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author | wenzelm |

Wed, 26 May 1999 22:45:59 +0200 | |

changeset 6737 | 03f0ff7ee029 |

parent 6736 | a0b2cfa12d0d |

child 6738 | 06189132c67b |

ex/Points Isar'ized;

src/HOL/IsaMakefile | file | annotate | diff | comparison | revisions | |

src/HOL/ex/Points.ML | file | annotate | diff | comparison | revisions | |

src/HOL/ex/Points.thy | file | annotate | diff | comparison | revisions |

--- a/src/HOL/IsaMakefile Wed May 26 22:45:08 1999 +0200 +++ b/src/HOL/IsaMakefile Wed May 26 22:45:59 1999 +0200 @@ -318,7 +318,7 @@ ex/Lagrange.thy ex/Ring.ML ex/Ring.thy ex/StringEx.ML \ ex/StringEx.thy ex/BinEx.ML ex/BinEx.thy ex/MonoidGroup.thy \ ex/PiSets.thy ex/PiSets.ML ex/LocaleGroup.thy ex/LocaleGroup.ML \ - ex/Antiquote.thy ex/Antiquote.ML ex/Points.thy ex/Points.ML + ex/Antiquote.thy ex/Antiquote.ML ex/Points.thy @$(ISATOOL) usedir $(OUT)/HOL ex

--- a/src/HOL/ex/Points.ML Wed May 26 22:45:08 1999 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,46 +0,0 @@ -(* Title: HOL/ex/Points.thy - ID: $Id$ - Author: Wolfgang Naraschewski and Markus Wenzel, TU Muenchen - -Basic use of extensible records in HOL, including the famous points -and coloured points. - -Note: any of these goals may be solved at a stroke by Auto_tac or Force_tac -*) - - -(* some basic simplifications *) - -Goal "x (| x = m, y = n, ... = p |) = m"; -by (Simp_tac 1); -result(); - -Goal "(| x = m, y = n, ... = p |) (| x:= 0 |) = (| x = 0, y = n, ... = p |)"; -by (Simp_tac 1); -result(); - - -(* splitting quantifiers: the !!r is NECESSARY *) - -Goal "!!r. r (| x := n |) (| y := m |) = r (| y := m |) (| x := n |)"; -by (record_split_tac 1); -by (Simp_tac 1); -result(); - -Goal "!!r. r (| x := n |) (| x := m |) = r (| x := m |)"; -by (record_split_tac 1); -by (Simp_tac 1); -result(); - - -(* record equality *) - -Goal "(| x = n, y = p |) = (| x = n', y = p' |) & n = 0 ==> n' = 0"; -by (Asm_full_simp_tac 1); -by (Blast_tac 1); -result(); - -Goalw [getX_def, setX_def, incX_def] "!!r n. incX r = setX r (Suc (getX r))"; -by (record_split_tac 1); -by (Simp_tac 1); -result();

