doc-src/Main/Docs/Main_Doc.thy
author haftmann
Mon, 22 Feb 2010 09:36:29 +0100
changeset 35277 f228929a6fab
parent 35061 be1e25a62ec8
child 35805 1c4a8d3b26d2
permissions -rw-r--r--
adjusted to cs. 8dfd816713c6
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     1
(*<*)
30401
nipkow
parents: 30386
diff changeset
     2
theory Main_Doc
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     3
imports Main
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     4
begin
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     5
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     6
ML {*
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     7
fun pretty_term_type_only ctxt (t, T) =
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     8
  (if fastype_of t = Sign.certify_typ (ProofContext.theory_of ctxt) T then ()
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
     9
   else error "term_type_only: type mismatch";
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    10
   Syntax.pretty_typ ctxt T)
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    11
30392
9fe4bbb90297 adapted to simplified ThyOutput.antiquotation interface;
wenzelm
parents: 30386
diff changeset
    12
val _ = ThyOutput.antiquotation "term_type_only" (Args.term -- Args.typ_abbrev)
9fe4bbb90297 adapted to simplified ThyOutput.antiquotation interface;
wenzelm
parents: 30386
diff changeset
    13
  (fn {source, context, ...} => fn arg =>
9fe4bbb90297 adapted to simplified ThyOutput.antiquotation interface;
wenzelm
parents: 30386
diff changeset
    14
    ThyOutput.output
9fe4bbb90297 adapted to simplified ThyOutput.antiquotation interface;
wenzelm
parents: 30386
diff changeset
    15
      (ThyOutput.maybe_pretty_source (pretty_term_type_only context) source [arg]));
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    16
*}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    17
(*>*)
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    18
text{*
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    19
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    20
\begin{abstract}
30442
1bc0638d554d Added "What's in Main" to doc sources
nipkow
parents: 30440
diff changeset
    21
This document lists the main types, functions and syntax provided by theory @{theory Main}. It is meant as a quick overview of what is available. The sophisticated class structure is only hinted at. For details see \url{http://isabelle.in.tum.de/dist/library/HOL/}.
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    22
\end{abstract}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    23
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    24
\section{HOL}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    25
30440
nipkow
parents: 30425
diff changeset
    26
The basic logic: @{prop "x = y"}, @{const True}, @{const False}, @{prop"Not P"}, @{prop"P & Q"}, @{prop "P | Q"}, @{prop "P --> Q"}, @{prop"ALL x. P"}, @{prop"EX x. P"}, @{prop"EX! x. P"}, @{term"THE x. P"}.
nipkow
parents: 30425
diff changeset
    27
\smallskip
nipkow
parents: 30425
diff changeset
    28
nipkow
parents: 30425
diff changeset
    29
\begin{tabular}{@ {} l @ {~::~} l @ {}}
nipkow
parents: 30425
diff changeset
    30
@{const HOL.undefined} & @{typeof HOL.undefined}\\
nipkow
parents: 30425
diff changeset
    31
@{const HOL.default} & @{typeof HOL.default}\\
nipkow
parents: 30425
diff changeset
    32
\end{tabular}
nipkow
parents: 30425
diff changeset
    33
nipkow
parents: 30425
diff changeset
    34
\subsubsection*{Syntax}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    35
30440
nipkow
parents: 30425
diff changeset
    36
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
nipkow
parents: 30425
diff changeset
    37
@{term"~(x = y)"} & @{term[source]"\<not> (x = y)"} & (\verb$~=$)\\
nipkow
parents: 30425
diff changeset
    38
@{term[source]"P \<longleftrightarrow> Q"} & @{term"P \<longleftrightarrow> Q"} \\
nipkow
parents: 30425
diff changeset
    39
@{term"If x y z"} & @{term[source]"If x y z"}\\
nipkow
parents: 30425
diff changeset
    40
@{term"Let e\<^isub>1 (%x. e\<^isub>2)"} & @{term[source]"Let e\<^isub>1 (\<lambda>x. e\<^isub>2)"}\\
nipkow
parents: 30425
diff changeset
    41
\end{supertabular}
nipkow
parents: 30425
diff changeset
    42
nipkow
parents: 30425
diff changeset
    43
nipkow
parents: 30425
diff changeset
    44
\section{Orderings}
nipkow
parents: 30425
diff changeset
    45
nipkow
parents: 30425
diff changeset
    46
A collection of classes defining basic orderings:
nipkow
parents: 30425
diff changeset
    47
preorder, partial order, linear order, dense linear order and wellorder.
