src/HOL/Eisbach/Tests.thy

some simpler, cleaner proofs

(*  Title:      HOL/Eisbach/Tests.thy
    Author:     Daniel Matichuk, NICTA/UNSW
*)

section \<open>Miscellaneous Eisbach tests\<close>

theory Tests
imports Main Eisbach_Tools
begin


subsection \<open>Named Theorems Tests\<close>

named_theorems foo

method foo declares foo = (rule foo)

lemma
  assumes A [foo]: A
  shows A
  apply foo
  done

method abs_used for P = (match (P) in "\<lambda>a. ?Q" \<Rightarrow> fail \<bar> _ \<Rightarrow> -)


subsection \<open>Match Tests\<close>

notepad
begin
  have dup: "\<And>A. A \<Longrightarrow> A \<Longrightarrow> A" by simp

  fix A y
  have "(\<And>x. A x) \<Longrightarrow> A y"
    apply (rule dup, match premises in Y: "\<And>B. P B" for P \<Rightarrow> \<open>match (P) in A \<Rightarrow> \<open>print_fact Y, rule Y\<close>\<close>)
    apply (rule dup, match premises in Y: "\<And>B :: 'a. P B" for P \<Rightarrow> \<open>match (P) in A \<Rightarrow> \<open>print_fact Y, rule Y\<close>\<close>)
    apply (rule dup, match premises in Y: "\<And>B :: 'a. P B" for P \<Rightarrow> \<open>match conclusion in "P y" for y \<Rightarrow> \<open>print_fact Y, print_term y, rule Y[where B=y]\<close>\<close>)
    apply (rule dup, match premises in Y: "\<And>B :: 'a. P B" for P \<Rightarrow> \<open>match conclusion in "P z" for z \<Rightarrow> \<open>print_fact Y, print_term y, rule Y[where B=z]\<close>\<close>)
    apply (rule dup, match conclusion in "P y" for P \<Rightarrow> \<open>match premises in Y: "\<And>z. P z" \<Rightarrow> \<open>print_fact Y, rule Y[where z=y]\<close>\<close>)
    apply (match premises in Y: "\<And>z :: 'a. P z" for P \<Rightarrow> \<open>match conclusion in "P y" \<Rightarrow> \<open>print_fact Y, rule Y[where z=y]\<close>\<close>)
    done

  assume X: "\<And>x. A x" "A y"
  have "A y"
    apply (match X in Y:"\<And>B. A B" and Y':"B ?x" for B \<Rightarrow> \<open>print_fact Y[where B=y], print_term B\<close>)
    apply (match X in Y:"B ?x" and Y':"B ?x" for B \<Rightarrow> \<open>print_fact Y, print_term B\<close>)
    apply (match X in Y:"B x" and Y':"B x" for B x \<Rightarrow> \<open>print_fact Y, print_term B, print_term x\<close>)
    apply (insert X)
    apply (match premises in Y:"\<And>B. A B" and Y':"B y" for B and y :: 'a \<Rightarrow> \<open>print_fact Y[where B=y], print_term B\<close>)
    apply (match premises in Y:"B ?x" and Y':"B ?x" for B \<Rightarrow> \<open>print_fact Y, print_term B\<close>)
    apply (match premises in Y:"B x" and Y':"B x" for B x \<Rightarrow> \<open>print_fact Y, print_term B\<close>)
    apply (match conclusion in "P x" and "P y" for P x \<Rightarrow> \<open>print_term P, print_term x\<close>)
    apply assumption
    done

  {
   fix B x y
   assume X: "\<And>x y. B x x y"
   have "B x x y"
     by (match X in Y:"\<And>y. B y y z" for z \<Rightarrow> \<open>rule Y[where y=x]\<close>)

   fix A B
   have "(\<And>x y. A (B x) y) \<Longrightarrow> A (B x) y"
     by (match premises in Y: "\<And>xx. ?H (B xx)" \<Rightarrow> \<open>rule Y\<close>)
  }

