src/FOL/ex/NewLocaleTest.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/NewLocaleTest.thy	Fri Nov 21 18:02:19 2008 +0100
@@ -0,0 +1,139 @@
+(*  Title:      FOL/ex/NewLocaleTest.thy
+    ID:         $Id$
+    Author:     Clemens Ballarin, TU Muenchen
+
+Testing environment for locale expressions --- experimental.
+*)
+
+theory NewLocaleTest
+imports NewLocaleSetup
+begin
+
+ML_val {* set new_locales *}
+ML_val {* set Toplevel.debug *}
+ML_val {* set show_hyps *}
+
+
+typedecl int arities int :: "term"
+consts plus :: "int => int => int" (infixl "+" 60)
+  zero :: int ("0")
+  minus :: "int => int" ("- _")
+
+
+text {* Inference of parameter types *}
+
+locale param1 = fixes p
+print_locale! param1
+
+locale param2 = fixes p :: 'a
+print_locale! param2
+
+(*
+locale param_top = param2 r for r :: "'b :: {}"
+print_locale! param_top
+*)
+
+locale param3 = fixes p (infix ".." 50)
+print_locale! param3
+
+locale param4 = fixes p :: "'a => 'a => 'a" (infix ".." 50)
+print_locale! param4
+
+
+text {* 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
+
+
+text {* Groups *}
+
+locale semi =
+  fixes prod (infixl "**" 65)
+  assumes assoc: "(x ** y) ** z = x ** (y ** z)"
+    and comm: "x ** y = y ** x"
+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
+
+
+text {* Logic *}
+
+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
+
+(*
+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
+*)
+
+locale rgrp = semi +
+  fixes one and inv
+  assumes rone: "x ** one = x"
+    and rinv: "x ** inv(x) = one"
+
+(*
+lemma (in rgrp) 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