nipkow
parents: 30425
diff changeset
    48
\smallskip
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    49
30425
nipkow
parents: 30403
diff changeset
    50
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
35277
f228929a6fab adjusted to cs. 8dfd816713c6
haftmann
parents: 35061
diff changeset
    51
@{const Orderings.less_eq} & @{typeof Orderings.less_eq} & (\verb$<=$)\\
f228929a6fab adjusted to cs. 8dfd816713c6
haftmann
parents: 35061
diff changeset
    52
@{const Orderings.less} & @{typeof Orderings.less}\\
30440
nipkow
parents: 30425
diff changeset
    53
@{const Orderings.Least} & @{typeof Orderings.Least}\\
nipkow
parents: 30425
diff changeset
    54
@{const Orderings.min} & @{typeof Orderings.min}\\
nipkow
parents: 30425
diff changeset
    55
@{const Orderings.max} & @{typeof Orderings.max}\\
nipkow
parents: 30425
diff changeset
    56
@{const[source] top} & @{typeof Orderings.top}\\
nipkow
parents: 30425
diff changeset
    57
@{const[source] bot} & @{typeof Orderings.bot}\\
nipkow
parents: 30425
diff changeset
    58
@{const Orderings.mono} & @{typeof Orderings.mono}\\
nipkow
parents: 30425
diff changeset
    59
@{const Orderings.strict_mono} & @{typeof Orderings.strict_mono}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    60
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    61
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    62
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    63
30440
nipkow
parents: 30425
diff changeset
    64
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
nipkow
parents: 30425
diff changeset
    65
@{term[source]"x \<ge> y"} & @{term"x \<ge> y"} & (\verb$>=$)\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    66
@{term[source]"x > y"} & @{term"x > y"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    67
@{term"ALL x<=y. P"} & @{term[source]"\<forall>x. x \<le> y \<longrightarrow> P"}\\
30440
nipkow
parents: 30425
diff changeset
    68
@{term"EX x<=y. P"} & @{term[source]"\<exists>x. x \<le> y \<and> P"}\\
nipkow
parents: 30425
diff changeset
    69
\multicolumn{2}{@ {}l@ {}}{Similarly for $<$, $\ge$ and $>$}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    70
@{term"LEAST x. P"} & @{term[source]"Least (\<lambda>x. P)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    71
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
    72
30401
nipkow
parents: 30386
diff changeset
    73
nipkow
parents: 30386
diff changeset
    74
\section{Lattices}
nipkow
parents: 30386
diff changeset
    75
nipkow
parents: 30386
diff changeset
    76
Classes semilattice, lattice, distributive lattice and complete lattice (the
nipkow
parents: 30386
diff changeset
    77
latter in theory @{theory Set}).
nipkow
parents: 30386
diff changeset
    78
nipkow
parents: 30386
diff changeset
    79
\begin{tabular}{@ {} l @ {~::~} l @ {}}
nipkow
parents: 30386
diff changeset
    80
@{const Lattices.inf} & @{typeof Lattices.inf}\\
nipkow
parents: 30386
diff changeset
    81
@{const Lattices.sup} & @{typeof Lattices.sup}\\
32885
5cab25b2dcf9 Inf/Sup now purely syntactic
haftmann
parents: 32243
diff changeset
    82
@{const Complete_Lattice.Inf} & @{term_type_only Complete_Lattice.Inf "'a set \<Rightarrow> 'a::Inf"}\\
5cab25b2dcf9 Inf/Sup now purely syntactic
haftmann
parents: 32243
diff changeset
    83
@{const Complete_Lattice.Sup} & @{term_type_only Complete_Lattice.Sup "'a set \<Rightarrow> 'a::Sup"}\\
30401
nipkow
parents: 30386
diff changeset
    84
\end{tabular}
nipkow
parents: 30386
diff changeset
    85
nipkow
parents: 30386
diff changeset
    86
\subsubsection*{Syntax}
nipkow
parents: 30386
diff changeset
    87
30440
nipkow
parents: 30425
diff changeset
    88
Available by loading theory @{text Lattice_Syntax} in directory @{text
nipkow
parents: 30425
diff changeset
    89
Library}.
