--- a/src/HOL/ex/Points.thy Thu Sep 21 18:33:48 2000 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,211 +0,0 @@
-(* Title: HOL/ex/Points.thy
- ID: $Id$
- Author: Wolfgang Naraschewski and Markus Wenzel, TU Muenchen
- License: GPL (GNU GENERAL PUBLIC LICENSE)
-*)
-
-header {* Points and coloured points --- using extensible records in HOL *}
-
-theory Points = Main:
-
-
-subsection {* Points *}
-
-record point =
- x :: nat
- y :: nat
-
-text {*
- Apart many other things, above record declaration produces the
- following theorems:
-*}
-
-thm "point.simps"
-thm "point.iffs"
-thm "point.update_defs"
-
-text {*
- The set of theorems "point.simps" is added automatically to the
- standard simpset, "point.iffs" is added to the claset and simpset.
-*}
-
-text {*
- Record declarations define new type abbreviations:
-
- point = "(| x :: nat, y :: nat |)"
- 'a point_scheme = "(| x :: nat, y :: nat, ... :: 'a |)"
-
- Extensions `...' must be in type class `more'!
-*}
-
-consts foo1 :: point
-consts foo2 :: "(| x :: nat, y :: nat |)"
-consts foo3 :: "'a => ('a::more) point_scheme"
-consts foo4 :: "'a => (| x :: nat, y :: nat, ... :: 'a |)"
-
-
-subsubsection {* Introducing concrete records and record schemes *}
-
-defs
- foo1_def: "foo1 == (| x = 1, y = 0 |)"
- foo3_def: "foo3 ext == (| x = 1, y = 0, ... = ext |)"
-
-
-subsubsection {* Record selection and record update *}
-
-constdefs
- getX :: "('a::more) point_scheme => nat"
- "getX r == x r"
- setX :: "('a::more) point_scheme => nat => 'a point_scheme"
- "setX r n == r (| x := n |)"
-
-
-subsubsection {* Some lemmas about records *}
-
-text {* Basic simplifications *}
-
-lemma "point.make n p = (| x = n, y = p |)"
- by simp
-
-lemma "x (| x = m, y = n, ... = p |) = m"
- by simp
-
-lemma "(| x = m, y = n, ... = p |) (| x:= 0 |) = (| x = 0, y = n, ... = p |)"
- by simp
-
-
-text {* Equality of records *}
-
-lemma "n = n' ==> p = p' ==> (| x = n, y = p |) = (| x = n', y = p' |)"
- -- "introduction of concrete record equality"
- by simp
-
-lemma "(| x = n, y = p |) = (| x = n', y = p' |) ==> n = n'"
- -- "elimination of concrete record equality"
- by simp
-
-lemma "r (| x := n |) (| y := m |) = r (| y := m |) (| x := n |)"
- -- "introduction of abstract record equality"
- by simp
-
-lemma "r (| x := n |) = r (| x := n' |) ==> n = n'"
- -- "elimination of abstract record equality (manual proof)"
-proof -
- assume "r (| x := n |) = r (| x := n' |)" (is "?lhs = ?rhs")
- hence "x ?lhs = x ?rhs" by simp
- thus ?thesis by simp
-qed
-
-
-text {* Surjective pairing *}
-
-lemma "r = (| x = x r, y = y r |)"
- by simp
-
-lemma "r = (| x = x r, y = y r, ... = more r |)"
- by simp
-
-
-text {* Splitting quantifiers: the !!r is NECESSARY here *}
-
-lemma "!!r. r (| x := n |) (| y := m |) = r (| y := m |) (| x := n |)"
-proof record_split
- fix x y more
- show "(| x = x, y = y, ... = more |)(| x := n, y := m |) =
- (| x = x, y = y, ... = more |)(| y := m, x := n |)"
- by simp
-qed
-
-lemma "!!r. r (| x := n |) (| x := m |) = r (| x := m |)"
-proof record_split
- fix x y more
- show "(| x = x, y = y, ... = more |)(| x := n, x := m |) =
- (| x = x, y = y, ... = more |)(| x := m |)"
- by simp
-qed
-
-
-
-text {* Concrete records are type instances of record schemes *}
-
-constdefs
- foo5 :: nat
- "foo5 == getX (| x = 1, y = 0 |)"
-
-
-text {* Manipulating the `...' (more) part *}
-
-constdefs
- incX :: "('a::more) point_scheme => 'a point_scheme"
- "incX r == (| x = Suc (x r), y = y r, ... = point.more r |)"
-
-lemma "!!r n. incX r = setX r (Suc (getX r))"
-proof (unfold getX_def setX_def incX_def)
- show "!!r n. (| x = Suc (x r), y = y r, ... = more r |) = r(| x := Suc (x r) |)"
- by record_split simp
-qed
-
-
-text {* alternative definition *}
-
-constdefs
- incX' :: "('a::more) point_scheme => 'a point_scheme"
- "incX' r == r (| x := Suc (x r) |)"
-
-
-subsection {* Coloured points: record extension *}
-
-datatype colour = Red | Green | Blue
-
-record cpoint = point +
- colour :: colour
-
-
-text {*
- The record declaration defines new type constructors:
-
- cpoint = (| x :: nat, y :: nat, colour :: colour |)
- 'a cpoint_scheme = (| x :: nat, y :: nat, colour :: colour, ... :: 'a |)
-*}
-
-consts foo6 :: cpoint
-consts foo7 :: "(| x :: nat, y :: nat, colour :: colour |)"
-consts foo8 :: "('a::more) cpoint_scheme"
-consts foo9 :: "(| x :: nat, y :: nat, colour :: colour, ... :: 'a |)"
-
-
-text {* Functions on point schemes work for cpoints as well *}
-
-constdefs
- foo10 :: nat
- "foo10 == getX (| x = 2, y = 0, colour = Blue |)"
-
-
-subsubsection {* Non-coercive structural subtyping *}
-
-text {* foo11 has type cpoint, not type point --- Great! *}
-
-constdefs
- foo11 :: cpoint
- "foo11 == setX (| x = 2, y = 0, colour = Blue |) 0"
-
-
-subsection {* Other features *}
-
-text {* field names contribute to record identity *}
-
-record point' =
- x' :: nat
- y' :: nat
-
-text {* May not apply @{term getX} to @{term "(| x' = 2, y' = 0 |)"} *}
-
-
-text {* Polymorphic records *}
-
-record 'a point'' = point +
- content :: 'a
-
-types cpoint'' = "colour point''"
-
-end