
diff -r 6a19d9f6021d -r ff4ba1ed4527 src/FOL/ex/NewLocaleTest.thy
--- a/src/FOL/ex/NewLocaleTest.thy	Tue Jan 06 09:03:37 2009 -0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,486 +0,0 @@
-(*  Title:      FOL/ex/NewLocaleTest.thy
-    Author:     Clemens Ballarin, TU Muenchen
-
-Testing environment for locale expressions --- experimental.
-*)
-
-theory NewLocaleTest
-imports NewLocaleSetup
-begin
-
-ML_val {* set Toplevel.debug *}
-
-
-typedecl int arities int :: "term"
-consts plus :: "int => int => int" (infixl "+" 60)
-  zero :: int ("0")
-  minus :: "int => int" ("- _")
-
-axioms
-  int_assoc: "(x + y::int) + z = x + (y + z)"
-  int_zero: "0 + x = x"
-  int_minus: "(-x) + x = 0"
-  int_minus2: "-(-x) = x"
-
-section {* Inference of parameter types *}
-
-locale param1 = fixes p
-print_locale! param1
-
-locale param2 = fixes p :: 'b
-print_locale! param2
-
-(*
-locale param_top = param2 r for r :: "'b :: {}"
-  Fails, cannot generalise parameter.
-*)
-
-locale param3 = fixes p (infix ".." 50)
-print_locale! param3
-
-locale param4 = fixes p :: "'a => 'a => 'a" (infix ".." 50)
-print_locale! param4
-
-
-subsection {* Incremental type constraints *}
-
-locale constraint1 =
-  fixes  prod (infixl "**" 65)
-  assumes l_id: "x ** y = x"
-  assumes assoc: "(x ** y) ** z = x ** (y ** z)"
-print_locale! constraint1
-
-locale constraint2 =
-  fixes p and q
-  assumes "p = q"
-print_locale! constraint2
-
-
-section {* Inheritance *}
-
-locale semi =
-  fixes prod (infixl "**" 65)
-  assumes assoc: "(x ** y) ** z = x ** (y ** z)"
-print_locale! semi thm semi_def
-
-locale lgrp = semi +
-  fixes one and inv
-  assumes lone: "one ** x = x"
-    and linv: "inv(x) ** x = one"
-print_locale! lgrp thm lgrp_def lgrp_axioms_def
-
-locale add_lgrp = semi "op ++" for sum (infixl "++" 60) +
-  fixes zero and neg
-  assumes lzero: "zero ++ x = x"
-    and lneg: "neg(x) ++ x = zero"
-print_locale! add_lgrp thm add_lgrp_def add_lgrp_axioms_def
-
-locale rev_lgrp = semi "%x y. y ++ x" for sum (infixl "++" 60)
-print_locale! rev_lgrp thm rev_lgrp_def
-
-locale hom = f: semi f + g: semi g for f and g
-print_locale! hom thm hom_def
-
-locale perturbation = semi + d: semi "%x y. delta(x) ** delta(y)" for delta
-print_locale! perturbation thm perturbation_def
-
-locale pert_hom = d1: perturbation f d1 + d2: perturbation f d2 for f d1 d2
-print_locale! pert_hom thm pert_hom_def
-
-text {* Alternative expression, obtaining nicer names in @{text "semi f"}. *}
-locale pert_hom' = semi f + d1: perturbation f d1 + d2: perturbation f d2 for f d1 d2
-print_locale! pert_hom' thm pert_hom'_def
-
-
-section {* Syntax declarations *}
-
-locale logic =
-  fixes land (infixl "&&" 55)
-    and lnot ("-- _" [60] 60)
-  assumes assoc: "(x && y) && z = x && (y && z)"
-    and notnot: "-- (-- x) = x"
-begin
-
-definition lor (infixl "||" 50) where
-  "x || y = --(-- x && -- y)"
-
-end
-print_locale! logic
-
-locale use_decl = logic + semi "op ||"
-print_locale! use_decl thm use_decl_def
-
-locale extra_type =
-  fixes a :: 'a
-    and P :: "'a => 'b => o"
-begin
-
-definition test :: "'a => o" where
-  "test(x) <-> (ALL b. P(x, b))"
-
-end
-
-term extra_type.test thm extra_type.test_def
-
-interpretation var: extra_type "0" "%x y. x = 0" .