30401
nipkow
parents: 30386
diff changeset
    90
nipkow
parents: 30386
diff changeset
    91
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
nipkow
parents: 30386
diff changeset
    92
@{text[source]"x \<sqsubseteq> y"} & @{term"x \<le> y"}\\
nipkow
parents: 30386
diff changeset
    93
@{text[source]"x \<sqsubset> y"} & @{term"x < y"}\\
nipkow
parents: 30386
diff changeset
    94
@{text[source]"x \<sqinter> y"} & @{term"inf x y"}\\
nipkow
parents: 30386
diff changeset
    95
@{text[source]"x \<squnion> y"} & @{term"sup x y"}\\
nipkow
parents: 30386
diff changeset
    96
@{text[source]"\<Sqinter> A"} & @{term"Sup A"}\\
nipkow
parents: 30386
diff changeset
    97
@{text[source]"\<Squnion> A"} & @{term"Inf A"}\\
30440
nipkow
parents: 30425
diff changeset
    98
@{text[source]"\<top>"} & @{term[source] top}\\
nipkow
parents: 30425
diff changeset
    99
@{text[source]"\<bottom>"} & @{term[source] bot}\\
30401
nipkow
parents: 30386
diff changeset
   100
\end{supertabular}
nipkow
parents: 30386
diff changeset
   101
nipkow
parents: 30386
diff changeset
   102
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   103
\section{Set}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   104
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   105
Sets are predicates: @{text[source]"'a set  =  'a \<Rightarrow> bool"}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   106
\bigskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   107
30425
nipkow
parents: 30403
diff changeset
   108
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
30370
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   109
@{const Set.empty} & @{term_type_only "Set.empty" "'a set"}\\
32142
0ddf61f96b2a fixed doc
haftmann
parents: 30988
diff changeset
   110
@{const Set.insert} & @{term_type_only insert "'a\<Rightarrow>'a set\<Rightarrow>'a set"}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   111
@{const Collect} & @{term_type_only Collect "('a\<Rightarrow>bool)\<Rightarrow>'a set"}\\
30425
nipkow
parents: 30403
diff changeset
   112
@{const "op :"} & @{term_type_only "op :" "'a\<Rightarrow>'a set\<Rightarrow>bool"} & (\texttt{:})\\
32208
e6a42620e6c1 adapted to changed prefixes
haftmann
parents: 32142
diff changeset
   113
@{const Set.union} & @{term_type_only Set.union "'a set\<Rightarrow>'a set \<Rightarrow> 'a set"} & (\texttt{Un})\\
e6a42620e6c1 adapted to changed prefixes
haftmann
parents: 32142
diff changeset
   114
@{const Set.inter} & @{term_type_only Set.inter "'a set\<Rightarrow>'a set \<Rightarrow> 'a set"} & (\texttt{Int})\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   115
@{const UNION} & @{term_type_only UNION "'a set\<Rightarrow>('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   116
@{const INTER} & @{term_type_only INTER "'a set\<Rightarrow>('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   117
@{const Union} & @{term_type_only Union "'a set set\<Rightarrow>'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   118
@{const Inter} & @{term_type_only Inter "'a set set\<Rightarrow>'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   119
@{const Pow} & @{term_type_only Pow "'a set \<Rightarrow>'a set set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   120
@{const UNIV} & @{term_type_only UNIV "'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   121
@{const image} & @{term_type_only image "('a\<Rightarrow>'b)\<Rightarrow>'a set\<Rightarrow>'b set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   122
@{const Ball} & @{term_type_only Ball "'a set\<Rightarrow>('a\<Rightarrow>bool)\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   123
@{const Bex} & @{term_type_only Bex "'a set\<Rightarrow>('a\<Rightarrow>bool)\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   124
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   125
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   126
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   127
30425
nipkow
parents: 30403
diff changeset
   128
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   129
@{text"{x\<^isub>1,\<dots>,x\<^isub>n}"} & @{text"insert x\<^isub>1 (\<dots> (insert x\<^isub>n {})\<dots>)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   130
@{term"x ~: A"} & @{term[source]"\<not>(x \<in> A)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   131
@{term"A \<subseteq> B"} & @{term[source]"A \<le> B"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   132
@{term"A \<subset> B"} & @{term[source]"A < B"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   133
@{term[source]"A \<supseteq> B"} & @{term[source]"B \<le> A"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   134
@{term[source]"A \<supset> B"} & @{term[source]"B < A"}\\
30440
nipkow
parents: 30425
diff changeset
   135
@{term"{x. P}"} & @{term[source]"Collect (\<lambda>x. P)"}\\
30425
nipkow
parents: 30403
diff changeset
   136
@{term[mode=xsymbols]"UN x:I. A"} & @{term[source]"UNION I (\<lambda>x. A)"} & (\texttt{UN})\\
30370
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   137
@{term[mode=xsymbols]"UN x. A"} & @{term[source]"UNION UNIV (\<lambda>x. A)"}\\
30425
nipkow
parents: 30403
diff changeset
   138
@{term[mode=xsymbols]"INT x:I. A"} & @{term[source]"INTER I (\<lambda>x. A)"} & (\texttt{INT})\\
30370
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   139
@{term[mode=xsymbols]"INT x. A"} & @{term[source]"INTER UNIV (\<lambda>x. A)"}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   140
@{term"ALL x:A. P"} & @{term[source]"Ball A (\<lambda>x. P)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   141
@{term"EX x:A. P"} & @{term[source]"Bex A (\<lambda>x. P)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   142
@{term"range f"} & @{term[source]"f ` UNIV"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   143
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   144
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   145
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   146
\section{Fun}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   147
32933
ba14400f7f34 added List.nth
nipkow
parents: 32885
diff changeset
   148
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   149
@{const "Fun.id"} & @{typeof Fun.id}\\
32933
ba14400f7f34 added List.nth
nipkow
parents: 32885
diff changeset
   150
@{const "Fun.comp"} & @{typeof Fun.comp} & (\texttt{o})\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   151
@{const "Fun.inj_on"} & @{term_type_only Fun.inj_on "('a\<Rightarrow>'b)\<Rightarrow>'a set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   152
@{const "Fun.inj"} & @{typeof Fun.inj}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   153
@{const "Fun.surj"} & @{typeof Fun.surj}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   154
@{const "Fun.bij"} & @{typeof Fun.bij}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   155
