwahn@33250
   466
  | is_pred_equation_term _ = false
bulwahn@33250
   467
  
bulwahn@33250
   468
val is_pred_equation = is_pred_equation_term o prop_of 
bulwahn@33250
   469
bulwahn@33250
   470
fun is_intro_term constname t =
bulwahn@34948
   471
  the_default false (try (fn t => case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
bulwahn@33250
   472
    Const (c, _) => c = constname
bulwahn@34948
   473
  | _ => false) t)
bulwahn@33250
   474
  
bulwahn@33250
   475
fun is_intro constname t = is_intro_term constname (prop_of t)
bulwahn@33250
   476
haftmann@38552
   477
fun is_pred thy constname = (body_type (Sign.the_const_type thy constname) = HOLogic.boolT);
bulwahn@33250
   478
bulwahn@35885
   479
fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = @{typ bool})
bulwahn@33250
   480
  | is_predT _ = false
bulwahn@33250
   481
bulwahn@33250
   482
(*** check if a term contains only constructor functions ***)
bulwahn@34948
   483
(* TODO: another copy in the core! *)
bulwahn@33623
   484
(* FIXME: constructor terms are supposed to be seen in the way the code generator
bulwahn@33623
   485
  sees constructors.*)
bulwahn@33250
   486
fun is_constrt thy =
bulwahn@33250
   487
  let
bulwahn@33250
   488
    val cnstrs = flat (maps
bulwahn@33250
   489
      (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
bulwahn@33250
   490
      (Symtab.dest (Datatype.get_all thy)));
bulwahn@33250
   491
    fun check t = (case strip_comb t of
bulwahn@36032
   492
        (Var _, []) => true
bulwahn@36032
   493
      | (Free _, []) => true
bulwahn@33250
   494
      | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
bulwahn@33250
   495
            (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
bulwahn@33250
   496
          | _ => false)
bulwahn@33250
   497
      | _ => false)
bulwahn@36032
   498
  in check end;
bulwahn@34948
   499
bulwahn@34948
   500
fun is_funtype (Type ("fun", [_, _])) = true
bulwahn@34948
   501
  | is_funtype _ = false;
bulwahn@34948
   502
bulwahn@34948
   503
fun is_Type (Type _) = true
bulwahn@34948
   504
  | is_Type _ = false
bulwahn@34948
   505
bulwahn@34948
   506
(* returns true if t is an application of an datatype constructor *)
bulwahn@34948
   507
(* which then consequently would be splitted *)
bulwahn@34948
   508
(* else false *)
bulwahn@34948
   509
(*
bulwahn@34948
   510
fun is_constructor thy t =
bulwahn@34948
   511
  if (is_Type (fastype_of t)) then
bulwahn@34948
   512
    (case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
bulwahn@34948
   513
      NONE => false
bulwahn@34948
   514
    | SOME info => (let
bulwahn@34948
   515
      val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
bulwahn@34948
   516
      val (c, _) = strip_comb t
bulwahn@34948
   517
      in (case c of
bulwahn@34948
   518
        Const (name, _) => name mem_string constr_consts
bulwahn@34948
   519
        | _ => false) end))
bulwahn@34948
   520
  else false
bulwahn@34948
   521
*)
bulwahn@34948
   522
bulwahn@35891
   523
val is_constr = Code.is_constr o ProofContext.theory_of;
bulwahn@34948
   524
bulwahn@36047
   525
fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
bulwahn@36047
   526
haftmann@38558
   527
fun strip_ex (Const (@{const_name Ex}, _) $ Abs (x, T, t)) =
bulwahn@33250
   528
  let
bulwahn@33250
   529
    val (xTs, t') = strip_ex t
bulwahn@33250
   530
  in
bulwahn@33250
   531
    ((x, T) :: xTs, t')
bulwahn@33250
   532
  end
bulwahn@33250
   533
  | strip_ex t = ([], t)
bulwahn@33250
   534
bulwahn@33250
   535
fun focus_ex t nctxt =
bulwahn@33250
   536
  let
bulwahn@33250
   537
    val ((xs, Ts), t') = apfst split_list (strip_ex t) 
bulwahn@33250
   538
    val (xs', nctxt') = Name.variants xs nctxt;
bulwahn@33250
   539
    val ps' = xs' ~~ Ts;
bulwahn@33250
   540
    val vs = map Free ps';
bulwahn@33250
   541
    val t'' = Term.subst_bounds (rev vs, t');
bulwahn@33250
   542
  in ((ps', t''), nctxt') end;
bulwahn@33250
   543