  (* match focusing retains prems *)
  fix B x
  have "(\<And>x. A x) \<Longrightarrow> (\<And>z. B z) \<Longrightarrow> A y \<Longrightarrow> B x"
    apply (match premises in Y: "\<And>z :: 'a. A z"  \<Rightarrow> \<open>match premises in Y': "\<And>z :: 'b. B z" \<Rightarrow> \<open>print_fact Y, print_fact Y', rule Y'[where z=x]\<close>\<close>)
    done

  (*Attributes *)
  fix C
  have "(\<And>x :: 'a. A x)  \<Longrightarrow> (\<And>z. B z) \<Longrightarrow> A y \<Longrightarrow> B x \<and> B x \<and> A y"
    apply (intro conjI)
    apply (match premises in Y: "\<And>z :: 'a. A z" and Y'[intro]:"\<And>z :: 'b. B z" \<Rightarrow> fastforce)
    apply (match premises in Y: "\<And>z :: 'a. A z"  \<Rightarrow> \<open>match premises in Y'[intro]:"\<And>z :: 'b. B z" \<Rightarrow> fastforce\<close>)
    apply (match premises in Y[thin]: "\<And>z :: 'a. A z"  \<Rightarrow> \<open>(match premises in Y':"\<And>z :: 'a. A z" \<Rightarrow> \<open>print_fact Y,fail\<close> \<bar> _ \<Rightarrow> \<open>print_fact Y\<close>)\<close>)
    (*apply (match premises in Y: "\<And>z :: 'b. B z"  \<Rightarrow> \<open>(match premises in Y'[thin]:"\<And>z :: 'b. B z" \<Rightarrow> \<open>(match premises in Y':"\<And>z :: 'a. A z" \<Rightarrow> fail \<bar> Y': _ \<Rightarrow> -)\<close>)\<close>)*)
    apply assumption
    done

  fix A B C D
  have "\<And>uu'' uu''' uu uu'. (\<And>x :: 'a. A uu' x)  \<Longrightarrow> D uu y \<Longrightarrow> (\<And>z. B uu z) \<Longrightarrow> C uu y \<Longrightarrow> (\<And>z y. C uu z)  \<Longrightarrow> B uu x \<and> B uu x \<and> C uu y"
    apply (match premises in Y[thin]: "\<And>z :: 'a. A ?zz' z" and
                          Y'[thin]: "\<And>rr :: 'b. B ?zz rr" \<Rightarrow>
          \<open>print_fact Y, print_fact Y', intro conjI, rule Y', insert Y', insert Y'[where rr=x]\<close>)
    apply (match premises in Y:"B ?u ?x" \<Rightarrow> \<open>rule Y\<close>)
    apply (insert TrueI)
    apply (match premises in Y'[thin]: "\<And>ff. B uu ff" for uu \<Rightarrow> \<open>insert Y', drule meta_spec[where x=x]\<close>)
    apply assumption
    done


  (* Multi-matches. As many facts as match are bound. *)
  fix A B C x
  have "(\<And>x :: 'a. A x) \<Longrightarrow> (\<And>y :: 'a. B y) \<Longrightarrow> C y \<Longrightarrow> (A x \<and> B y \<and> C y)"
    apply (match premises in Y[thin]: "\<And>z :: 'a. ?A z" (multi) \<Rightarrow> \<open>intro conjI, (rule Y)+\<close>)
    apply (match premises in Y[thin]: "\<And>z :: 'a. ?A z" (multi) \<Rightarrow> fail \<bar> "C y" \<Rightarrow> -) (* multi-match must bind something *)
    apply (match premises in Y: "C y" \<Rightarrow> \<open>rule Y\<close>)
    done

  fix A B C x
  have "(\<And>x :: 'a. A x) \<Longrightarrow> (\<And>y :: 'a. B y) \<Longrightarrow> C y \<Longrightarrow> (A x \<and> B y \<and> C y)"
    apply (match premises in Y[thin]: "\<And>z. ?A z" (multi) \<Rightarrow> \<open>intro conjI, (rule Y)+\<close>)
    apply (match premises in Y[thin]: "\<And>z. ?A z" (multi) \<Rightarrow> fail \<bar> "C y" \<Rightarrow> -) (* multi-match must bind something *)
    apply (match premises in Y: "C y" \<Rightarrow> \<open>rule Y\<close>)
    done

  fix A B C P Q and x :: 'a and y :: 'a
  have "(\<And>x y :: 'a. A x y \<and> Q) \<Longrightarrow> (\<And>a b. B (a :: 'a) (b :: 'a) \<and> Q) \<Longrightarrow> (\<And>x y. C (x :: 'a) (y :: 'a) \<and> P) \<Longrightarrow> A y x \<and> B y x"
    by (match premises in Y: "\<And>z a. ?A (z :: 'a) (a :: 'a) \<and> R" (multi) for R \<Rightarrow> \<open>rule conjI, rule Y[where z=x,THEN conjunct1], rule Y[THEN conjunct1]\<close>)