@{const "Fun.bij_betw"} & @{term_type_only Fun.bij_betw "('a\<Rightarrow>'b)\<Rightarrow>'a set\<Rightarrow>'b set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   156
@{const "Fun.fun_upd"} & @{typeof Fun.fun_upd}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   157
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   158
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   159
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   160
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   161
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   162
@{term"fun_upd f x y"} & @{term[source]"fun_upd f x y"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   163
@{text"f(x\<^isub>1:=y\<^isub>1,\<dots>,x\<^isub>n:=y\<^isub>n)"} & @{text"f(x\<^isub>1:=y\<^isub>1)\<dots>(x\<^isub>n:=y\<^isub>n)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   164
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   165
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   166
33019
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   167
\section{Hilbert\_Choice}
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   168
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   169
Hilbert's selection ($\varepsilon$) operator: @{term"SOME x. P"}.
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   170
\smallskip
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   171
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   172
\begin{tabular}{@ {} l @ {~::~} l @ {}}
33057
764547b68538 inv_onto -> inv_into
nipkow
parents: 33019
diff changeset
   173
@{const Hilbert_Choice.inv_into} & @{term_type_only Hilbert_Choice.inv_into "'a set \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> ('b \<Rightarrow> 'a)"}
33019
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   174
\end{tabular}
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   175
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   176
\subsubsection*{Syntax}
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   177
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   178
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
33057
764547b68538 inv_onto -> inv_into
nipkow
parents: 33019
diff changeset
   179
@{term inv} & @{term[source]"inv_into UNIV"}
33019
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   180
\end{tabular}
bcf56a64ce1a added Hilbert_Choice section
nipkow
parents: 32933
diff changeset
   181
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   182
\section{Fixed Points}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   183
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   184
Theory: @{theory Inductive}.
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   185
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   186
Least and greatest fixed points in a complete lattice @{typ 'a}:
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   187
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   188
\begin{tabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   189
@{const Inductive.lfp} & @{typeof Inductive.lfp}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   190
@{const Inductive.gfp} & @{typeof Inductive.gfp}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   191
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   192
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   193
Note that in particular sets (@{typ"'a \<Rightarrow> bool"}) are complete lattices.
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   194
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   195
\section{Sum\_Type}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   196
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   197
Type constructor @{text"+"}.
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   198
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   199
\begin{tabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   200
@{const Sum_Type.Inl} & @{typeof Sum_Type.Inl}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   201
@{const Sum_Type.Inr} & @{typeof Sum_Type.Inr}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   202
@{const Sum_Type.Plus} & @{term_type_only Sum_Type.Plus "'a set\<Rightarrow>'b set\<Rightarrow>('a+'b)set"}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   203
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   204
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   205
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   206
\section{Product\_Type}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   207
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   208
Types @{typ unit} and @{text"\<times>"}.
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   209
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   210
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   211
@{const Product_Type.Unity} & @{typeof Product_Type.Unity}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   212
@{const Pair} & @{typeof Pair}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   213
@{const fst} & @{typeof fst}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   214
@{const snd} & @{typeof snd}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   215
@{const split} & @{typeof split}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   216
@{const curry} & @{typeof curry}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   217
@{const Product_Type.Sigma} & @{term_type_only Product_Type.Sigma "'a set\<Rightarrow>('a\<Rightarrow>'b set)\<Rightarrow>('a*'b)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   218
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   219
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   220
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   221
30440
nipkow
parents: 30425
diff changeset
   222
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} ll @ {}}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   223
@{term"Pair a b"} & @{term[source]"Pair a b"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   224
@{term"split (\<lambda>x y. t)"} & @{term[source]"split (\<lambda>x y. t)"}\\
30440
nipkow
parents: 30425
diff changeset
   225
@{term"A <*> B"} &  @{text"Sigma A (\<lambda>\<^raw:\_>. B)"} & (\verb$<*>$)
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   226
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   227
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   228
Pairs may be nested. Nesting to the right is printed as a tuple,
30440
nipkow
parents: 30425
diff changeset
   229
e.g.\ \mbox{@{term"(a,b,c)"}} is really \mbox{@{text"(a, (b, c))"}.}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   230
Pattern matching with pairs and tuples extends to all binders,
30440
nipkow
parents: 30425
diff changeset
   231
e.g.\ \mbox{@{prop"ALL (x,y):A. P"},} @{term"{(x,y). P}"}, etc.