bulwahn@33250
   544
(* introduction rule combinators *)
bulwahn@33250
   545
bulwahn@33250
   546
fun map_atoms f intro = 
bulwahn@33250
   547
  let
bulwahn@33250
   548
    val (literals, head) = Logic.strip_horn intro
bulwahn@33250
   549
    fun appl t = (case t of
bulwahn@35885
   550
        (@{term Not} $ t') => HOLogic.mk_not (f t')
bulwahn@33250
   551
      | _ => f t)
bulwahn@33250
   552
  in
bulwahn@33250
   553
    Logic.list_implies
bulwahn@33250
   554
      (map (HOLogic.mk_Trueprop o appl o HOLogic.dest_Trueprop) literals, head)
bulwahn@33250
   555
  end
bulwahn@33250
   556
bulwahn@33250
   557
fun fold_atoms f intro s =
bulwahn@33250
   558
  let
bulwahn@33250
   559
    val (literals, head) = Logic.strip_horn intro
bulwahn@33250
   560
    fun appl t s = (case t of
bulwahn@35885
   561
      (@{term Not} $ t') => f t' s
bulwahn@33250
   562
      | _ => f t s)
bulwahn@33250
   563
  in fold appl (map HOLogic.dest_Trueprop literals) s end
bulwahn@33250
   564
bulwahn@33250
   565
fun fold_map_atoms f intro s =
bulwahn@33250
   566
  let
bulwahn@33250
   567
    val (literals, head) = Logic.strip_horn intro
bulwahn@33250
   568
    fun appl t s = (case t of
bulwahn@35885
   569
      (@{term Not} $ t') => apfst HOLogic.mk_not (f t' s)
bulwahn@33250
   570
      | _ => f t s)
bulwahn@33250
   571
    val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
bulwahn@33250
   572
  in
bulwahn@33250
   573
    (Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
bulwahn@33250
   574
  end;
bulwahn@33250
   575
bulwahn@36246
   576
fun map_premises f intro =
bulwahn@36246
   577
  let
bulwahn@36246
   578
    val (premises, head) = Logic.strip_horn intro
bulwahn@36246
   579
  in
bulwahn@36246
   580
    Logic.list_implies (map f premises, head)
bulwahn@36246
   581
  end
bulwahn@36246
   582
bulwahn@36246
   583
fun map_filter_premises f intro =
bulwahn@36246
   584
  let
bulwahn@36246
   585
    val (premises, head) = Logic.strip_horn intro
bulwahn@36246
   586
  in
bulwahn@36246
   587
    Logic.list_implies (map_filter f premises, head)
bulwahn@36246
   588
  end
bulwahn@36246
   589
bulwahn@33250
   590
fun maps_premises f intro =
bulwahn@33250
   591
  let
bulwahn@33250
   592
    val (premises, head) = Logic.strip_horn intro
bulwahn@33250
   593
  in
bulwahn@33250
   594
    Logic.list_implies (maps f premises, head)
bulwahn@33250
   595
  end
bulwahn@35324
   596
bulwahn@35875
   597
fun map_concl f intro =
bulwahn@35875
   598
  let
bulwahn@35875
   599
    val (premises, head) = Logic.strip_horn intro
bulwahn@35875
   600
  in
bulwahn@35875
   601
    Logic.list_implies (premises, f head)
bulwahn@35875
   602
  end
bulwahn@35875
   603
bulwahn@35875
   604
(* combinators to apply a function to all basic parts of nested products *)
bulwahn@35875
   605
haftmann@37391
   606
fun map_products f (Const (@{const_name Pair}, T) $ t1 $ t2) =
haftmann@37391
   607
  Const (@{const_name Pair}, T) $ map_products f t1 $ map_products f t2
bulwahn@35875
   608
  | map_products f t = f t
bulwahn@35324
   609
bulwahn@35324
   610
(* split theorems of case expressions *)
bulwahn@35324
   611
bulwahn@35324
   612
fun prepare_split_thm ctxt split_thm =
bulwahn@35324
   613
    (split_thm RS @{thm iffD2})
wenzelm@35624
   614
    |> Local_Defs.unfold ctxt [@{thm atomize_conjL[symmetric]},
bulwahn@35324
   615
      @{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
bulwahn@35324
   616
bulwahn@36029
   617
fun find_split_thm thy (Const (name, T)) = Option.map #split (Datatype_Data.info_of_case thy name)
bulwahn@36029
   618
  | find_split_thm thy _ = NONE
bulwahn@35324
   619
bulwahn@33250
   620
(* lifting term operations to theorems *)
bulwahn@33250
   621
bulwahn@33250
   622
fun map_term thy f th =
bulwahn@33250
   623
  Skip_Proof.make_thm thy (f (prop_of th))
bulwahn@33250
   624
bulwahn@33250
   625
(*
bulwahn@33250
   626
fun equals_conv lhs_cv rhs_cv ct =
bulwahn@33250
   627
  case Thm.term_of ct of
