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src/HOL/ex/Records.thy

changeset 10052 | 5fa8d8d5c852 |

child 10357 | 0d0cac129618 |

--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/ex/Records.thy Thu Sep 21 15:58:13 2000 +0200 @@ -0,0 +1,210 @@ +(* Title: HOL/ex/Records.thy + ID: $Id$ + Author: Wolfgang Naraschewski and Markus Wenzel, TU Muenchen + License: GPL (GNU GENERAL PUBLIC LICENSE) +*) + +header {* Using extensible records in HOL -- points and coloured points *} + +theory Records = 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