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   232
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   233
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   234
\section{Relation}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   235
30440
nipkow
parents: 30425
diff changeset
   236
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   237
@{const Relation.converse} & @{term_type_only Relation.converse "('a * 'b)set \<Rightarrow> ('b*'a)set"}\\
32243
64660a887b15 adapted doc to type of "op O"
krauss
parents: 32208
diff changeset
   238
@{const Relation.rel_comp} & @{term_type_only Relation.rel_comp "('a*'b)set\<Rightarrow>('b*'c)set\<Rightarrow>('a*'c)set"}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   239
@{const Relation.Image} & @{term_type_only Relation.Image "('a*'b)set\<Rightarrow>'a set\<Rightarrow>'b set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   240
@{const Relation.inv_image} & @{term_type_only Relation.inv_image "('a*'a)set\<Rightarrow>('b\<Rightarrow>'a)\<Rightarrow>('b*'b)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   241
@{const Relation.Id_on} & @{term_type_only Relation.Id_on "'a set\<Rightarrow>('a*'a)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   242
@{const Relation.Id} & @{term_type_only Relation.Id "('a*'a)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   243
@{const Relation.Domain} & @{term_type_only Relation.Domain "('a*'b)set\<Rightarrow>'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   244
@{const Relation.Range} & @{term_type_only Relation.Range "('a*'b)set\<Rightarrow>'b set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   245
@{const Relation.Field} & @{term_type_only Relation.Field "('a*'a)set\<Rightarrow>'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   246
@{const Relation.refl_on} & @{term_type_only Relation.refl_on "'a set\<Rightarrow>('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   247
@{const Relation.refl} & @{term_type_only Relation.refl "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   248
@{const Relation.sym} & @{term_type_only Relation.sym "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   249
@{const Relation.antisym} & @{term_type_only Relation.antisym "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   250
@{const Relation.trans} & @{term_type_only Relation.trans "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   251
@{const Relation.irrefl} & @{term_type_only Relation.irrefl "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   252
@{const Relation.total_on} & @{term_type_only Relation.total_on "'a set\<Rightarrow>('a*'a)set\<Rightarrow>bool"}\\
30440
nipkow
parents: 30425
diff changeset
   253
@{const Relation.total} & @{term_type_only Relation.total "('a*'a)set\<Rightarrow>bool"}\\
nipkow
parents: 30425
diff changeset
   254
\end{supertabular}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   255
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   256
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   257
30440
nipkow
parents: 30425
diff changeset
   258
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
nipkow
parents: 30425
diff changeset
   259
@{term"converse r"} & @{term[source]"converse r"} & (\verb$^-1$)
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   260
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   261
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   262
\section{Equiv\_Relations}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   263
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   264
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   265
@{const Equiv_Relations.equiv} & @{term_type_only Equiv_Relations.equiv "'a set \<Rightarrow> ('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   266
@{const Equiv_Relations.quotient} & @{term_type_only Equiv_Relations.quotient "'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> 'a set set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   267
@{const Equiv_Relations.congruent} & @{term_type_only Equiv_Relations.congruent "('a*'a)set\<Rightarrow>('a\<Rightarrow>'b)\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   268
@{const Equiv_Relations.congruent2} & @{term_type_only Equiv_Relations.congruent2 "('a*'a)set\<Rightarrow>('b*'b)set\<Rightarrow>('a\<Rightarrow>'b\<Rightarrow>'c)\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   269
%@ {const Equiv_Relations.} & @ {term_type_only Equiv_Relations. ""}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   270
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   271
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   272
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   273
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   274
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   275
@{term"congruent r f"} & @{term[source]"congruent r f"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   276
@{term"congruent2 r r f"} & @{term[source]"congruent2 r r f"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   277
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   278
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   279
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   280
\section{Transitive\_Closure}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   281
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   282
\begin{tabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   283