bulwahn@33250
   628
    Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct  
bulwahn@33250
   629
  | _ => error "equals_conv"  
bulwahn@33250
   630
*)
bulwahn@33250
   631
bulwahn@36038
   632
(* Different compilations *)
bulwahn@33250
   633
bulwahn@35881
   634
datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
bulwahn@36018
   635
  | Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq
bulwahn@35324
   636
bulwahn@35324
   637
fun negative_compilation_of Pos_Random_DSeq = Neg_Random_DSeq
bulwahn@35324
   638
  | negative_compilation_of Neg_Random_DSeq = Pos_Random_DSeq
bulwahn@36018
   639
  | negative_compilation_of New_Pos_Random_DSeq = New_Neg_Random_DSeq
bulwahn@36018
   640
  | negative_compilation_of New_Neg_Random_DSeq = New_Pos_Random_DSeq
bulwahn@35324
   641
  | negative_compilation_of c = c
bulwahn@35324
   642
  
bulwahn@35324
   643
fun compilation_for_polarity false Pos_Random_DSeq = Neg_Random_DSeq
bulwahn@36018
   644
  | compilation_for_polarity false New_Pos_Random_DSeq = New_Neg_Random_DSeq
bulwahn@35324
   645
  | compilation_for_polarity _ c = c
bulwahn@34948
   646
bulwahn@35885
   647
fun string_of_compilation c =
bulwahn@35885
   648
  case c of
bulwahn@34948
   649
    Pred => ""
bulwahn@34948
   650
  | Random => "random"
bulwahn@34948
   651
  | Depth_Limited => "depth limited"
bulwahn@35881
   652
  | Depth_Limited_Random => "depth limited random"
bulwahn@34948
   653
  | DSeq => "dseq"
bulwahn@34948
   654
  | Annotated => "annotated"
bulwahn@35324
   655
  | Pos_Random_DSeq => "pos_random dseq"
bulwahn@35324
   656
  | Neg_Random_DSeq => "neg_random_dseq"
bulwahn@36018
   657
  | New_Pos_Random_DSeq => "new_pos_random dseq"
bulwahn@36018
   658
  | New_Neg_Random_DSeq => "new_neg_random_dseq"
bulwahn@36038
   659
bulwahn@36018
   660
val compilation_names = [("pred", Pred),
bulwahn@36018
   661
  ("random", Random),
bulwahn@36018
   662
  ("depth_limited", Depth_Limited),
bulwahn@36018
   663
  ("depth_limited_random", Depth_Limited_Random),
bulwahn@36018
   664
  (*("annotated", Annotated),*)
bulwahn@36018
   665
  ("dseq", DSeq), ("random_dseq", Pos_Random_DSeq),
bulwahn@36018
   666
  ("new_random_dseq", New_Pos_Random_DSeq)]
bulwahn@36038
   667
bulwahn@36038
   668
val non_random_compilations = [Pred, Depth_Limited, DSeq, Annotated]
bulwahn@36038
   669
bulwahn@36038
   670
bulwahn@36038
   671
val random_compilations = [Random, Depth_Limited_Random,
bulwahn@36038
   672
  Pos_Random_DSeq, Neg_Random_DSeq, New_Pos_Random_DSeq, New_Neg_Random_DSeq]
bulwahn@36038
   673
bulwahn@36046
   674
(* datastructures and setup for generic compilation *)
bulwahn@36046
   675
bulwahn@36046
   676
datatype compilation_funs = CompilationFuns of {
bulwahn@36046
   677
  mk_predT : typ -> typ,
bulwahn@36046
   678
  dest_predT : typ -> typ,
bulwahn@36046
   679
  mk_bot : typ -> term,
bulwahn@36046
   680
  mk_single : term -> term,
bulwahn@36046
   681
  mk_bind : term * term -> term,
bulwahn@36046
   682
  mk_sup : term * term -> term,
bulwahn@36046
   683
  mk_if : term -> term,
bulwahn@36049
   684
  mk_iterate_upto : typ -> term * term * term -> term,
bulwahn@36046
   685
  mk_not : term -> term,
bulwahn@36046
   686
  mk_map : typ -> typ -> term -> term -> term
bulwahn@36046
   687
};
bulwahn@36038
   688
bulwahn@36046
   689
fun mk_predT (CompilationFuns funs) = #mk_predT funs
bulwahn@36046
   690
fun dest_predT (CompilationFuns funs) = #dest_predT funs
bulwahn@36046
   691
fun mk_bot (CompilationFuns funs) = #mk_bot funs
bulwahn@36046
   692
fun mk_single (CompilationFuns funs) = #mk_single funs
bulwahn@36046
   693
fun mk_bind (CompilationFuns funs) = #mk_bind funs
bulwahn@36046
   694
fun mk_sup (CompilationFuns funs) = #mk_sup funs
bulwahn@36046
   695
fun mk_if (CompilationFuns funs) = #mk_if funs
bulwahn@36049
   696
fun mk_iterate_upto (CompilationFuns funs) = #mk_iterate_upto funs
bulwahn@36046
   697
fun mk_not (CompilationFuns funs) = #mk_not funs
