src/FOL/simpdata.ML
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(*  Title:      FOL/simpdata.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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Simplification data for FOL.
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*)
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(*Make meta-equalities.  The operator below is Trueprop*)
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fun mk_meta_eq th =
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  (case Thm.concl_of th of
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    _ $ (Const(\<^const_name>\<open>eq\<close>,_)$_$_)   => th RS @{thm eq_reflection}
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  | _ $ (Const(\<^const_name>\<open>iff\<close>,_)$_$_) => th RS @{thm iff_reflection}
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  | _ => error "conclusion must be a =-equality or <->");
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fun mk_eq th =
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  (case Thm.concl_of th of
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    Const(\<^const_name>\<open>Pure.eq\<close>,_)$_$_ => th
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  | _ $ (Const(\<^const_name>\<open>eq\<close>,_)$_$_)   => mk_meta_eq th
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  | _ $ (Const(\<^const_name>\<open>iff\<close>,_)$_$_) => mk_meta_eq th
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  | _ $ (Const(\<^const_name>\<open>Not\<close>,_)$_)      => th RS @{thm iff_reflection_F}
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  | _  => th RS @{thm iff_reflection_T});
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(*Replace premises x=y, X<->Y by X==Y*)
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fun mk_meta_prems ctxt =
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    rule_by_tactic ctxt
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      (REPEAT_FIRST (resolve_tac ctxt [@{thm meta_eq_to_obj_eq}, @{thm def_imp_iff}]));
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(*Congruence rules for = or <-> (instead of ==)*)
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fun mk_meta_cong ctxt rl =
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  Drule.zero_var_indexes (mk_meta_eq (mk_meta_prems ctxt rl))
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    handle THM _ =>
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      error("Premises and conclusion of congruence rules must use =-equality or <->");
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val mksimps_pairs =
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  [(\<^const_name>\<open>imp\<close>, [@{thm mp}]), (\<^const_name>\<open>conj\<close>, [@{thm conjunct1}, @{thm conjunct2}]),
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   (\<^const_name>\<open>All\<close>, [@{thm spec}]), (\<^const_name>\<open>True\<close>, []), (\<^const_name>\<open>False\<close>, [])];
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fun mk_atomize pairs =
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  let
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    fun atoms th =
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      (case Thm.concl_of th of
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         Const(\<^const_name>\<open>Trueprop\<close>,_) $ p =>
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           (case head_of p of
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              Const(a,_) =>
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                (case AList.lookup (op =) pairs a of
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                   SOME(rls) => maps atoms ([th] RL rls)
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                 | NONE => [th])
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            | _ => [th])
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       | _ => [th])
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  in atoms end;
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fun mksimps pairs ctxt = map mk_eq o mk_atomize pairs o Variable.gen_all ctxt;
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(** make simplification procedures for quantifier elimination **)
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structure Quantifier1 = Quantifier1
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(
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  (*abstract syntax*)
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  fun dest_eq (Const (\<^const_name>\<open>eq\<close>, _) $ s $ t) = SOME (s, t)
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    | dest_eq _ = NONE
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  fun dest_conj (Const (\<^const_name>\<open>conj\<close>, _) $ s $ t) = SOME (s, t)
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    | dest_conj _ = NONE
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  fun dest_imp (Const (\<^const_name>\<open>imp\<close>, _) $ s $ t) = SOME (s, t)
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    | dest_imp _ = NONE
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  val conj = FOLogic.conj
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  val imp  = FOLogic.imp
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  (*rules*)
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  val iff_reflection = @{thm iff_reflection}
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  val iffI = @{thm iffI}
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  val iff_trans = @{thm iff_trans}
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  val conjI= @{thm conjI}
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  val conjE= @{thm conjE}
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  val impI = @{thm impI}
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  val mp   = @{thm mp}
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  val uncurry = @{thm uncurry}
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  val exI  = @{thm exI}
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  val exE  = @{thm exE}
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  val iff_allI = @{thm iff_allI}
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  val iff_exI = @{thm iff_exI}
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  val all_comm = @{thm all_comm}
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  val ex_comm = @{thm ex_comm}
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);
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(*** Case splitting ***)
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structure Splitter = Splitter
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(
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  val context = \<^context>
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  val mk_eq = mk_eq
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  val meta_eq_to_iff = @{thm meta_eq_to_iff}
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  val iffD = @{thm iffD2}
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  val disjE = @{thm disjE}
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  val conjE = @{thm conjE}
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  val exE = @{thm exE}
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  val contrapos = @{thm contrapos}
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  val contrapos2 = @{thm contrapos2}
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  val notnotD = @{thm notnotD}
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  val safe_tac = Cla.safe_tac
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);
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val split_tac = Splitter.split_tac;
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val split_inside_tac = Splitter.split_inside_tac;
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val split_asm_tac = Splitter.split_asm_tac;
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(*** Standard simpsets ***)
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val triv_rls = [@{thm TrueI}, @{thm refl}, reflexive_thm, @{thm iff_refl}, @{thm notFalseI}];
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fun unsafe_solver ctxt =
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  FIRST' [resolve_tac ctxt (triv_rls @ Simplifier.prems_of ctxt),
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    assume_tac ctxt,
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    eresolve_tac ctxt @{thms FalseE}];
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(*No premature instantiation of variables during simplification*)
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fun safe_solver ctxt =
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  FIRST' [match_tac ctxt (triv_rls @ Simplifier.prems_of ctxt),
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    eq_assume_tac, ematch_tac ctxt @{thms FalseE}];
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(*No simprules, but basic infastructure for simplification*)
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val FOL_basic_ss =
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  empty_simpset \<^context>
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  setSSolver (mk_solver "FOL safe" safe_solver)
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  setSolver (mk_solver "FOL unsafe" unsafe_solver)
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  |> Simplifier.set_subgoaler asm_simp_tac
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  |> Simplifier.set_mksimps (mksimps mksimps_pairs)
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  |> Simplifier.set_mkcong mk_meta_cong
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  |> simpset_of;
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fun unfold_tac ctxt ths =
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  ALLGOALS (full_simp_tac (clear_simpset (put_simpset FOL_basic_ss ctxt) addsimps ths));
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(*** integration of simplifier with classical reasoner ***)
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structure Clasimp = Clasimp
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(
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  structure Simplifier = Simplifier
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    and Splitter = Splitter
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    and Classical = Cla
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    and Blast = Blast
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  val iffD1 = @{thm iffD1}
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  val iffD2 = @{thm iffD2}
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  val notE = @{thm notE}
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);
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open Clasimp;
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