Revise locale test theory layout.
--- a/src/FOL/IsaMakefile Wed May 26 21:20:18 2010 +0200
+++ b/src/FOL/IsaMakefile Wed May 26 21:20:18 2010 +0200
@@ -46,7 +46,9 @@
$(LOG)/FOL-ex.gz: $(OUT)/FOL ex/First_Order_Logic.thy ex/If.thy \
ex/Iff_Oracle.thy ex/Nat.thy ex/Nat_Class.thy ex/Natural_Numbers.thy \
- ex/LocaleTest.thy ex/Miniscope.thy ex/Prolog.thy ex/ROOT.ML \
+ ex/Locale_Test/Locale_Test.thy ex/Locale_Test/Locale_Test1.thy \
+ ex/Locale_Test/Locale_Test2.thy ex/Locale_Test/Locale_Test3.thy \
+ ex/Miniscope.thy ex/Prolog.thy ex/ROOT.ML \
ex/Classical.thy ex/document/root.tex ex/Foundation.thy \
ex/Intuitionistic.thy ex/Intro.thy ex/Propositional_Int.thy \
ex/Propositional_Cla.thy ex/Quantifiers_Int.thy \
--- a/src/FOL/ex/LocaleTest.thy Wed May 26 21:20:18 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,712 +0,0 @@
-(* Title: FOL/ex/LocaleTest.thy
- Author: Clemens Ballarin, TU Muenchen
-
-Test environment for the locale implementation.
-*)
-
-theory LocaleTest
-imports FOL
-begin
-
-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
-
-
-text {* Under which circumstances term syntax remains active. *}
-
-locale "syntax" =
- fixes p1 :: "'a => 'b"
- and p2 :: "'b => o"
-begin
-
-definition d1 :: "'a => o" where "d1(x) <-> ~ p2(p1(x))"
-definition d2 :: "'b => o" where "d2(x) <-> ~ p2(x)"
-
-thm d1_def d2_def
-
-end
-
-thm syntax.d1_def syntax.d2_def
-
-locale syntax' = "syntax" p1 p2 for p1 :: "'a => 'a" and p2 :: "'a => o"
-begin
-
-thm d1_def d2_def (* should print as "d1(?x) <-> ..." and "d2(?x) <-> ..." *)
-
-ML {*
- fun check_syntax ctxt thm expected =
- let
- val obtained = PrintMode.setmp [] (Display.string_of_thm ctxt) thm;
- in
- if obtained <> expected
- then error ("Theorem syntax '" ^ obtained ^ "' obtained, but '" ^ expected ^ "' expected.")
- else ()
- end;
-*}
-
-ML {*
- check_syntax @{context} @{thm d1_def} "d1(?x) <-> ~ p2(p1(?x))";
- check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
-*}
-
-end
-
-locale syntax'' = "syntax" p3 p2 for p3 :: "'a => 'b" and p2 :: "'b => o"
-begin
-
-thm d1_def d2_def
- (* should print as "syntax.d1(p3, p2, ?x) <-> ..." and "d2(?x) <-> ..." *)
-
-ML {*
- check_syntax @{context} @{thm d1_def} "syntax.d1(p3, p2, ?x) <-> ~ p2(p3(?x))";
- check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
-*}
-
-end
-
-
-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
-
-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 *)
-
-ML {* (PureThy.get_thms @{theory} "int2.assoc";
- error "thm int2.assoc was generated")
- handle ERROR "Unknown fact \"int2.assoc\"" => ([]:thm list); *}
-
-thm int.lone int.right.rone
- (* the latter comes through the sublocale relation *)
-
-
-subsection {* Interpretation in theory, then sublocale *}
-
-interpretation fol: logic "op +" "minus"
- 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
-
-definition lor (infixl "||" 50) where
- "x || y = --(-- x && -- y)"
-
-end
-
-sublocale logic < two: logic2
- by unfold_locales (rule assoc notnot)+
-
-thm fol.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 {* Inheritance of mixins *}
-
-locale reflexive =
- fixes le :: "'a => 'a => o" (infix "\<sqsubseteq>" 50)
- assumes refl: "x \<sqsubseteq> x"
-begin
-
-definition less (infix "\<sqsubset>" 50) where "x \<sqsubset> y <-> x \<sqsubseteq> y & x ~= y"