@{const Transitive_Closure.rtrancl} & @{term_type_only Transitive_Closure.rtrancl "('a*'a)set\<Rightarrow>('a*'a)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   284
@{const Transitive_Closure.trancl} & @{term_type_only Transitive_Closure.trancl "('a*'a)set\<Rightarrow>('a*'a)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   285
@{const Transitive_Closure.reflcl} & @{term_type_only Transitive_Closure.reflcl "('a*'a)set\<Rightarrow>('a*'a)set"}\\
30988
b53800e3ee47 adjusted to changes in power syntax
haftmann
parents: 30457
diff changeset
   286
@{const compower} & @{term_type_only "op ^^ :: ('a*'a)set\<Rightarrow>nat\<Rightarrow>('a*'a)set" "('a*'a)set\<Rightarrow>nat\<Rightarrow>('a*'a)set"}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   287
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   288
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   289
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   290
30440
nipkow
parents: 30425
diff changeset
   291
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
nipkow
parents: 30425
diff changeset
   292
@{term"rtrancl r"} & @{term[source]"rtrancl r"} & (\verb$^*$)\\
nipkow
parents: 30425
diff changeset
   293
@{term"trancl r"} & @{term[source]"trancl r"} & (\verb$^+$)\\
nipkow
parents: 30425
diff changeset
   294
@{term"reflcl r"} & @{term[source]"reflcl r"} & (\verb$^=$)
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   295
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   296
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   297
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   298
\section{Algebra}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   299
35061
be1e25a62ec8 adjusted to cs. 9f841f20dca6
haftmann
parents: 35007
diff changeset
   300
Theories @{theory Groups}, @{theory Rings}, @{theory Fields} and @{theory
30440
nipkow
parents: 30425
diff changeset
   301
Divides} define a large collection of classes describing common algebraic
nipkow
parents: 30425
diff changeset
   302
structures from semigroups up to fields. Everything is done in terms of
nipkow
parents: 30425
diff changeset
   303
overloaded operators:
nipkow
parents: 30425
diff changeset
   304
nipkow
parents: 30425
diff changeset
   305
\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
nipkow
parents: 30425
diff changeset
   306
@{text "0"} & @{typeof zero}\\
nipkow
parents: 30425
diff changeset
   307
@{text "1"} & @{typeof one}\\
nipkow
parents: 30425
diff changeset
   308
@{const plus} & @{typeof plus}\\
nipkow
parents: 30425
diff changeset
   309
@{const minus} & @{typeof minus}\\
nipkow
parents: 30425
diff changeset
   310
@{const uminus} & @{typeof uminus} & (\verb$-$)\\
nipkow
parents: 30425
diff changeset
   311
@{const times} & @{typeof times}\\
nipkow
parents: 30425
diff changeset
   312
@{const inverse} & @{typeof inverse}\\
nipkow
parents: 30425
diff changeset
   313
@{const divide} & @{typeof divide}\\
nipkow
parents: 30425
diff changeset
   314
@{const abs} & @{typeof abs}\\
nipkow
parents: 30425
diff changeset
   315
@{const sgn} & @{typeof sgn}\\
nipkow
parents: 30425
diff changeset
   316
@{const dvd_class.dvd} & @{typeof "dvd_class.dvd"}\\
nipkow
parents: 30425
diff changeset
   317
@{const div_class.div} & @{typeof "div_class.div"}\\
nipkow
parents: 30425
diff changeset
   318
@{const div_class.mod} & @{typeof "div_class.mod"}\\
nipkow
parents: 30425
diff changeset
   319
\end{supertabular}
nipkow
parents: 30425
diff changeset
   320
nipkow
parents: 30425
diff changeset
   321
\subsubsection*{Syntax}
nipkow
parents: 30425
diff changeset
   322
nipkow
parents: 30425
diff changeset
   323
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
nipkow
parents: 30425
diff changeset
   324
@{term"abs x"} & @{term[source]"abs x"}
nipkow
parents: 30425
diff changeset
   325
\end{tabular}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   326
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   327
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   328
\section{Nat}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   329
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   330
@{datatype nat}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   331
\bigskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   332
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   333
\begin{tabular}{@ {} lllllll @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   334
@{term "op + :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   335
@{term "op - :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   336
@{term "op * :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   337
@{term "op div :: nat \<Rightarrow> nat \<Rightarrow> nat"}&
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   338
@{term "op mod :: nat \<Rightarrow> nat \<Rightarrow> nat"}&
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   339
@{term "op dvd :: nat \<Rightarrow> nat \<Rightarrow> bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   340
@{term "op \<le> :: nat \<Rightarrow> nat \<Rightarrow> bool"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   341
@{term "op < :: nat \<Rightarrow> nat \<Rightarrow> bool"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   342
@{term "min :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   343
@{term "max :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   344
@{term "Min :: nat set \<Rightarrow> nat"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   345
