author | haftmann |
Tue, 20 Mar 2007 08:27:15 +0100 | |
changeset 22473 | 753123c89d72 |
parent 21404 | eb85850d3eb7 |
child 22737 | d87ccbcc2702 |
permissions | -rw-r--r-- |
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(* Title: HOL/ex/Records.thy |
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ID: $Id$ |
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Author: Wolfgang Naraschewski, Norbert Schirmer and Markus Wenzel, |
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TU Muenchen |
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*) |
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header {* Using extensible records in HOL -- points and coloured points *} |
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theory Records imports Main begin |
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subsection {* Points *} |
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record point = |
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xpos :: nat |
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ypos :: nat |
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text {* |
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Apart many other things, above record declaration produces the |
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following theorems: |
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*} |
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thm "point.simps" |
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thm "point.iffs" |
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thm "point.defs" |
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text {* |
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The set of theorems @{thm [source] point.simps} is added |
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automatically to the standard simpset, @{thm [source] point.iffs} is |
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added to the Classical Reasoner and Simplifier context. |
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\medskip Record declarations define new types and type abbreviations: |
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@{text [display] |
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" point = \<lparr>xpos :: nat, ypos :: nat\<rparr> = () point_ext_type |
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'a point_scheme = \<lparr>xpos :: nat, ypos :: nat, ... :: 'a\<rparr> = 'a point_ext_type"} |
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*} |
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consts foo1 :: point |
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consts foo2 :: "(| xpos :: nat, ypos :: nat |)" |
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consts foo3 :: "'a => 'a point_scheme" |
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consts foo4 :: "'a => (| xpos :: nat, ypos :: nat, ... :: 'a |)" |
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subsubsection {* Introducing concrete records and record schemes *} |
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defs |
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foo1_def: "foo1 == (| xpos = 1, ypos = 0 |)" |
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foo3_def: "foo3 ext == (| xpos = 1, ypos = 0, ... = ext |)" |
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subsubsection {* Record selection and record update *} |
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definition |
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getX :: "'a point_scheme => nat" where |
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"getX r = xpos r" |
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definition |
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setX :: "'a point_scheme => nat => 'a point_scheme" where |
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"setX r n = r (| xpos := n |)" |
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subsubsection {* Some lemmas about records *} |
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text {* Basic simplifications. *} |
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lemma "point.make n p = (| xpos = n, ypos = p |)" |
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by (simp only: point.make_def) |
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lemma "xpos (| xpos = m, ypos = n, ... = p |) = m" |
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by simp |
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lemma "(| xpos = m, ypos = n, ... = p |) (| xpos:= 0 |) = (| xpos = 0, ypos = n, ... = p |)" |
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by simp |
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text {* \medskip Equality of records. *} |
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lemma "n = n' ==> p = p' ==> (| xpos = n, ypos = p |) = (| xpos = n', ypos = p' |)" |
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-- "introduction of concrete record equality" |
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by simp |
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lemma "(| xpos = n, ypos = p |) = (| xpos = n', ypos = p' |) ==> n = n'" |
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-- "elimination of concrete record equality" |
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by simp |
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lemma "r (| xpos := n |) (| ypos := m |) = r (| ypos := m |) (| xpos := n |)" |
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-- "introduction of abstract record equality" |
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by simp |
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lemma "r (| xpos := n |) = r (| xpos := n' |) ==> n = n'" |
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-- "elimination of abstract record equality (manual proof)" |
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proof - |
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assume "r (| xpos := n |) = r (| xpos := n' |)" (is "?lhs = ?rhs") |
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hence "xpos ?lhs = xpos ?rhs" by simp |
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thus ?thesis by simp |
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qed |
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text {* \medskip Surjective pairing *} |
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lemma "r = (| xpos = xpos r, ypos = ypos r |)" |
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by simp |
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lemma "r = (| xpos = xpos r, ypos = ypos r, ... = point.more r |)" |
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by simp |
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text {* |
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\medskip Representation of records by cases or (degenerate) |
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induction. |
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*} |
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lemma "r(| xpos := n |) (| ypos := m |) = r (| ypos := m |) (| xpos := n |)" |
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proof (cases r) |