bulwahn@36046
   698
fun mk_map (CompilationFuns funs) = #mk_map funs
bulwahn@36046
   699
bulwahn@36046
   700
(** function types and names of different compilations **)
bulwahn@36046
   701
bulwahn@36046
   702
fun funT_of compfuns mode T =
bulwahn@36046
   703
  let
bulwahn@36046
   704
    val Ts = binder_types T
bulwahn@36046
   705
    val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
bulwahn@36046
   706
  in
bulwahn@36046
   707
    inTs ---> (mk_predT compfuns (HOLogic.mk_tupleT outTs))
bulwahn@36046
   708
  end;
bulwahn@36046
   709
bulwahn@36046
   710
(* Different options for compiler *)
bulwahn@34948
   711
bulwahn@33250
   712
datatype options = Options of {  
bulwahn@34948
   713
  expected_modes : (string * mode list) option,
bulwahn@39382
   714
  proposed_modes : (string * mode list) list,
bulwahn@34948
   715
  proposed_names : ((string * mode) * string) list,
bulwahn@33250
   716
  show_steps : bool,
bulwahn@33250
   717
  show_proof_trace : bool,
bulwahn@33250
   718
  show_intermediate_results : bool,
bulwahn@33251
   719
  show_mode_inference : bool,
bulwahn@33251
   720
  show_modes : bool,
bulwahn@33250
   721
  show_compilation : bool,
bulwahn@35324
   722
  show_caught_failures : bool,
bulwahn@39383
   723
  show_invalid_clauses : bool,
bulwahn@33250
   724
  skip_proof : bool,
bulwahn@35324
   725
  no_topmost_reordering : bool,
bulwahn@35324
   726
  function_flattening : bool,
bulwahn@36248
   727
  specialise : bool,
bulwahn@35324
   728
  fail_safe_function_flattening : bool,
bulwahn@35324
   729
  no_higher_order_predicate : string list,
bulwahn@33250
   730
  inductify : bool,
bulwahn@36254
   731
  detect_switches : bool,
bulwahn@34948
   732
  compilation : compilation
bulwahn@33250
   733
};
bulwahn@33250
   734
bulwahn@33250
   735
fun expected_modes (Options opt) = #expected_modes opt
bulwahn@39382
   736
fun proposed_modes (Options opt) = AList.lookup (op =) (#proposed_modes opt)
bulwahn@34948
   737
fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode)
bulwahn@33623
   738
  (#proposed_names opt) (name, mode)
bulwahn@33620
   739
bulwahn@33250
   740
fun show_steps (Options opt) = #show_steps opt
bulwahn@33250
   741
fun show_intermediate_results (Options opt) = #show_intermediate_results opt
bulwahn@33250
   742
fun show_proof_trace (Options opt) = #show_proof_trace opt
bulwahn@33251
   743
fun show_modes (Options opt) = #show_modes opt
bulwahn@33251
   744
fun show_mode_inference (Options opt) = #show_mode_inference opt
bulwahn@33250
   745
fun show_compilation (Options opt) = #show_compilation opt
bulwahn@35324
   746
fun show_caught_failures (Options opt) = #show_caught_failures opt
bulwahn@39383
   747
fun show_invalid_clauses (Options opt) = #show_invalid_clauses opt
bulwahn@33250
   748
fun skip_proof (Options opt) = #skip_proof opt
bulwahn@33250
   749
bulwahn@35324
   750
fun function_flattening (Options opt) = #function_flattening opt
bulwahn@35324
   751
fun fail_safe_function_flattening (Options opt) = #fail_safe_function_flattening opt
bulwahn@36248
   752
fun specialise (Options opt) = #specialise opt
bulwahn@35324
   753
fun no_topmost_reordering (Options opt) = #no_topmost_reordering opt
bulwahn@35324
   754
fun no_higher_order_predicate (Options opt) = #no_higher_order_predicate opt
bulwahn@35324
   755
bulwahn@33250
   756
fun is_inductify (Options opt) = #inductify opt
bulwahn@34948
   757
bulwahn@34948
   758
fun compilation (Options opt) = #compilation opt
bulwahn@33250
   759
bulwahn@36254
   760
fun detect_switches (Options opt) = #detect_switches opt
bulwahn@36254
   761
bulwahn@33250
   762
val default_options = Options {
bulwahn@33250
   763
  expected_modes = NONE,
bulwahn@39382
   764
  proposed_modes = [],
bulwahn@33623
   765
  proposed_names = [],
bulwahn@33250
   766
  show_steps = false,
bulwahn@33250
   767
  show_intermediate_results = false,
bulwahn@33250
   768
  show_proof_trace = false,
bulwahn@33251
   769
  show_modes = false,