@{term "Max :: nat set \<Rightarrow> nat"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   346
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   347
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   348
\begin{tabular}{@ {} l @ {~::~} l @ {}}
30988
b53800e3ee47 adjusted to changes in power syntax
haftmann
parents: 30457
diff changeset
   349
@{const Nat.of_nat} & @{typeof Nat.of_nat}\\
b53800e3ee47 adjusted to changes in power syntax
haftmann
parents: 30457
diff changeset
   350
@{term "op ^^ :: ('a \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a"} &
b53800e3ee47 adjusted to changes in power syntax
haftmann
parents: 30457
diff changeset
   351
  @{term_type_only "op ^^ :: ('a \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a" "('a \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a"}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   352
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   353
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   354
\section{Int}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   355
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   356
Type @{typ int}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   357
\bigskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   358
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   359
\begin{tabular}{@ {} llllllll @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   360
@{term "op + :: int \<Rightarrow> int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   361
@{term "op - :: int \<Rightarrow> int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   362
@{term "uminus :: int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   363
@{term "op * :: int \<Rightarrow> int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   364
@{term "op ^ :: int \<Rightarrow> nat \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   365
@{term "op div :: int \<Rightarrow> int \<Rightarrow> int"}&
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   366
@{term "op mod :: int \<Rightarrow> int \<Rightarrow> int"}&
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   367
@{term "op dvd :: int \<Rightarrow> int \<Rightarrow> bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   368
@{term "op \<le> :: int \<Rightarrow> int \<Rightarrow> bool"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   369
@{term "op < :: int \<Rightarrow> int \<Rightarrow> bool"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   370
@{term "min :: int \<Rightarrow> int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   371
@{term "max :: int \<Rightarrow> int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   372
@{term "Min :: int set \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   373
@{term "Max :: int set \<Rightarrow> int"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   374
@{term "abs :: int \<Rightarrow> int"} &
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   375
@{term "sgn :: int \<Rightarrow> int"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   376
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   377
30440
nipkow
parents: 30425
diff changeset
   378
\begin{tabular}{@ {} l @ {~::~} l l @ {}}
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   379
@{const Int.nat} & @{typeof Int.nat}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   380
@{const Int.of_int} & @{typeof Int.of_int}\\
30440
nipkow
parents: 30425
diff changeset
   381
@{const Int.Ints} & @{term_type_only Int.Ints "'a::ring_1 set"} & (\verb$Ints$)
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   382
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   383
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   384
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   385
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   386
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   387
@{term"of_nat::nat\<Rightarrow>int"} & @{term[source]"of_nat"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   388
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   389
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   390
30401
nipkow
parents: 30386
diff changeset
   391
\section{Finite\_Set}
nipkow
parents: 30386
diff changeset
   392
nipkow
parents: 30386
diff changeset
   393
nipkow
parents: 30386
diff changeset
   394
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
nipkow
parents: 30386
diff changeset
   395
@{const Finite_Set.finite} & @{term_type_only Finite_Set.finite "'a set\<Rightarrow>bool"}\\
nipkow
parents: 30386
diff changeset
   396
@{const Finite_Set.card} & @{term_type_only Finite_Set.card "'a set => nat"}\\
nipkow
parents: 30386
diff changeset
   397
@{const Finite_Set.fold} & @{term_type_only Finite_Set.fold "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> 'b \<Rightarrow> 'a set \<Rightarrow> 'b"}\\
nipkow
parents: 30386
diff changeset
   398
@{const Finite_Set.fold_image} & @{typ "('b \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'b \<Rightarrow> 'a set \<Rightarrow> 'b"}\\
nipkow
parents: 30386
diff changeset
   399
@{const Finite_Set.setsum} & @{term_type_only Finite_Set.setsum "('a => 'b) => 'a set => 'b::comm_monoid_add"}\\
nipkow
parents: 30386
diff changeset
   400
@{const Finite_Set.setprod} & @{term_type_only Finite_Set.setprod "('a => 'b) => 'a set => 'b::comm_monoid_mult"}\\
nipkow
parents: 30386
diff changeset
   401
\end{supertabular}
nipkow
parents: 30386
diff changeset
   402
nipkow
parents: 30386
diff changeset
   403
nipkow
parents: 30386