  (*We may use for-fixes in multi-matches too. All bound facts must agree on the fixed term *)
  fix A B C x
  have "(\<And>y :: 'a. B y \<and> C y) \<Longrightarrow> (\<And>x :: 'a. A x \<and> B x) \<Longrightarrow> (\<And>y :: 'a. A y \<and> C y) \<Longrightarrow> C y \<Longrightarrow> (A x \<and> B y \<and> C y)"
    apply (match premises in Y: "\<And>x :: 'a. P x \<and> ?U x" (multi) for P \<Rightarrow>
                                  \<open>match (P) in B \<Rightarrow> fail
                                        \<bar> "\<lambda>a. B" \<Rightarrow> fail
                                        \<bar> _ \<Rightarrow> -,
                                  intro conjI, (rule Y[THEN conjunct1])\<close>)
    apply (rule dup)
    apply (match premises in Y':"\<And>x :: 'a. ?U x \<and> Q x" and Y: "\<And>x :: 'a. Q x \<and> ?U x" (multi)  for Q \<Rightarrow> \<open>insert Y[THEN conjunct1]\<close>)
    apply assumption (* Previous match requires that Q is consistent *)
    apply (match premises in Y: "\<And>z :: 'a. ?A z \<longrightarrow> False" (multi) \<Rightarrow> \<open>print_fact Y, fail\<close> \<bar> "C y" \<Rightarrow> \<open>print_term C\<close>) (* multi-match must bind something *)
    apply (match premises in Y: "\<And>x. B x \<and> C x" \<Rightarrow> \<open>intro conjI Y[THEN conjunct1]\<close>)
    apply (match premises in Y: "C ?x" \<Rightarrow> \<open>rule Y\<close>)
    done

  (* All bindings must be tried for a particular theorem.
     However all combinations are NOT explored. *)
  fix B A C
  assume asms:"\<And>a b. B (a :: 'a) (b :: 'a) \<and> Q" "\<And>x :: 'a. A x x \<and> Q" "\<And>a b. C (a :: 'a) (b :: 'a) \<and> Q"
  have "B y x \<and> C x y \<and> B x y \<and> C y x \<and> A x x"
    apply (intro conjI)
    apply (match asms in Y: "\<And>z a. ?A (z :: 'a) (a :: 'a) \<and> R" (multi) for R \<Rightarrow> \<open>rule Y[where z=x,THEN conjunct1]\<close>)
    apply (match asms in Y: "\<And>z a. ?A (z :: 'a) (a :: 'a) \<and> R" (multi) for R \<Rightarrow> \<open>rule Y[where a=x,THEN conjunct1]\<close>)
    apply (match asms in Y: "\<And>z a. ?A (z :: 'a) (a :: 'a) \<and> R" (multi) for R \<Rightarrow> \<open>rule Y[where a=x,THEN conjunct1]\<close>)
    apply (match asms in Y: "\<And>z a. ?A (z :: 'a) (a :: 'a) \<and> R" (multi) for R \<Rightarrow> \<open>rule Y[where z=x,THEN conjunct1]\<close>)
    apply (match asms in Y: "\<And>z a. A (z :: 'a) (a :: 'a) \<and> R"  for R \<Rightarrow> fail \<bar> _ \<Rightarrow> -)
    apply (rule asms[THEN conjunct1])
    done