bulwahn@33250
   770
  show_mode_inference = false,
bulwahn@33250
   771
  show_compilation = false,
bulwahn@35324
   772
  show_caught_failures = false,
bulwahn@39383
   773
  show_invalid_clauses = false,
bulwahn@34948
   774
  skip_proof = true,
bulwahn@35324
   775
  no_topmost_reordering = false,
bulwahn@35324
   776
  function_flattening = false,
bulwahn@36248
   777
  specialise = false,
bulwahn@35324
   778
  fail_safe_function_flattening = false,
bulwahn@35324
   779
  no_higher_order_predicate = [],
bulwahn@33250
   780
  inductify = false,
bulwahn@36254
   781
  detect_switches = true,
bulwahn@34948
   782
  compilation = Pred
bulwahn@33250
   783
}
bulwahn@33250
   784
bulwahn@34948
   785
val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
bulwahn@39383
   786
  "show_mode_inference", "show_compilation", "show_invalid_clauses", "skip_proof", "inductify",
bulwahn@39383
   787
  "no_function_flattening", "detect_switches", "specialise", "no_topmost_reordering"]
bulwahn@34948
   788
bulwahn@33250
   789
fun print_step options s =
bulwahn@33250
   790
  if show_steps options then tracing s else ()
bulwahn@33250
   791
bulwahn@36047
   792
(* simple transformations *)
bulwahn@36047
   793
bulwahn@36047
   794
(** tuple processing **)
bulwahn@33250
   795
bulwahn@39657
   796
fun rewrite_args [] (pats, intro_t, ctxt) = (pats, intro_t, ctxt)
bulwahn@39657
   797
  | rewrite_args (arg::args) (pats, intro_t, ctxt) = 
bulwahn@39657
   798
    (case HOLogic.strip_tupleT (fastype_of arg) of
bulwahn@39657
   799
      (Ts as _ :: _ :: _) =>
bulwahn@39657
   800
      let
bulwahn@39657
   801
        fun rewrite_arg' (Const (@{const_name Pair}, _) $ _ $ t2, Type (@{type_name Product_Type.prod}, [_, T2]))
bulwahn@39657
   802
          (args, (pats, intro_t, ctxt)) = rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
bulwahn@39657
   803
          | rewrite_arg' (t, Type (@{type_name Product_Type.prod}, [T1, T2])) (args, (pats, intro_t, ctxt)) =
bulwahn@39657
   804
            let
bulwahn@39657
   805
              val thy = ProofContext.theory_of ctxt
bulwahn@39657
   806
              val ([x, y], ctxt') = Variable.variant_fixes ["x", "y"] ctxt
bulwahn@39657
   807
              val pat = (t, HOLogic.mk_prod (Free (x, T1), Free (y, T2)))
bulwahn@39657
   808
              val intro_t' = Pattern.rewrite_term thy [pat] [] intro_t
bulwahn@39657
   809
              val args' = map (Pattern.rewrite_term thy [pat] []) args
bulwahn@39657
   810
            in
bulwahn@39657
   811
              rewrite_arg' (Free (y, T2), T2) (args', (pat::pats, intro_t', ctxt'))
bulwahn@39657
   812
            end
bulwahn@39657
   813
          | rewrite_arg' _ (args, (pats, intro_t, ctxt)) = (args, (pats, intro_t, ctxt))
bulwahn@39657
   814
        val (args', (pats, intro_t', ctxt')) = rewrite_arg' (arg, fastype_of arg)
bulwahn@39657
   815
          (args, (pats, intro_t, ctxt))
bulwahn@39657
   816
      in
bulwahn@39657
   817
        rewrite_args args' (pats, intro_t', ctxt')
bulwahn@39657
   818
      end
bulwahn@39657
   819
  | _ => rewrite_args args (pats, intro_t, ctxt))
bulwahn@39657
   820
bulwahn@39657
   821
fun rewrite_prem atom =
bulwahn@39657
   822
  let
bulwahn@39657
   823
    val (_, args) = strip_comb atom
bulwahn@39657
   824
  in rewrite_args args end
bulwahn@39657
   825
bulwahn@39787
   826
fun split_conjuncts_in_assms ctxt th =
bulwahn@39787
   827
  let
bulwahn@39787
   828
    val ((_, [fixed_th]), ctxt') = Variable.import false [th] ctxt 
bulwahn@39787
   829
    fun split_conjs i nprems th =
bulwahn@39787
   830
      if i > nprems then th
bulwahn@39787
   831
      else
bulwahn@39787
   832
        case try Drule.RSN (@{thm conjI}, (i, th)) of
bulwahn@39787
   833
          SOME th' => split_conjs i (nprems+1) th'
bulwahn@39787
   834
        | NONE => split_conjs (i+1) nprems th
bulwahn@39787
   835
  in
bulwahn@39787
   836
    singleton (Variable.export ctxt' ctxt) (split_conjs 1 (Thm.nprems_of fixed_th) fixed_th)