-
-end
-
-consts
- gle :: "'a => 'a => o" gless :: "'a => 'a => o"
- gle' :: "'a => 'a => o" gless' :: "'a => 'a => o"
-
-axioms
- grefl: "gle(x, x)" gless_def: "gless(x, y) <-> gle(x, y) & x ~= y"
- grefl': "gle'(x, x)" gless'_def: "gless'(x, y) <-> gle'(x, y) & x ~= y"
-
-text {* Setup *}
-
-locale mixin = reflexive
-begin
-lemmas less_thm = less_def
-end
-
-interpretation le: mixin gle where "reflexive.less(gle, x, y) <-> gless(x, y)"
-proof -
- show "mixin(gle)" by unfold_locales (rule grefl)
- note reflexive = this[unfolded mixin_def]
- show "reflexive.less(gle, x, y) <-> gless(x, y)"
- by (simp add: reflexive.less_def[OF reflexive] gless_def)
-qed
-
-text {* Mixin propagated along the locale hierarchy *}
-
-locale mixin2 = mixin
-begin
-lemmas less_thm2 = less_def
-end
-
-interpretation le: mixin2 gle
- by unfold_locales
-
-thm le.less_thm2 (* mixin applied *)
-lemma "gless(x, y) <-> gle(x, y) & x ~= y"
- by (rule le.less_thm2)
-
-text {* Mixin does not leak to a side branch. *}
-
-locale mixin3 = reflexive
-begin
-lemmas less_thm3 = less_def
-end
-
-interpretation le: mixin3 gle
- by unfold_locales
-
-thm le.less_thm3 (* mixin not applied *)
-lemma "reflexive.less(gle, x, y) <-> gle(x, y) & x ~= y" by (rule le.less_thm3)
-
-text {* Mixin only available in original context *}
-
-locale mixin4_base = reflexive
-
-locale mixin4_mixin = mixin4_base
-
-interpretation le: mixin4_mixin gle
- where "reflexive.less(gle, x, y) <-> gless(x, y)"
-proof -
- show "mixin4_mixin(gle)" by unfold_locales (rule grefl)
- note reflexive = this[unfolded mixin4_mixin_def mixin4_base_def mixin_def]
- show "reflexive.less(gle, x, y) <-> gless(x, y)"
- by (simp add: reflexive.less_def[OF reflexive] gless_def)
-qed
-
-locale mixin4_copy = mixin4_base
-begin
-lemmas less_thm4 = less_def
-end
-
-locale mixin4_combined = le1: mixin4_mixin le' + le2: mixin4_copy le for le' le
-begin
-lemmas less_thm4' = less_def
-end
-
-interpretation le4: mixin4_combined gle' gle
- by unfold_locales (rule grefl')
-
-thm le4.less_thm4' (* mixin not applied *)
-lemma "reflexive.less(gle, x, y) <-> gle(x, y) & x ~= y"
- by (rule le4.less_thm4')
-
-text {* Inherited mixin applied to new theorem *}
-
-locale mixin5_base = reflexive
-
-locale mixin5_inherited = mixin5_base
-
-interpretation le5: mixin5_base gle
- where "reflexive.less(gle, x, y) <-> gless(x, y)"
-proof -
- show "mixin5_base(gle)" by unfold_locales
- note reflexive = this[unfolded mixin5_base_def mixin_def]
- show "reflexive.less(gle, x, y) <-> gless(x, y)"
- by (simp add: reflexive.less_def[OF reflexive] gless_def)
-qed
-
-interpretation le5: mixin5_inherited gle
- by unfold_locales
-
-lemmas (in mixin5_inherited) less_thm5 = less_def
-
-thm le5.less_thm5 (* mixin applied *)
-lemma "gless(x, y) <-> gle(x, y) & x ~= y"
- by (rule le5.less_thm5)
-
-text {* Mixin pushed down to existing inherited locale *}
-
-locale mixin6_base = reflexive
-
-locale mixin6_inherited = mixin5_base
-
-interpretation le6: mixin6_base gle
- by unfold_locales
-interpretation le6: mixin6_inherited gle
- by unfold_locales
-interpretation le6: mixin6_base gle
- where "reflexive.less(gle, x, y) <-> gless(x, y)"
-proof -
- show "mixin6_base(gle)" by unfold_locales