  (* Attributes *)
  fix A B C x
  have "(\<And>x :: 'a. A x \<and> B x) \<Longrightarrow> (\<And>y :: 'a. A y \<and> C y) \<Longrightarrow> (\<And>y :: 'a. B y \<and> C y) \<Longrightarrow> C y \<Longrightarrow> (A x \<and> B y \<and> C y)"
    apply (match premises in Y: "\<And>x :: 'a. P x \<and> ?U x" (multi) for P \<Rightarrow> \<open>match Y[THEN conjunct1]  in Y':"?H"  (multi) \<Rightarrow> \<open>intro conjI,rule Y'\<close>\<close>)
    apply (match premises in Y: "\<And>x :: 'a. P x \<and> ?U x" (multi) for P \<Rightarrow> \<open>match Y[THEN conjunct2]  in Y':"?H"  (multi) \<Rightarrow> \<open>rule Y'\<close>\<close>)
    apply assumption
    done

(* Removed feature for now *)
(*
  fix A B C x
  have "(\<And>x :: 'a. A x \<and> B x) \<Longrightarrow> (\<And>y :: 'a. A y \<and> C y) \<Longrightarrow> (\<And>y :: 'a. B y \<and> C y) \<Longrightarrow> C y \<Longrightarrow> (A x \<and> B y \<and> C y)"
  apply (match prems in Y: "\<And>x :: 'a. P x \<and> ?U x" (multi) for P \<Rightarrow> \<open>match \<open>K @{thms Y TrueI}\<close> in Y':"?H"  (multi) \<Rightarrow> \<open>rule conjI; (rule Y')?\<close>\<close>)
  apply (match prems in Y: "\<And>x :: 'a. P x \<and> ?U x" (multi) for P \<Rightarrow> \<open>match \<open>K [@{thm Y}]\<close> in Y':"?H"  (multi) \<Rightarrow> \<open>rule Y'\<close>\<close>)
  done
*)
  (* Testing THEN_ALL_NEW within match *)
  fix A B C x
  have "(\<And>x :: 'a. A x \<and> B x) \<Longrightarrow> (\<And>y :: 'a. A y \<and> C y) \<Longrightarrow> (\<And>y :: 'a. B y \<and> C y) \<Longrightarrow> C y \<Longrightarrow> (A x \<and> B y \<and> C y)"
    apply (match premises in Y: "\<And>x :: 'a. P x \<and> ?U x" (multi) for P \<Rightarrow> \<open>intro conjI ; ((rule Y[THEN conjunct1])?); rule Y[THEN conjunct2] \<close>)
    done

  (* Cut tests *)
  fix A B C

  have "D \<and> C  \<Longrightarrow> A \<and> B  \<Longrightarrow> A \<longrightarrow> C \<Longrightarrow> D \<longrightarrow> True \<Longrightarrow> C"
    by (((match premises in I: "P \<and> Q" (cut)
              and I': "P \<longrightarrow> ?U" for P Q \<Rightarrow> \<open>rule mp [OF I' I[THEN conjunct1]]\<close>)?), simp)

  have "D \<and> C  \<Longrightarrow> A \<and> B  \<Longrightarrow> A \<longrightarrow> C \<Longrightarrow> D \<longrightarrow> True \<Longrightarrow> C"
    by (match premises in I: "P \<and> Q" (cut 2)
              and I': "P \<longrightarrow> ?U" for P Q \<Rightarrow> \<open>rule mp [OF I' I[THEN conjunct1]]\<close>)

  have "A \<and> B \<Longrightarrow> A \<longrightarrow> C \<Longrightarrow> C"
    by (((match premises in I: "P \<and> Q" (cut)
              and I': "P \<longrightarrow> ?U" for P Q \<Rightarrow> \<open>rule mp [OF I' I[THEN conjunct1]]\<close>)?, simp) | simp)

  fix f x y
  have "f x y \<Longrightarrow> f x y"
    by (match conclusion in "f x y" for f x y  \<Rightarrow> \<open>print_term f\<close>)

  fix A B C
  assume X: "A \<and> B" "A \<and> C" C
  have "A \<and> B \<and> C"
    by (match X in H: "A \<and> ?H" (multi, cut) \<Rightarrow>
          \<open>match H in "A \<and> C" and "A \<and> B" \<Rightarrow> fail\<close>
        | simp add: X)