bulwahn@39787
   837
  end
bulwahn@39787
   838
  
bulwahn@33250
   839
fun expand_tuples thy intro =
bulwahn@33250
   840
  let
wenzelm@36610
   841
    val ctxt = ProofContext.init_global thy
bulwahn@33250
   842
    val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
bulwahn@33250
   843
    val intro_t = prop_of intro'
bulwahn@33250
   844
    val concl = Logic.strip_imp_concl intro_t
bulwahn@33250
   845
    val (p, args) = strip_comb (HOLogic.dest_Trueprop concl)
bulwahn@33250
   846
    val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
bulwahn@33250
   847
    val (pats', intro_t', ctxt3) = 
bulwahn@33250
   848
      fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
bulwahn@33250
   849
    fun rewrite_pat (ct1, ct2) =
bulwahn@33250
   850
      (ct1, cterm_of thy (Pattern.rewrite_term thy pats' [] (term_of ct2)))
bulwahn@33250
   851
    val t_insts' = map rewrite_pat t_insts
bulwahn@33250
   852
    val intro'' = Thm.instantiate (T_insts, t_insts') intro
bulwahn@33250
   853
    val [intro'''] = Variable.export ctxt3 ctxt [intro'']
bulwahn@33250
   854
    val intro'''' = Simplifier.full_simplify
bulwahn@33250
   855
      (HOL_basic_ss addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}])
bulwahn@33250
   856
      intro'''
bulwahn@33250
   857
    (* splitting conjunctions introduced by Pair_eq*)
bulwahn@39787
   858
    val intro''''' = split_conjuncts_in_assms ctxt intro''''
bulwahn@33250
   859
  in
bulwahn@33250
   860
    intro'''''
bulwahn@33250
   861
  end
bulwahn@33250
   862
bulwahn@39802
   863
(** making case distributivity rules **)
bulwahn@39802
   864
(*** this should be part of the datatype package ***)
bulwahn@39802
   865
bulwahn@39802
   866
fun datatype_names_of_case_name thy case_name =
bulwahn@39802
   867
  map (#1 o #2) (#descr (the (Datatype_Data.info_of_case thy case_name)))
bulwahn@39802
   868
bulwahn@39802
   869
fun make_case_distribs new_type_names descr sorts thy =
bulwahn@39802
   870
  let
bulwahn@39802
   871
    val case_combs = Datatype_Prop.make_case_combs new_type_names descr sorts thy "f";
bulwahn@39802
   872
    fun make comb =
bulwahn@39802
   873
      let
bulwahn@39802
   874
        val Type ("fun", [T, T']) = fastype_of comb;
bulwahn@39802
   875
        val (Const (case_name, _), fs) = strip_comb comb
bulwahn@39802
   876
        val used = Term.add_tfree_names comb []
bulwahn@39802
   877
        val U = TFree (Name.variant used "'t", HOLogic.typeS)
bulwahn@39802
   878
        val x = Free ("x", T)
bulwahn@39802
   879
        val f = Free ("f", T' --> U)
bulwahn@39802
   880
        fun apply_f f' =
bulwahn@39802
   881
          let
bulwahn@39802
   882
            val Ts = binder_types (fastype_of f')
bulwahn@39802
   883
            val bs = map Bound ((length Ts - 1) downto 0)
bulwahn@39802
   884
          in
bulwahn@39802
   885
            fold (curry absdummy) (rev Ts) (f $ (list_comb (f', bs)))
bulwahn@39802
   886
          end
bulwahn@39802
   887
        val fs' = map apply_f fs
bulwahn@39802
   888
        val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U)
bulwahn@39802
   889
      in
bulwahn@39802
   890
        HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x)
bulwahn@39802
   891
      end
bulwahn@39802
   892
  in
bulwahn@39802
   893
    map make case_combs
bulwahn@39802
   894
  end
bulwahn@39802
   895
bulwahn@39802
   896
fun case_rewrites thy Tcon =
bulwahn@39802
   897
  let
bulwahn@39802
   898
    val info = Datatype.the_info thy Tcon
bulwahn@39802
   899
    val descr = #descr info
bulwahn@39802
   900
    val sorts = #sorts info
bulwahn@39802
   901
    val typ_names = the_default [Tcon] (#alt_names info)
bulwahn@39802
   902
  in
bulwahn@39802
   903
    map (Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop)
bulwahn@39802
   904
      (make_case_distribs typ_names [descr] sorts thy)
bulwahn@39802
   905
  end
bulwahn@39802
   906
bulwahn@39802
   907