- note reflexive = this[unfolded mixin6_base_def mixin_def]
- show "reflexive.less(gle, x, y) <-> gless(x, y)"
- by (simp add: reflexive.less_def[OF reflexive] gless_def)
-qed
-
-lemmas (in mixin6_inherited) less_thm6 = less_def
-
-thm le6.less_thm6 (* mixin applied *)
-lemma "gless(x, y) <-> gle(x, y) & x ~= y"
- by (rule le6.less_thm6)
-
-text {* Existing mixin inherited through sublocale relation *}
-
-locale mixin7_base = reflexive
-
-locale mixin7_inherited = reflexive
-
-interpretation le7: mixin7_base gle
- where "reflexive.less(gle, x, y) <-> gless(x, y)"
-proof -
- show "mixin7_base(gle)" by unfold_locales
- note reflexive = this[unfolded mixin7_base_def mixin_def]
- show "reflexive.less(gle, x, y) <-> gless(x, y)"
- by (simp add: reflexive.less_def[OF reflexive] gless_def)
-qed
-
-interpretation le7: mixin7_inherited gle
- by unfold_locales
-
-lemmas (in mixin7_inherited) less_thm7 = less_def
-
-thm le7.less_thm7 (* before, mixin not applied *)
-lemma "reflexive.less(gle, x, y) <-> gle(x, y) & x ~= y"
- by (rule le7.less_thm7)
-
-sublocale mixin7_inherited < mixin7_base
- by unfold_locales
-
-lemmas (in mixin7_inherited) less_thm7b = less_def
-
-thm le7.less_thm7b (* after, mixin applied *)
-lemma "gless(x, y) <-> gle(x, y) & x ~= y"
- by (rule le7.less_thm7b)
-
-
-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
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Locale_Test/Locale_Test.thy Wed May 26 21:20:18 2010 +0200
@@ -0,0 +1,24 @@
+(* Title: FOL/ex/Locale_Test/Locale_Test.thy
+ Author: Clemens Ballarin
+
+Test environment for the locale implementation.
+*)
+
+theory Locale_Test
+imports Locale_Test1 Locale_Test2 Locale_Test3
+begin
+
+text {* Result of theory merge with distinct but identical interpretations *}
+
+context mixin_thy_merge
+begin
+lemmas less_mixin_thy_merge1 = le.less_def
+lemmas less_mixin_thy_merge2 = le'.less_def
+end
+
+lemma "gless(x, y) <-> gle(x, y) & x ~= y" (* mixin from first interpretation applied *)
+ by (rule le1.less_mixin_thy_merge1)
+lemma "gless'(x, y) <-> gle'(x, y) & x ~= y" (* mixin from second interpretation applied *)
+ by (rule le1.less_mixin_thy_merge2)
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Locale_Test/Locale_Test1.thy Wed May 26 21:20:18 2010 +0200
@@ -0,0 +1,717 @@
+(* Title: FOL/ex/Locale_Test/Locale_Test1.thy
+ Author: Clemens Ballarin, TU Muenchen
+
+Test environment for the locale implementation.
+*)
+
+theory Locale_Test1
+imports FOL
+begin
+
+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
+
+
+text {* Under which circumstances term syntax remains active. *}
+
+locale "syntax" =
+ fixes p1 :: "'a => 'b"
+ and p2 :: "'b => o"
+begin
+
+definition d1 :: "'a => o" where "d1(x) <-> ~ p2(p1(x))"
+definition d2 :: "'b => o" where "d2(x) <-> ~ p2(x)"
+
+thm d1_def d2_def
+
+end
+
+thm syntax.d1_def syntax.d2_def
+
+locale syntax' = "syntax" p1 p2 for p1 :: "'a => 'a" and p2 :: "'a => o"
+begin
+
+thm d1_def d2_def (* should print as "d1(?x) <-> ..." and "d2(?x) <-> ..." *)
+
+ML {*
+ fun check_syntax ctxt thm expected =
+ let
+ val obtained = PrintMode.setmp [] (Display.string_of_thm ctxt) thm;
+ in
+ if obtained <> expected
+ then error ("Theorem syntax '" ^ obtained ^ "' obtained, but '" ^ expected ^ "' expected.")