-
-thm var.test_def
-
-
-section {* Foundational versions of theorems *}
-
-thm logic.assoc
-thm logic.lor_def
-
-
-section {* Defines *}
-
-locale logic_def =
-  fixes land (infixl "&&" 55)
-    and lor (infixl "||" 50)
-    and lnot ("-- _" [60] 60)
-  assumes assoc: "(x && y) && z = x && (y && z)"
-    and notnot: "-- (-- x) = x"
-  defines "x || y == --(-- x && -- y)"
-begin
-
-thm lor_def
-(* Can we get rid the the additional hypothesis, caused by LocalTheory.notes? *)
-
-lemma "x || y = --(-- x && --y)"
-  by (unfold lor_def) (rule refl)
-
-end
-
-(* Inheritance of defines *)
-
-locale logic_def2 = logic_def
-begin
-
-lemma "x || y = --(-- x && --y)"
-  by (unfold lor_def) (rule refl)
-
-end
-
-
-section {* Notes *}
-
-(* A somewhat arcane homomorphism example *)
-
-definition semi_hom where
-  "semi_hom(prod, sum, h) <-> (ALL x y. h(prod(x, y)) = sum(h(x), h(y)))"
-
-lemma semi_hom_mult:
-  "semi_hom(prod, sum, h) ==> h(prod(x, y)) = sum(h(x), h(y))"
-  by (simp add: semi_hom_def)
-
-locale semi_hom_loc = prod: semi prod + sum: semi sum
-  for prod and sum and h +
-  assumes semi_homh: "semi_hom(prod, sum, h)"
-  notes semi_hom_mult = semi_hom_mult [OF semi_homh]
-
-thm semi_hom_loc.semi_hom_mult
-(* unspecified, attribute not applied in backgroud theory !!! *)
-
-lemma (in semi_hom_loc) "h(prod(x, y)) = sum(h(x), h(y))"
-  by (rule semi_hom_mult)
-
-(* Referring to facts from within a context specification *)
-
-lemma
-  assumes x: "P <-> P"
-  notes y = x
-  shows True ..
-
-
-section {* Theorem statements *}
-
-lemma (in lgrp) lcancel:
-  "x ** y = x ** z <-> y = z"
-proof
-  assume "x ** y = x ** z"
-  then have "inv(x) ** x ** y = inv(x) ** x ** z" by (simp add: assoc)
-  then show "y = z" by (simp add: lone linv)
-qed simp
-print_locale! lgrp
-
-
-locale rgrp = semi +
-  fixes one and inv
-  assumes rone: "x ** one = x"
-    and rinv: "x ** inv(x) = one"
-begin
-
-lemma rcancel:
-  "y ** x = z ** x <-> y = z"
-proof
-  assume "y ** x = z ** x"
-  then have "y ** (x ** inv(x)) = z ** (x ** inv(x))"
-    by (simp add: assoc [symmetric])
-  then show "y = z" by (simp add: rone rinv)
-qed simp
-
-end
-print_locale! rgrp
-
-
-subsection {* Patterns *}
-
-lemma (in rgrp)
-  assumes "y ** x = z ** x" (is ?a)
-  shows "y = z" (is ?t)
-proof -
-  txt {* Weird proof involving patterns from context element and conclusion. *}
-  {
-    assume ?a
-    then have "y ** (x ** inv(x)) = z ** (x ** inv(x))"
-      by (simp add: assoc [symmetric])
-    then have ?t by (simp add: rone rinv)
-  }
-  note x = this
-  show ?t by (rule x [OF `?a`])
-qed
-
-
-section {* Interpretation between locales: sublocales *}
-
-sublocale lgrp < right: rgrp
-print_facts
-proof unfold_locales
-  {
-    fix x
-    have "inv(x) ** x ** one = inv(x) ** x" by (simp add: linv lone)
-    then show "x ** one = x" by (simp add: assoc lcancel)
-  }
-  note rone = this
-  {
-    fix x
-    have "inv(x) ** x ** inv(x) = inv(x) ** one"
-      by (simp add: linv lone rone)
-    then show "x ** inv(x) = one" by (simp add: assoc lcancel)
-  }
-qed
-
-(* effect on printed locale *)
-
-print_locale! lgrp
-
-(* use of derived theorem *)
-
-lemma (in lgrp)
-  "y ** x = z ** x <-> y = z"
-  apply (rule rcancel)
-  done
-
-(* circular interpretation *)
-
-sublocale rgrp < left: lgrp
-proof unfold_locales
-  {
-    fix x
-    have "one ** (x ** inv(x)) = x ** inv(x)" by (simp add: rinv rone)
-    then show "one ** x = x" by (simp add: assoc [symmetric] rcancel)
-  }
-  note lone = this
-  {
-    fix x
-    have "inv(x) ** (x ** inv(x)) = one ** inv(x)"
-      by (simp add: rinv lone rone)
-    then show "inv(x) ** x = one" by (simp add: assoc [symmetric] rcancel)
-  }
-qed
-
-(* effect on printed locale *)
-
-print_locale! rgrp
-print_locale! lgrp
-
-
-(* Duality *)
-
-locale order =
-  fixes less :: "'a => 'a => o" (infix "<<" 50)
-  assumes refl: "x << x"
-    and trans: "[| x << y; y << z |] ==> x << z"
-
-sublocale order < dual: order "%x y. y << x"
-  apply unfold_locales apply (rule refl) apply (blast intro: trans)
-  done
-
-print_locale! order  (* Only two instances of order. *)