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fix xpos ypos more |
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assume "r = (| xpos = xpos, ypos = ypos, ... = more |)" |
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thus ?thesis by simp |
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qed |
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lemma "r (| xpos := n |) (| ypos := m |) = r (| ypos := m |) (| xpos := n |)" |
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proof (induct r) |
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fix xpos ypos more |
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show "(| xpos = xpos, ypos = ypos, ... = more |) (| xpos := n, ypos := m |) = |
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(| xpos = xpos, ypos = ypos, ... = more |) (| ypos := m, xpos := n |)" |
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by simp |
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qed |
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lemma "r (| xpos := n |) (| xpos := m |) = r (| xpos := m |)" |
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proof (cases r) |
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fix xpos ypos more |
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assume "r = \<lparr>xpos = xpos, ypos = ypos, \<dots> = more\<rparr>" |
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thus ?thesis by simp |
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qed |
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lemma "r (| xpos := n |) (| xpos := m |) = r (| xpos := m |)" |
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proof (cases r) |
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case fields |
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thus ?thesis by simp |
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qed |
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lemma "r (| xpos := n |) (| xpos := m |) = r (| xpos := m |)" |
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by (cases r) simp |
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text {* |
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\medskip Concrete records are type instances of record schemes. |
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*} |
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definition |
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foo5 :: nat where |
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"foo5 = getX (| xpos = 1, ypos = 0 |)" |
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text {* \medskip Manipulating the ``@{text "..."}'' (more) part. *} |
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definition |
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incX :: "'a point_scheme => 'a point_scheme" where |
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"incX r = (| xpos = xpos r + 1, ypos = ypos r, ... = point.more r |)" |
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lemma "incX r = setX r (Suc (getX r))" |
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by (simp add: getX_def setX_def incX_def) |
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text {* An alternative definition. *} |
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definition |
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incX' :: "'a point_scheme => 'a point_scheme" where |
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"incX' r = r (| xpos := xpos r + 1 |)" |
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subsection {* Coloured points: record extension *} |
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datatype colour = Red | Green | Blue |
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record cpoint = point + |
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colour :: colour |
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text {* |
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The record declaration defines a new type constructure and abbreviations: |
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@{text [display] |
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" cpoint = (| xpos :: nat, ypos :: nat, colour :: colour |) = |
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() cpoint_ext_type point_ext_type |
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'a cpoint_scheme = (| xpos :: nat, ypos :: nat, colour :: colour, ... :: 'a |) = |
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'a cpoint_ext_type point_ext_type"} |
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*} |
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consts foo6 :: cpoint |
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consts foo7 :: "(| xpos :: nat, ypos :: nat, colour :: colour |)" |
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consts foo8 :: "'a cpoint_scheme" |
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consts foo9 :: "(| xpos :: nat, ypos :: nat, colour :: colour, ... :: 'a |)" |
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text {* |
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Functions on @{text point} schemes work for @{text cpoints} as well. |
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*} |
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definition |
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foo10 :: nat where |
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"foo10 = getX (| xpos = 2, ypos = 0, colour = Blue |)" |
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subsubsection {* Non-coercive structural subtyping *} |
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text {* |
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Term @{term foo11} has type @{typ cpoint}, not type @{typ point} --- |
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Great! |
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*} |
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definition |
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foo11 :: cpoint where |
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"foo11 = setX (| xpos = 2, ypos = 0, colour = Blue |) 0" |
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subsection {* Other features *} |
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text {* Field names contribute to record identity. *} |
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record point' = |
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xpos' :: nat |
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ypos' :: nat |
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text {* |
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\noindent May not apply @{term getX} to @{term [source] "(| xpos' = |
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2, ypos' = 0 |)"} -- type error. |
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*} |
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text {* \medskip Polymorphic records. *} |
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record 'a point'' = point + |
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content :: 'a |
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types cpoint'' = "colour point''" |
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end |