+ else ()
+ end;
+*}
+
+ML {*
+ check_syntax @{context} @{thm d1_def} "d1(?x) <-> ~ p2(p1(?x))";
+ check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
+*}
+
+end
+
+locale syntax'' = "syntax" p3 p2 for p3 :: "'a => 'b" and p2 :: "'b => o"
+begin
+
+thm d1_def d2_def
+ (* should print as "syntax.d1(p3, p2, ?x) <-> ..." and "d2(?x) <-> ..." *)
+
+ML {*
+ check_syntax @{context} @{thm d1_def} "syntax.d1(p3, p2, ?x) <-> ~ p2(p3(?x))";
+ check_syntax @{context} @{thm d2_def} "d2(?x) <-> ~ p2(?x)";
+*}
+
+end
+
+
+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
+
+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 *)
+
+ML {* (PureThy.get_thms @{theory} "int2.assoc";
+ error "thm int2.assoc was generated")
+ handle ERROR "Unknown fact \"int2.assoc\"" => ([]:thm list); *}
+
+thm int.lone int.right.rone
+ (* the latter comes through the sublocale relation *)
+
+
+subsection {* Interpretation in theory, then sublocale *}
+
+interpretation fol: logic "op +" "minus"
+ 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
+
+definition lor (infixl "||" 50) where
+ "x || y = --(-- x && -- y)"
+
+end
+
+sublocale logic < two: logic2
+ by unfold_locales (rule assoc notnot)+
+
+thm fol.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 {* Inheritance of mixins *}
+
+locale reflexive =
+ fixes le :: "'a => 'a => o" (infix "\<sqsubseteq>" 50)
+ assumes refl: "x \<sqsubseteq> x"
+begin
+
+definition less (infix "\<sqsubset>" 50) where "x \<sqsubset> y <-> x \<sqsubseteq> y & x ~= y"
+
+end
+
+consts
+ gle :: "'a => 'a => o" gless :: "'a => 'a => o"
+ gle' :: "'a => 'a => o" gless' :: "'a => 'a => o"
+
+axioms
+ grefl: "gle(x, x)" gless_def: "gless(x, y) <-> gle(x, y) & x ~= y"
+ grefl': "gle'(x, x)" gless'_def: "gless'(x, y) <-> gle'(x, y) & x ~= y"
+
+text {* Setup *}
+
+locale mixin = reflexive
+begin
+lemmas less_thm = less_def
+end
+
+interpretation le: mixin gle where "reflexive.less(gle, x, y) <-> gless(x, y)"
+proof -
+ show "mixin(gle)" by unfold_locales (rule grefl)
+ note reflexive = this[unfolded mixin_def]
+ show "reflexive.less(gle, x, y) <-> gless(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless_def)
+qed
+
+text {* Mixin propagated along the locale hierarchy *}
+
+locale mixin2 = mixin
+begin
+lemmas less_thm2 = less_def
+end
+
+interpretation le: mixin2 gle
+ by unfold_locales
+
+thm le.less_thm2 (* mixin applied *)
+lemma "gless(x, y) <-> gle(x, y) & x ~= y"
+ by (rule le.less_thm2)
+
+text {* Mixin does not leak to a side branch. *}
+
+locale mixin3 = reflexive
+begin
+lemmas less_thm3 = less_def
+end
+
+interpretation le: mixin3 gle
+ by unfold_locales
+
+thm le.less_thm3 (* mixin not applied *)
+lemma "reflexive.less(gle, x, y) <-> gle(x, y) & x ~= y" by (rule le.less_thm3)
+
+text {* Mixin only available in original context *}
+
+locale mixin4_base = reflexive
+
+locale mixin4_mixin = mixin4_base
+
+interpretation le: mixin4_mixin gle
+ where "reflexive.less(gle, x, y) <-> gless(x, y)"
+proof -
+ show "mixin4_mixin(gle)" by unfold_locales (rule grefl)
+ note reflexive = this[unfolded mixin4_mixin_def mixin4_base_def mixin_def]
+ show "reflexive.less(gle, x, y) <-> gless(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless_def)
+qed
+
+locale mixin4_copy = mixin4_base
+begin
+lemmas less_thm4 = less_def
+end
+
+locale mixin4_combined = le1: mixin4_mixin le' + le2: mixin4_copy le for le' le
+begin
+lemmas less_thm4' = less_def
+end
+
+interpretation le4: mixin4_combined gle' gle
+ by unfold_locales (rule grefl')
+
+thm le4.less_thm4' (* mixin not applied *)
+lemma "reflexive.less(gle, x, y) <-> gle(x, y) & x ~= y"
+ by (rule le4.less_thm4')
+
+text {* Inherited mixin applied to new theorem *}
+
+locale mixin5_base = reflexive
+
+locale mixin5_inherited = mixin5_base
+
+interpretation le5: mixin5_base gle
+ where "reflexive.less(gle, x, y) <-> gless(x, y)"
+proof -
+ show "mixin5_base(gle)" by unfold_locales
