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src/HOL/ex/Records.thy

author | wenzelm |

Fri, 05 Oct 2001 21:52:39 +0200 | |

changeset 11701 | 3d51fbf81c17 |

parent 10357 | 0d0cac129618 |

child 11704 | 3c50a2cd6f00 |

permissions | -rw-r--r-- |

sane numerals (stage 1): added generic 1, removed 1' and 2 on nat,
"num" syntax (still with "#"), Numeral0, Numeral1;

(* 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 @{thm [source] point.simps} is added automatically to the standard simpset, @{thm [source] point.iffs} is added to the Classical Reasoner and Simplifier context. *} text {* Record declarations define new type abbreviations: @{text [display] " point = (| x :: nat, y :: nat |) 'a point_scheme = (| x :: nat, y :: nat, ... :: 'a |)"} Extensions `...' must be in type class @{text 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 {* \medskip 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 {* \medskip 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 {* \medskip Splitting quantifiers: the @{text "!!r"} is \emph{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 {* \medskip Concrete records are type instances of record schemes. *} constdefs foo5 :: nat "foo5 == getX (| x = 1, y = 0 |)" text {* \medskip 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 {* An 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: @{text [display] " 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 @{text point} schemes work for @{text cpoints} as well. *} constdefs foo10 :: nat "foo10 == getX (| x = # 2, y = 0, colour = Blue |)" subsubsection {* Non-coercive structural subtyping *} text {* Term @{term foo11} has type @{typ cpoint}, not type @{typ 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 {* \noindent May not apply @{term getX} to @{term [source] "(| x' = # 2, y' = 0 |)"}. *} text {* \medskip Polymorphic records. *} record 'a point'' = point + content :: 'a types cpoint'' = "colour point''" end