fun instantiated_case_rewrites thy Tcon =
bulwahn@39802
   908
  let
bulwahn@39802
   909
    val rew_ths = case_rewrites thy Tcon
bulwahn@39802
   910
    val ctxt = ProofContext.init_global thy
bulwahn@39802
   911
    fun instantiate th =
bulwahn@39802
   912
    let
bulwahn@39802
   913
      val f = (fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th))))))
bulwahn@39802
   914
      val Type ("fun", [uninst_T, uninst_T']) = fastype_of f
bulwahn@39802
   915
      val ([tname, tname', uname, yname], ctxt') = Variable.add_fixes ["'t", "'t'", "'u", "y"] ctxt
bulwahn@39802
   916
      val T = TFree (tname, HOLogic.typeS)
bulwahn@39802
   917
      val T' = TFree (tname', HOLogic.typeS)
bulwahn@39802
   918
      val U = TFree (uname, HOLogic.typeS)
bulwahn@39802
   919
      val y = Free (yname, U)
bulwahn@39802
   920
      val f' = absdummy (U --> T', Bound 0 $ y)
bulwahn@39802
   921
      val th' = Thm.certify_instantiate
bulwahn@39802
   922
        ([(dest_TVar uninst_T, U --> T'), (dest_TVar uninst_T', T')],
bulwahn@39802
   923
         [((fst (dest_Var f), (U --> T') --> T'), f')]) th
bulwahn@39802
   924
      val [th'] = Variable.export ctxt' ctxt [th']
bulwahn@39802
   925
   in
bulwahn@39802
   926
     th'
bulwahn@39802
   927
   end
bulwahn@39802
   928
 in
bulwahn@39802
   929
   map instantiate rew_ths
bulwahn@39802
   930
 end
bulwahn@39802
   931
bulwahn@39802
   932
fun case_betapply thy t =
bulwahn@39802
   933
  let
bulwahn@39802
   934
    val case_name = fst (dest_Const (fst (strip_comb t)))
bulwahn@39802
   935
    val Tcons = datatype_names_of_case_name thy case_name
bulwahn@39802
   936
    val ths = maps (instantiated_case_rewrites thy) Tcons
bulwahn@39802
   937
  in
bulwahn@39802
   938
    MetaSimplifier.rewrite_term thy
bulwahn@39802
   939
      (map (fn th => th RS @{thm eq_reflection}) ths) [] t
bulwahn@39802
   940
  end
bulwahn@39802
   941
bulwahn@39657
   942
(*** conversions ***)
bulwahn@39657
   943
bulwahn@39657
   944
fun imp_prems_conv cv ct =
bulwahn@39657
   945
  case Thm.term_of ct of
bulwahn@39657
   946
    Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
bulwahn@39657
   947
  | _ => Conv.all_conv ct
bulwahn@39657
   948
bulwahn@39657
   949
fun all_params_conv cv ctxt ct =
bulwahn@39657
   950
  if Logic.is_all (Thm.term_of ct)
bulwahn@39657
   951
  then Conv.arg_conv (Conv.abs_conv (all_params_conv cv o #2) ctxt) ct
bulwahn@39657
   952
  else cv ctxt ct;
bulwahn@39657
   953
  
bulwahn@36047
   954
(** eta contract higher-order arguments **)
bulwahn@35875
   955
bulwahn@35875
   956
fun eta_contract_ho_arguments thy intro =
bulwahn@35875
   957
  let
bulwahn@35875
   958
    fun f atom = list_comb (apsnd ((map o map_products) Envir.eta_contract) (strip_comb atom))
bulwahn@35875
   959
  in
bulwahn@35875
   960
    map_term thy (map_concl f o map_atoms f) intro
bulwahn@35875
   961
  end
bulwahn@35875
   962
bulwahn@36047
   963
(** remove equalities **)
bulwahn@36022
   964
bulwahn@36022
   965
fun remove_equalities thy intro =
bulwahn@36022
   966
  let
bulwahn@36022
   967
    fun remove_eqs intro_t =
bulwahn@36022
   968
      let
bulwahn@36022
   969
        val (prems, concl) = Logic.strip_horn intro_t
bulwahn@36022
   970
        fun remove_eq (prems, concl) =
bulwahn@36022
   971
          let
bulwahn@36022
   972
            fun removable_eq prem =
bulwahn@36022
   973
              case try (HOLogic.dest_eq o HOLogic.dest_Trueprop) prem of
bulwahn@36022
   974
                SOME (lhs, rhs) => (case lhs of
bulwahn@36022
   975
                  Var _ => true
bulwahn@36022
   976
                  | _ => (case rhs of Var _ => true | _ => false))
bulwahn@36022
   977
              | NONE => false
bulwahn@36022
   978
          in
bulwahn@36022
   979
            case find_first removable_eq prems of
bulwahn@36022
   980
              NONE => (prems, concl)
bulwahn@36022
   981
            | SOME eq =>
bulwahn@36022
   982
              let