+ note reflexive = this[unfolded mixin5_base_def mixin_def]
+ show "reflexive.less(gle, x, y) <-> gless(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless_def)
+qed
+
+interpretation le5: mixin5_inherited gle
+ by unfold_locales
+
+lemmas (in mixin5_inherited) less_thm5 = less_def
+
+thm le5.less_thm5 (* mixin applied *)
+lemma "gless(x, y) <-> gle(x, y) & x ~= y"
+ by (rule le5.less_thm5)
+
+text {* Mixin pushed down to existing inherited locale *}
+
+locale mixin6_base = reflexive
+
+locale mixin6_inherited = mixin5_base
+
+interpretation le6: mixin6_base gle
+ by unfold_locales
+interpretation le6: mixin6_inherited gle
+ by unfold_locales
+interpretation le6: mixin6_base gle
+ where "reflexive.less(gle, x, y) <-> gless(x, y)"
+proof -
+ show "mixin6_base(gle)" by unfold_locales
+ note reflexive = this[unfolded mixin6_base_def mixin_def]
+ show "reflexive.less(gle, x, y) <-> gless(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless_def)
+qed
+
+lemmas (in mixin6_inherited) less_thm6 = less_def
+
+thm le6.less_thm6 (* mixin applied *)
+lemma "gless(x, y) <-> gle(x, y) & x ~= y"
+ by (rule le6.less_thm6)
+
+text {* Existing mixin inherited through sublocale relation *}
+
+locale mixin7_base = reflexive
+
+locale mixin7_inherited = reflexive
+
+interpretation le7: mixin7_base gle
+ where "reflexive.less(gle, x, y) <-> gless(x, y)"
+proof -
+ show "mixin7_base(gle)" by unfold_locales
+ note reflexive = this[unfolded mixin7_base_def mixin_def]
+ show "reflexive.less(gle, x, y) <-> gless(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless_def)
+qed
+
+interpretation le7: mixin7_inherited gle
+ by unfold_locales
+
+lemmas (in mixin7_inherited) less_thm7 = less_def
+
+thm le7.less_thm7 (* before, mixin not applied *)
+lemma "reflexive.less(gle, x, y) <-> gle(x, y) & x ~= y"
+ by (rule le7.less_thm7)
+
+sublocale mixin7_inherited < mixin7_base
+ by unfold_locales
+
+lemmas (in mixin7_inherited) less_thm7b = less_def
+
+thm le7.less_thm7b (* after, mixin applied *)
+lemma "gless(x, y) <-> gle(x, y) & x ~= y"
+ by (rule le7.less_thm7b)
+
+
+text {* This locale will be interpreted in later theories. *}
+
+locale mixin_thy_merge = le: reflexive le + le': reflexive le' for le le'
+
+
+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
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Locale_Test/Locale_Test2.thy Wed May 26 21:20:18 2010 +0200
@@ -0,0 +1,20 @@
+(* Title: FOL/ex/Locale_Test/Locale_Test2.thy
+ Author: Clemens Ballarin, TU Muenchen
+
+Test environment for the locale implementation.
+*)
+
+theory Locale_Test2
+imports Locale_Test1
+begin
+
+interpretation le1: mixin_thy_merge gle gle'
+ where "reflexive.less(gle, x, y) <-> gless(x, y)"
+proof -
+ show "mixin_thy_merge(gle, gle')" by unfold_locales
+ note reflexive = this[unfolded mixin_thy_merge_def, THEN conjunct1]
+ show "reflexive.less(gle, x, y) <-> gless(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless_def)
+qed
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/Locale_Test/Locale_Test3.thy Wed May 26 21:20:18 2010 +0200
@@ -0,0 +1,20 @@
+(* Title: FOL/ex/Locale_Test/Locale_Test3.thy
+ Author: Clemens Ballarin
+
+Test environment for the locale implementation.
+*)
+
+theory Locale_Test3
+imports Locale_Test1
+begin
+
+interpretation le2: mixin_thy_merge gle gle'
+ where "reflexive.less(gle', x, y) <-> gless'(x, y)"
+proof -
+ show "mixin_thy_merge(gle, gle')" by unfold_locales
+ note reflexive = this[unfolded mixin_thy_merge_def, THEN conjunct2]
+ show "reflexive.less(gle', x, y) <-> gless'(x, y)"
+ by (simp add: reflexive.less_def[OF reflexive] gless'_def)
+qed
+
+end
--- a/src/FOL/ex/ROOT.ML Wed May 26 21:20:18 2010 +0200
+++ b/src/FOL/ex/ROOT.ML Wed May 26 21:20:18 2010 +0200
@@ -23,4 +23,4 @@
];
(*regression test for locales -- sets several global flags!*)
-no_document use_thy "LocaleTest";
+no_document use_thy "Locale_Test/Locale_Test";