author | paulson |
Mon, 22 Oct 2001 11:54:22 +0200 | |
changeset 11868 | 56db9f3a6b3e |
parent 11704 | 3c50a2cd6f00 |
child 11928 | d0bae2c3abad |
permissions | -rw-r--r-- |
10052 | 1 |
(* Title: HOL/ex/Records.thy |
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ID: $Id$ |
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Author: Wolfgang Naraschewski and Markus Wenzel, TU Muenchen |
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License: GPL (GNU GENERAL PUBLIC LICENSE) |
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*) |
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header {* Using extensible records in HOL -- points and coloured points *} |
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theory Records = Main: |
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subsection {* Points *} |
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record point = |
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x :: nat |
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y :: 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.update_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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*} |
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text {* |
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Record declarations define new type abbreviations: |
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@{text [display] |
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" point = (| x :: nat, y :: nat |) |
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'a point_scheme = (| x :: nat, y :: nat, ... :: 'a |)"} |
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Extensions `...' must be in type class @{text more}. |
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*} |
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consts foo1 :: point |
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consts foo2 :: "(| x :: nat, y :: nat |)" |
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consts foo3 :: "'a => ('a::more) point_scheme" |
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consts foo4 :: "'a => (| x :: nat, y :: 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 == (| x = 1, y = 0 |)" |
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foo3_def: "foo3 ext == (| x = 1, y = 0, ... = ext |)" |
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subsubsection {* Record selection and record update *} |
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constdefs |
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getX :: "('a::more) point_scheme => nat" |
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"getX r == x r" |
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setX :: "('a::more) point_scheme => nat => 'a point_scheme" |
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"setX r n == r (| x := 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 = (| x = n, y = p |)" |
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by simp |
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lemma "x (| x = m, y = n, ... = p |) = m" |
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by simp |
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lemma "(| x = m, y = n, ... = p |) (| x:= 0 |) = (| x = 0, y = 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' ==> (| x = n, y = p |) = (| x = n', y = p' |)" |
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-- "introduction of concrete record equality" |
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by simp |
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lemma "(| x = n, y = p |) = (| x = n', y = p' |) ==> n = n'" |
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-- "elimination of concrete record equality" |
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by simp |
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lemma "r (| x := n |) (| y := m |) = r (| y := m |) (| x := n |)" |
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-- "introduction of abstract record equality" |
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by simp |
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lemma "r (| x := n |) = r (| x := 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 (| x := n |) = r (| x := n' |)" (is "?lhs = ?rhs") |
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hence "x ?lhs = x ?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 = (| x = x r, y = y r |)" |
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by simp |
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lemma "r = (| x = x r, y = y r, ... = more r |)" |
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by simp |
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text {* |
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\medskip Splitting quantifiers: the @{text "!!r"} is \emph{necessary} |
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here! |
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*} |
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lemma "!!r. r (| x := n |) (| y := m |) = r (| y := m |) (| x := n |)" |
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proof record_split |
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fix x y more |
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show "(| x = x, y = y, ... = more |)(| x := n, y := m |) = |
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(| x = x, y = y, ... = more |)(| y := m, x := n |)" |
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by simp |
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qed |
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lemma "!!r. r (| x := n |) (| x := m |) = r (| x := m |)" |
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proof record_split |
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fix x y more |
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show "(| x = x, y = y, ... = more |)(| x := n, x := m |) = |
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(| x = x, y = y, ... = more |)(| x := m |)" |
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by simp |
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qed |
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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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constdefs |
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foo5 :: nat |
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"foo5 == getX (| x = 1, y = 0 |)" |
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text {* \medskip Manipulating the `...' (more) part. *} |
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constdefs |
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incX :: "('a::more) point_scheme => 'a point_scheme" |
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"incX r == (| x = Suc (x r), y = y r, ... = point.more r |)" |
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lemma "!!r n. incX r = setX r (Suc (getX r))" |
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proof (unfold getX_def setX_def incX_def) |
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show "!!r n. (| x = Suc (x r), y = y r, ... = more r |) = r(| x := Suc (x r) |)" |
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by record_split simp |
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qed |
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text {* An alternative definition. *} |
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constdefs |
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incX' :: "('a::more) point_scheme => 'a point_scheme" |
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"incX' r == r (| x := Suc (x r) |)" |
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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 new type constructors: |
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@{text [display] |
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" cpoint = (| x :: nat, y :: nat, colour :: colour |) |
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'a cpoint_scheme = (| x :: nat, y :: nat, colour :: colour, ... :: 'a |)"} |
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*} |
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consts foo6 :: cpoint |
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consts foo7 :: "(| x :: nat, y :: nat, colour :: colour |)" |
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consts foo8 :: "('a::more) cpoint_scheme" |
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consts foo9 :: "(| x :: nat, y :: 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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constdefs |
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foo10 :: nat |
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11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
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"foo10 == getX (| x = 2, y = 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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constdefs |
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foo11 :: cpoint |
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11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
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"foo11 == setX (| x = 2, y = 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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x' :: nat |
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y' :: nat |
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text {* |
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\noindent May not apply @{term getX} to |
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11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset
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@{term [source] "(| x' = 2, y' = 0 |)"}. |
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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 |