  (* Thinning an inner focus *)
  (* Thinning should persist within a match, even when on an external premise *)

  fix A
  have "(\<And>x. A x \<and> B) \<Longrightarrow> B \<and> C \<Longrightarrow> C"
    apply (match premises in H:"\<And>x. A x \<and> B" \<Rightarrow>
                     \<open>match premises in H'[thin]: "\<And>x. A x \<and> B" \<Rightarrow>
                      \<open>match premises in H'':"\<And>x. A x \<and> B" \<Rightarrow> fail
                                         \<bar> _ \<Rightarrow> -\<close>
                      ,match premises in H'':"\<And>x. A x \<and> B" \<Rightarrow> fail \<bar> _ \<Rightarrow> -\<close>)
    apply (match premises in H:"\<And>x. A x \<and> B" \<Rightarrow> fail
                              \<bar> H':_ \<Rightarrow> \<open>rule H'[THEN conjunct2]\<close>)
    done


  (* Local premises *)
  (* Only match premises which actually existed in the goal we just focused.*)

  fix A
  assume asms: "C \<and> D"
  have "B \<and> C \<Longrightarrow> C"
    by (match premises in _ \<Rightarrow> \<open>insert asms,
            match premises (local) in "B \<and> C" \<Rightarrow> fail
                                  \<bar> H:"C \<and> D" \<Rightarrow> \<open>rule H[THEN conjunct1]\<close>\<close>)
end



(* Testing inner focusing. This fails if we don't smash flex-flex pairs produced
   by retrofitting. This needs to be done more carefully to avoid smashing
   legitimate pairs.*)

schematic_goal "?A x \<Longrightarrow> A x"
  apply (match conclusion in "H" for H \<Rightarrow> \<open>match conclusion in Y for Y \<Rightarrow> \<open>print_term Y\<close>\<close>)
  apply assumption
  done

(* Ensure short-circuit after first match failure *)
lemma
  assumes A: "P \<and> Q"
  shows "P"
  by ((match A in "P \<and> Q" \<Rightarrow> fail \<bar> "?H" \<Rightarrow> -) | simp add: A)

lemma
  assumes A: "D \<and> C" "A \<and> B" "A \<longrightarrow> B"
  shows "A"
  apply ((match A in U: "P \<and> Q" (cut) and "P' \<longrightarrow> Q'" for P Q P' Q' \<Rightarrow>
      \<open>simp add: U\<close> \<bar> "?H" \<Rightarrow> -) | -)
  apply (simp add: A)
  done


subsection \<open>Uses Tests\<close>

ML \<open>
  fun test_internal_fact ctxt factnm =
    (case try (Proof_Context.get_thms ctxt) factnm of
      NONE => ()
    | SOME _ => error "Found internal fact");
\<close>

method uses_test\<^sub>1 uses uses_test\<^sub>1_uses = (rule uses_test\<^sub>1_uses)

lemma assumes A shows A by (uses_test\<^sub>1 uses_test\<^sub>1_uses: assms)

ML \<open>test_internal_fact @{context} "uses_test\<^sub>1_uses"\<close>

ML \<open>test_internal_fact @{context} "Tests.uses_test\<^sub>1_uses"\<close>
ML \<open>test_internal_fact @{context} "Tests.uses_test\<^sub>1.uses_test\<^sub>1_uses"\<close>

subsection \<open>Basic fact passing\<close>

method find_fact for x y :: bool uses facts1 facts2 =
  (match facts1 in U: "x" \<Rightarrow> \<open>insert U,
      match facts2 in U: "y" \<Rightarrow> \<open>insert U\<close>\<close>)

lemma assumes A: A and B: B shows "A \<and> B"
  apply (find_fact "A" "B" facts1: A facts2: B)
  apply (rule conjI; assumption)
  done


subsection \<open>Testing term and fact passing in recursion\<close>


method recursion_example for x :: bool uses facts =
  (match (x) in
    "A \<and> B" for A B \<Rightarrow> \<open>(recursion_example A facts: facts, recursion_example B facts: facts)\<close>
  \<bar> "?H" \<Rightarrow> \<open>match facts in U: "x" \<Rightarrow> \<open>insert U\<close>\<close>)

lemma
  assumes asms: "A" "B" "C" "D"
  shows "(A \<and> B) \<and> (C \<and> D)"
  apply (recursion_example "(A \<and> B) \<and> (C \<and> D)" facts: asms)
  apply simp
  done