--- a/src/HOL/ex/Points.thy Wed May 26 22:45:08 1999 +0200 +++ b/src/HOL/ex/Points.thy Wed May 26 22:45:59 1999 +0200 @@ -1,143 +1,194 @@ (* Title: HOL/ex/Points.thy ID: $Id$ Author: Wolfgang Naraschewski and Markus Wenzel, TU Muenchen - -Basic use of extensible records in HOL, including the famous points -and coloured points. *) -Points = Main + +theory Points = Main:; + +title "Basic use of extensible records in HOL, including the famous points + and coloured points."; -(** points **) +section "Points"; record point = x :: nat - y :: nat + y :: nat; -(* - To find out, which theorems are produced by the record declaration, - type the following commands: +text {| + Apart many other things, above record declaration produces the + following theorems: - thms "point.simps"; - thms "point.iffs"; - thms "point.update_defs"; + thms "point.simps" + thms "point.iffs" + thms "point.update_defs" 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 |) + 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 |)"; + + +subsection "Introducing concrete records and record schemes"; + +defs + foo1_def: "foo1 == (| x = 1, y = 0 |)" + foo3_def: "foo3 ext == (| x = 1, y = 0, ... = ext |)"; -consts foo1 :: point -consts foo2 :: "(| x :: nat, y :: nat |)" -consts foo3 :: 'a => ('a::more) point_scheme -consts foo4 :: "'a => (| x :: nat, y :: nat, ... :: 'a |)" + +subsection "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 |)"; + + +subsection "Some lemmas about records"; + +text "Note: any of these goals may be solved with a single + stroke of auto or force."; -(* Introducing concrete records and record schemes *) +text "basic simplifications"; -defs - foo1_def "foo1 == (| x = 1, y = 0 |)" - foo3_def "foo3 ext == (| x = 1, y = 0, ... = ext |)" +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; -(* Record selection and record update *) +text "splitting quantifiers: the !!r is NECESSARY"; -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 |)" +lemma "!!r. r (| x := n |) (| y := m |) = r (| y := m |) (| x := n |)"; +proof record_split; + fix a b rest; + show "(| x = a, y = b, ... = rest |)(| x := n, y := m |) = + (| x = a, y = b, ... = rest |)(| y := m, x := n |)"; + by simp; +qed; + +lemma "!!r. r (| x := n |) (| x := m |) = r (| x := m |)"; +proof record_split; + fix a b rest; + show "(| x = a, y = b, ... = rest |)(| x := n, x := m |) = + (| x = a, y = b, ... = rest |)(| x := m |)"; + by simp; +qed; -(* concrete records are type instances of record schemes *) +text "equality of records"; + +lemma "(| x = n, y = p |) = (| x = n', y = p' |) --> n = n'" (is "??EQ --> _"); +proof; + assume ??EQ; + thus "n = n'"; by simp; +qed; + + +text "concrete records are type instances of record schemes"; constdefs foo5 :: nat - "foo5 == getX (| x = 1, y = 0 |)" + "foo5 == getX (| x = 1, y = 0 |)"; -(* manipulating the `...' (more-part) *) +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 |)" + incX :: "('a::more) point_scheme => 'a point_scheme" + "incX r == (| x = Suc (x r), y = y r, ... = point.more r |)"; -(*alternative definition*) +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) |)" + incX' :: "('a::more) point_scheme => 'a point_scheme" + "incX' r == r (| x := Suc (x r) |)"; -(** coloured points: record extension **) +section "coloured points: record extension"; -datatype colour = Red | Green | Blue +datatype colour = Red | Green | Blue; record cpoint = point + - colour :: colour + 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 |)" +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 |)"; -(* functions on point schemes work for cpoints as well *) +text "functions on point schemes work for cpoints as well"; constdefs foo10 :: nat - "foo10 == getX (| x = 2, y = 0, colour = Blue |)" + "foo10 == getX (| x = 2, y = 0, colour = Blue |)"; -(* non-coercive structural subtyping *) +subsection "Non-coercive structural subtyping"; -(*foo11 has type cpoint, not type point*) (*Great!*) +text "foo11 has type cpoint, not type point --- Great!"; + constdefs foo11 :: cpoint - "foo11 == setX (| x = 2, y = 0, colour = Blue |) 0" + "foo11 == setX (| x = 2, y = 0, colour = Blue |) 0"; -(** other features **) +section "Other features"; -(* field names contribute to record identity *) +text "field names contribute to record identity"; record point' = x' :: nat - y' :: nat + y' :: nat; consts - foo12 :: nat -(*"foo12 == getX (| x' = 2, y' = 0 |)"*) (*invalid*) + foo12 :: nat; + +text {| Definition @{term "foo12 == getX (| x' = 2, y' = 0 |)"} is invalid |}; -(* polymorphic records *) +text "polymorphic records"; record 'a point'' = point + - content :: 'a + content :: 'a; -types cpoint'' = colour point'' +types cpoint'' = "colour point''"; +text "Have a lot of fun!"; -(*Have a lot of fun!*) - -end +end;