-
-locale order' =
-  fixes less :: "'a => 'a => o" (infix "<<" 50)
-  assumes refl: "x << x"
-    and trans: "[| x << y; y << z |] ==> x << z"
-
-locale order_with_def = order'
-begin
-
-definition greater :: "'a => 'a => o" (infix ">>" 50) where
-  "x >> y <-> y << x"
-
-end
-
-sublocale order_with_def < dual: order' "op >>"
-  apply unfold_locales
-  unfolding greater_def
-  apply (rule refl) apply (blast intro: trans)
-  done
-
-print_locale! order_with_def
-(* Note that decls come after theorems that make use of them. *)
-
-
-(* locale with many parameters ---
-   interpretations generate alternating group A5 *)
-
-
-locale A5 =
-  fixes A and B and C and D and E
-  assumes eq: "A <-> B <-> C <-> D <-> E"
-
-sublocale A5 < 1: A5 _ _ D E C
-print_facts
-  using eq apply (blast intro: A5.intro) done
-
-sublocale A5 < 2: A5 C _ E _ A
-print_facts
-  using eq apply (blast intro: A5.intro) done
-
-sublocale A5 < 3: A5 B C A _ _
-print_facts
-  using eq apply (blast intro: A5.intro) done
-
-(* Any even permutation of parameters is subsumed by the above. *)
-
-print_locale! A5
-
-
-(* Free arguments of instance *)
-
-locale trivial =
-  fixes P and Q :: o
-  assumes Q: "P <-> P <-> Q"
-begin
-
-lemma Q_triv: "Q" using Q by fast
-
-end
-
-sublocale trivial < x: trivial x _
-  apply unfold_locales using Q by fast
-
-print_locale! trivial
-
-context trivial begin thm x.Q [where ?x = True] end
-
-sublocale trivial < y: trivial Q Q
-  by unfold_locales
-  (* Succeeds since previous interpretation is more general. *)
-
-print_locale! trivial  (* No instance for y created (subsumed). *)
-
-
-subsection {* Sublocale, then interpretation in theory *}
-
-interpretation int: lgrp "op +" "0" "minus"
-proof unfold_locales
-qed (rule int_assoc int_zero int_minus)+
-
-thm int.assoc int.semi_axioms
-
-interpretation int2: semi "op +"
-  by unfold_locales  (* subsumed, thm int2.assoc not generated *)
-
-thm int.lone int.right.rone
-  (* the latter comes through the sublocale relation *)
-
-
-subsection {* Interpretation in theory, then sublocale *}
-
-interpretation (* fol: *) logic "op +" "minus"
-(* FIXME declaration of qualified names *)
-  by unfold_locales (rule int_assoc int_minus2)+
-
-locale logic2 =
-  fixes land (infixl "&&" 55)
-    and lnot ("-- _" [60] 60)
-  assumes assoc: "(x && y) && z = x && (y && z)"
-    and notnot: "-- (-- x) = x"
-begin
-
-(* FIXME interpretation below fails
-definition lor (infixl "||" 50) where
-  "x || y = --(-- x && -- y)"
-*)
-
-end
-
-sublocale logic < two: logic2
-  by unfold_locales (rule assoc notnot)+
-
-thm two.assoc
-
-
-subsection {* Declarations and sublocale *}
-
-locale logic_a = logic
-locale logic_b = logic
-
-sublocale logic_a < logic_b
-  by unfold_locales
-
-
-subsection {* Equations *}
-
-locale logic_o =
-  fixes land (infixl "&&" 55)
-    and lnot ("-- _" [60] 60)
-  assumes assoc_o: "(x && y) && z <-> x && (y && z)"
-    and notnot_o: "-- (-- x) <-> x"
-begin
-
-definition lor_o (infixl "||" 50) where
-  "x || y <-> --(-- x && -- y)"
-
-end
-
-interpretation x!: logic_o "op &" "Not"
-  where bool_logic_o: "logic_o.lor_o(op &, Not, x, y) <-> x | y"
-proof -
-  show bool_logic_o: "PROP logic_o(op &, Not)" by unfold_locales fast+
-  show "logic_o.lor_o(op &, Not, x, y) <-> x | y"
-    by (unfold logic_o.lor_o_def [OF bool_logic_o]) fast
-qed
-
-thm x.lor_o_def bool_logic_o
-
-lemma lor_triv: "z <-> z" ..
-
-lemma (in logic_o) lor_triv: "x || y <-> x || y" by fast
-
-thm lor_triv [where z = True] (* Check strict prefix. *)
-  x.lor_triv
-
-
-subsection {* Interpretation in proofs *}
-
-lemma True
-proof
-  interpret "local": lgrp "op +" "0" "minus"
-    by unfold_locales  (* subsumed *)
-  {
-    fix zero :: int
-    assume "!!x. zero + x = x" "!!x. (-x) + x = zero"
-    then interpret local_fixed: lgrp "op +" zero "minus"
-      by unfold_locales
-    thm local_fixed.lone
-  }
-  assume "!!x zero. zero + x = x" "!!x zero. (-x) + x = zero"
-  then interpret local_free: lgrp "op +" zero "minus" for zero
-    by unfold_locales
-  thm local_free.lone [where ?zero = 0]
-qed
-
-end