(* uses facts are not accumulated *)

method recursion_example' for A :: bool and B :: bool uses facts =
  (match facts in
    H: "A" and H': "B" \<Rightarrow> \<open>recursion_example' "A" "B" facts: H TrueI\<close>
  \<bar> "A" and "True" \<Rightarrow> \<open>recursion_example' "A" "B" facts: TrueI\<close>
  \<bar> "True" \<Rightarrow> -
  \<bar> "PROP ?P" \<Rightarrow> fail)

lemma
  assumes asms: "A" "B"
  shows "True"
  apply (recursion_example' "A" "B" facts: asms)
  apply simp
  done


(*Method.sections in existing method*)
method my_simp\<^sub>1 uses my_simp\<^sub>1_facts = (simp add: my_simp\<^sub>1_facts)
lemma assumes A shows A by (my_simp\<^sub>1 my_simp\<^sub>1_facts: assms)

(*Method.sections via Eisbach argument parser*)
method uses_test\<^sub>2 uses uses_test\<^sub>2_uses = (uses_test\<^sub>1 uses_test\<^sub>1_uses: uses_test\<^sub>2_uses)
lemma assumes A shows A by (uses_test\<^sub>2 uses_test\<^sub>2_uses: assms)


subsection \<open>Declaration Tests\<close>

named_theorems declare_facts\<^sub>1

method declares_test\<^sub>1 declares declare_facts\<^sub>1 = (rule declare_facts\<^sub>1)

lemma assumes A shows A by (declares_test\<^sub>1 declare_facts\<^sub>1: assms)

lemma assumes A[declare_facts\<^sub>1]: A shows A by declares_test\<^sub>1


subsection \<open>Rule Instantiation Tests\<close>

method my_allE\<^sub>1 for x :: 'a and P :: "'a \<Rightarrow> bool" =
  (erule allE [where x = x and P = P])

lemma "\<forall>x. Q x \<Longrightarrow> Q x" by (my_allE\<^sub>1 x Q)

method my_allE\<^sub>2 for x :: 'a and P :: "'a \<Rightarrow> bool" =
  (erule allE [of P x])

lemma "\<forall>x. Q x \<Longrightarrow> Q x" by (my_allE\<^sub>2 x Q)

method my_allE\<^sub>3 for x :: 'a and P :: "'a \<Rightarrow> bool" =
  (match allE [where 'a = 'a] in X: "\<And>(x :: 'a) P R. \<forall>x. P x \<Longrightarrow> (P x \<Longrightarrow> R) \<Longrightarrow> R" \<Rightarrow>
    \<open>erule X [where x = x and P = P]\<close>)

lemma "\<forall>x. Q x \<Longrightarrow> Q x" by (my_allE\<^sub>3 x Q)

method my_allE\<^sub>4 for x :: 'a and P :: "'a \<Rightarrow> bool" =
  (match allE [where 'a = 'a] in X: "\<And>(x :: 'a) P R. \<forall>x. P x \<Longrightarrow> (P x \<Longrightarrow> R) \<Longrightarrow> R" \<Rightarrow>
    \<open>erule X [of x P]\<close>)

lemma "\<forall>x. Q x \<Longrightarrow> Q x" by (my_allE\<^sub>4 x Q)



subsection \<open>Polymorphism test\<close>

axiomatization foo' :: "'a \<Rightarrow> 'b \<Rightarrow> 'c \<Rightarrow> bool"
axiomatization where foo'_ax1: "foo' x y z \<Longrightarrow> z \<and> y"
axiomatization where foo'_ax2: "foo' x y y \<Longrightarrow> x \<and> z"
axiomatization where foo'_ax3: "foo' (x :: int) y y \<Longrightarrow> y \<and> y"

lemmas my_thms = foo'_ax1 foo'_ax2 foo'_ax3

definition first_id where "first_id x = x"

lemmas my_thms' = my_thms[of "first_id x" for x]

method print_conclusion = (match conclusion in concl for concl \<Rightarrow> \<open>print_term concl\<close>)