bulwahn@36022
   983
                val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
bulwahn@36022
   984
                val prems' = remove (op =) eq prems
bulwahn@36022
   985
                val subst = (case lhs of
bulwahn@36022
   986
                  (v as Var _) =>
bulwahn@36022
   987
                    (fn t => if t = v then rhs else t)
bulwahn@36022
   988
                | _ => (case rhs of
bulwahn@36022
   989
                   (v as Var _) => (fn t => if t = v then lhs else t)))
bulwahn@36022
   990
              in
bulwahn@36022
   991
                remove_eq (map (map_aterms subst) prems', map_aterms subst concl)
bulwahn@36022
   992
              end
bulwahn@36022
   993
          end
bulwahn@36022
   994
      in
bulwahn@36022
   995
        Logic.list_implies (remove_eq (prems, concl))
bulwahn@36022
   996
      end
bulwahn@36022
   997
  in
bulwahn@36022
   998
    map_term thy remove_eqs intro
bulwahn@36022
   999
  end
bulwahn@35875
  1000
bulwahn@36246
  1001
(* Some last processing *)
bulwahn@36246
  1002
bulwahn@36246
  1003
fun remove_pointless_clauses intro =
bulwahn@36246
  1004
  if Logic.strip_imp_prems (prop_of intro) = [@{prop "False"}] then
bulwahn@36246
  1005
    []
bulwahn@36246
  1006
  else [intro]
bulwahn@36246
  1007
bulwahn@36246
  1008
(* some peephole optimisations *)
bulwahn@36246
  1009
bulwahn@36246
  1010
fun peephole_optimisation thy intro =
bulwahn@36246
  1011
  let
wenzelm@36610
  1012
    val process =
wenzelm@36610
  1013
      MetaSimplifier.rewrite_rule (Predicate_Compile_Simps.get (ProofContext.init_global thy))
bulwahn@36246
  1014
    fun process_False intro_t =
bulwahn@36246
  1015
      if member (op =) (Logic.strip_imp_prems intro_t) @{prop "False"} then NONE else SOME intro_t
bulwahn@36246
  1016
    fun process_True intro_t =
bulwahn@36246
  1017
      map_filter_premises (fn p => if p = @{prop True} then NONE else SOME p) intro_t
bulwahn@36246
  1018
  in
bulwahn@36246
  1019
    Option.map (Skip_Proof.make_thm thy)
bulwahn@36246
  1020
      (process_False (process_True (prop_of (process intro))))
bulwahn@36246
  1021
  end
bulwahn@36246
  1022
bulwahn@39541
  1023
(* defining a quickcheck predicate *)
bulwahn@39541
  1024
bulwahn@39541
  1025
fun strip_imp_prems (Const(@{const_name HOL.implies}, _) $ A $ B) = A :: strip_imp_prems B
bulwahn@39541
  1026
  | strip_imp_prems _ = [];
bulwahn@39541
  1027
bulwahn@39541
  1028
fun strip_imp_concl (Const(@{const_name HOL.implies}, _) $ A $ B) = strip_imp_concl B
bulwahn@39541
  1029
  | strip_imp_concl A = A : term;
bulwahn@39541
  1030
bulwahn@39541
  1031
fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);
bulwahn@39541
  1032
bulwahn@39541
  1033
fun define_quickcheck_predicate t thy =
bulwahn@39541
  1034
  let
bulwahn@39541
  1035
    val (vs, t') = strip_abs t
bulwahn@39541
  1036
    val vs' = Variable.variant_frees (ProofContext.init_global thy) [] vs
bulwahn@39541
  1037
    val t'' = subst_bounds (map Free (rev vs'), t')
bulwahn@39541
  1038
    val (prems, concl) = strip_horn t''
bulwahn@39541
  1039
    val constname = "quickcheck"
bulwahn@39541
  1040
    val full_constname = Sign.full_bname thy constname
bulwahn@39541
  1041
    val constT = map snd vs' ---> @{typ bool}
bulwahn@39541
  1042
    val thy1 = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
bulwahn@39541
  1043
    val const = Const (full_constname, constT)
bulwahn@39541
  1044
    val t = Logic.list_implies
bulwahn@39541
  1045
      (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
bulwahn@39541
  1046
       HOLogic.mk_Trueprop (list_comb (const, map Free vs')))
bulwahn@39541
  1047
    val tac = fn _ => Skip_Proof.cheat_tac thy1
bulwahn@39541
  1048
    val intro = Goal.prove (ProofContext.init_global thy1) (map fst vs') [] t tac
bulwahn@39541
  1049
  in
bulwahn@39541
  1050
    ((((full_constname, constT), vs'), intro), thy1)
bulwahn@39541
  1051
  end
bulwahn@39541
  1052
bulwahn@33250
  1053
end;