lemma
  assumes foo: "\<And>x (y :: bool). foo' (A x) B (A x)"
  shows "\<And>z. A z \<and> B"
  apply
    (match conclusion in "f x y" for f y and x :: "'d :: type" \<Rightarrow> \<open>
      match my_thms' in R:"\<And>(x :: 'f :: type). ?P (first_id x) \<Longrightarrow> ?R"
                     and R':"\<And>(x :: 'f :: type). ?P' (first_id x) \<Longrightarrow> ?R'" \<Rightarrow> \<open>
        match (x) in "q :: 'f" for q \<Rightarrow> \<open>
          rule R[of q,simplified first_id_def],
          print_conclusion,
          rule foo
      \<close>\<close>\<close>)
  done


subsection \<open>Unchecked rule instantiation, with the possibility of runtime errors\<close>

named_theorems my_thms_named

declare foo'_ax3[my_thms_named]

method foo_method3 declares my_thms_named =
  (match my_thms_named[of (unchecked) z for z] in R:"PROP ?H" \<Rightarrow> \<open>rule R\<close>)

notepad
begin

  (*FIXME: Shouldn't need unchecked keyword here. See Tests_Failing.thy *)
  fix A B x
  have "foo' x B A \<Longrightarrow> A \<and> B"
    by (match my_thms[of (unchecked) z for z] in R:"PROP ?H" \<Rightarrow> \<open>rule R\<close>)

  fix A B x
  note foo'_ax1[my_thms_named]
  have "foo' x B A \<Longrightarrow> A \<and> B"
    by (match my_thms_named[where x=z for z] in R:"PROP ?H" \<Rightarrow> \<open>rule R\<close>)

  fix A B x
  note foo'_ax1[my_thms_named] foo'_ax2[my_thms_named] foo'_ax3[my_thms_named]
  have "foo' x B A \<Longrightarrow> A \<and> B"
   by foo_method3

end


ML \<open>
structure Data = Generic_Data
(
  type T = thm list;
  val empty: T = [];
  val extend = I;
  fun merge data : T = Thm.merge_thms data;
);
\<close>

local_setup \<open>Local_Theory.add_thms_dynamic (@{binding test_dyn}, Data.get)\<close>

setup \<open>Context.theory_map (Data.put @{thms TrueI})\<close>

method dynamic_thms_test = (rule test_dyn)

locale foo =
  fixes A
  assumes A : "A"
begin

local_setup
  \<open>Local_Theory.declaration {pervasive = false, syntax = false}
    (fn phi => Data.put (Morphism.fact phi @{thms A}))\<close>

lemma A by dynamic_thms_test

end


notepad
begin
  fix A x
  assume X: "\<And>x. A x"
  have "A x"
    by (match X in H[of x]:"\<And>x. A x" \<Rightarrow> \<open>print_fact H,match H in "A x" \<Rightarrow> \<open>rule H\<close>\<close>)

  fix A x B
  assume X: "\<And>x :: bool. A x \<Longrightarrow> B" "\<And>x. A x"
  assume Y: "A B"
  have "B \<and> B \<and> B \<and> B \<and> B \<and> B"
    apply (intro conjI)
    apply (match X in H[OF X(2)]:"\<And>x. A x \<Longrightarrow> B" \<Rightarrow> \<open>print_fact H,rule H\<close>)
    apply (match X in H':"\<And>x. A x" and H[OF H']:"\<And>x. A x \<Longrightarrow> B" \<Rightarrow> \<open>print_fact H',print_fact H,rule H\<close>)
    apply (match X in H[of Q]:"\<And>x. A x \<Longrightarrow> ?R" and "?P \<Longrightarrow> Q" for Q \<Rightarrow> \<open>print_fact H,rule H, rule Y\<close>)
    apply (match X in H[of Q,OF Y]:"\<And>x. A x \<Longrightarrow> ?R" and "?P \<Longrightarrow> Q" for Q \<Rightarrow> \<open>print_fact H,rule H\<close>)
    apply (match X in H[OF Y,intro]:"\<And>x. A x \<Longrightarrow> ?R" \<Rightarrow> \<open>print_fact H,fastforce\<close>)
    apply (match X in H[intro]:"\<And>x. A x \<Longrightarrow> ?R" \<Rightarrow> \<open>rule H[where x=B], rule Y\<close>)
    done

  fix x :: "prop" and A
  assume X: "TERM x"
  assume Y: "\<And>x :: prop. A x"
  have "A TERM x"
    apply (match X in "PROP y" for y \<Rightarrow> \<open>rule Y[where x="PROP y"]\<close>)
    done
end

subsection \<open>Proper context for method parameters\<close>

method add_simp methods m uses f = (match f in H[simp]:_ \<Rightarrow> m)

method add_my_thms methods m uses f = (match f in H[my_thms_named]:_ \<Rightarrow> m)

method rule_my_thms = (rule my_thms_named)
method rule_my_thms' declares my_thms_named = (rule my_thms_named)

lemma
  assumes A: A and B: B
  shows
  "(A \<or> B) \<and> A \<and> A \<and> A"
  apply (intro conjI)
  apply (add_simp \<open>add_simp simp f: B\<close> f: A)
  apply (add_my_thms rule_my_thms f:A)
  apply (add_my_thms rule_my_thms' f:A)
  apply (add_my_thms \<open>rule my_thms_named\<close> f:A)
  done


subsection \<open>Shallow parser tests\<close>

method all_args for A B methods m1 m2 uses f1 f2 declares my_thms_named = fail

lemma True
  by (all_args True False - fail f1: TrueI f2: TrueI my_thms_named: TrueI | rule TrueI)


subsection \<open>Method name internalization test\<close>


method test2 = (simp)

method simp = fail

lemma "A \<Longrightarrow> A" by test2


subsection \<open>Dynamic facts\<close>

named_theorems my_thms_named'

method foo_method1 for x =
  (match my_thms_named' [of (unchecked) x] in R: "PROP ?H" \<Rightarrow> \<open>rule R\<close>)

lemma
  assumes A [my_thms_named']: "\<And>x. A x"
  shows "A y"
  by (foo_method1 y)


subsection \<open>Eisbach method invocation from ML\<close>

method test_method for x y uses r = (print_term x, print_term y, rule r)

method_setup test_method' = \<open>
  Args.term -- Args.term --
  (Scan.lift (Args.$$$ "rule" -- Args.colon) |-- Attrib.thms) >>
    (fn ((x, y), r) => fn ctxt =>
      Method_Closure.apply_method ctxt @{method test_method} [x, y] [r] [] ctxt);
\<close>

lemma
  fixes a b :: nat
  assumes "a = b"
  shows "b = a"
  apply (test_method a b)?
  apply (test_method' a b rule: refl)?
  apply (test_method' a b rule: assms [symmetric])?
  done

subsection \<open>Eisbach methods in locales\<close>

locale my_locale1 = fixes A assumes A: A begin

method apply_A =
  (match conclusion in "A" \<Rightarrow>
    \<open>match A in U:"A" \<Rightarrow>
      \<open>print_term A, print_fact A, rule U\<close>\<close>)

end

locale my_locale2 = fixes B assumes B: B begin

interpretation my_locale1 B by (unfold_locales; rule B)

lemma B by apply_A

end

context fixes C assumes C: C begin

interpretation my_locale1 C by (unfold_locales; rule C)

lemma C by apply_A

end

context begin

interpretation my_locale1 "True \<longrightarrow> True" by (unfold_locales; blast)

lemma "True \<longrightarrow> True" by apply_A

end

locale locale_poly = fixes P assumes P: "\<And>x :: 'a. P x" begin

method solve_P for z :: 'a = (rule P[where x = z]) 

end

context begin

interpretation locale_poly "\<lambda>x:: nat. 0 \<le> x" by (unfold_locales; blast)

lemma "0 \<le> (n :: nat)" by (solve_P n)

end

subsection \<open>Mutual recursion via higher-order methods\<close>

experiment begin

method inner_method methods passed_method = (rule conjI; passed_method)

method outer_method = (inner_method \<open>outer_method\<close> | assumption)

lemma "Q \<Longrightarrow> R \<Longrightarrow> P \<Longrightarrow> (Q \<and> R) \<and> P"
  by outer_method

end

end