diff changeset
   404
\subsubsection*{Syntax}
nipkow
parents: 30386
diff changeset
   405
30440
nipkow
parents: 30425
diff changeset
   406
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
nipkow
parents: 30425
diff changeset
   407
@{term"setsum (%x. x) A"} & @{term[source]"setsum (\<lambda>x. x) A"} & (\verb$SUM$)\\
30401
nipkow
parents: 30386
diff changeset
   408
@{term"setsum (%x. t) A"} & @{term[source]"setsum (\<lambda>x. t) A"}\\
nipkow
parents: 30386
diff changeset
   409
@{term[source]"\<Sum>x|P. t"} & @{term"\<Sum>x|P. t"}\\
30440
nipkow
parents: 30425
diff changeset
   410
\multicolumn{2}{@ {}l@ {}}{Similarly for @{text"\<Prod>"} instead of @{text"\<Sum>"}} & (\verb$PROD$)\\
30401
nipkow
parents: 30386
diff changeset
   411
\end{supertabular}
nipkow
parents: 30386
diff changeset
   412
nipkow
parents: 30386
diff changeset
   413
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   414
\section{Wellfounded}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   415
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   416
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   417
@{const Wellfounded.wf} & @{term_type_only Wellfounded.wf "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   418
@{const Wellfounded.acyclic} & @{term_type_only Wellfounded.acyclic "('a*'a)set\<Rightarrow>bool"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   419
@{const Wellfounded.acc} & @{term_type_only Wellfounded.acc "('a*'a)set\<Rightarrow>'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   420
@{const Wellfounded.measure} & @{term_type_only Wellfounded.measure "('a\<Rightarrow>nat)\<Rightarrow>('a*'a)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   421
@{const Wellfounded.lex_prod} & @{term_type_only Wellfounded.lex_prod "('a*'a)set\<Rightarrow>('b*'b)set\<Rightarrow>(('a*'b)*('a*'b))set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   422
@{const Wellfounded.mlex_prod} & @{term_type_only Wellfounded.mlex_prod "('a\<Rightarrow>nat)\<Rightarrow>('a*'a)set\<Rightarrow>('a*'a)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   423
@{const Wellfounded.less_than} & @{term_type_only Wellfounded.less_than "(nat*nat)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   424
@{const Wellfounded.pred_nat} & @{term_type_only Wellfounded.pred_nat "(nat*nat)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   425
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   426
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   427
30384
2f24531b2d3e fixed typing of UN/INT syntax
nipkow
parents: 30372
diff changeset
   428
\section{SetInterval}
30321
nipkow
parents: 30293
diff changeset
   429
nipkow
parents: 30293
diff changeset
   430
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
30370
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   431
@{const lessThan} & @{term_type_only lessThan "'a::ord \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   432
@{const atMost} & @{term_type_only atMost "'a::ord \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   433
@{const greaterThan} & @{term_type_only greaterThan "'a::ord \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   434
@{const atLeast} & @{term_type_only atLeast "'a::ord \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   435
@{const greaterThanLessThan} & @{term_type_only greaterThanLessThan "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   436
@{const atLeastLessThan} & @{term_type_only atLeastLessThan "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   437
@{const greaterThanAtMost} & @{term_type_only greaterThanAtMost "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   438
@{const atLeastAtMost} & @{term_type_only atLeastAtMost "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
30321
nipkow
parents: 30293
diff changeset
   439
\end{supertabular}
nipkow
parents: 30293
diff changeset
   440
nipkow
parents: 30293
diff changeset
   441
\subsubsection*{Syntax}
nipkow
parents: 30293
diff changeset
   442
nipkow
parents: 30293
diff changeset
   443
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
nipkow
parents: 30293
diff changeset
   444
@{term "lessThan y"} & @{term[source] "lessThan y"}\\
nipkow
parents: 30293
diff changeset
   445
@{term "atMost y"} & @{term[source] "atMost y"}\\
nipkow
parents: 30293
diff changeset
   446
@{term "greaterThan x"} & @{term[source] "greaterThan x"}\\
nipkow
parents: 30293
diff changeset
   447
@{term "atLeast x"} & @{term[source] "atLeast x"}\\
nipkow
parents: 30293
diff changeset
   448
@{term "greaterThanLessThan x y"} & @{term[source] "greaterThanLessThan x y"}\\
nipkow
parents: 30293
diff changeset
   449
@{term "atLeastLessThan x y"} & @{term[source] "atLeastLessThan x y"}\\
nipkow
parents: 30293
diff changeset
   450
@{term "greaterThanAtMost x y"} & @{term[source] "greaterThanAtMost x y"}\\
nipkow
parents: 30293
diff changeset
   451
@{term "atLeastAtMost x y"} & @{term[source] "atLeastAtMost x y"}\\
30370
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   452
@{term[mode=xsymbols] "UN i:{..n}. A"} & @{term[source] "\<Union> i \<in> {..n}. A"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   453
@{term[mode=xsymbols] "UN i:{..<n}. A"} & @{term[source] "\<Union> i \<in> {..<n}. A"}\\
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   454
\multicolumn{2}{@ {}l@ {}}{Similarly for @{text"\<Inter>"} instead of @{text"\<Union>"}}\\
30321
nipkow
parents: 30293
diff changeset
   455
@{term "setsum (%x. t) {a..b}"} & @{term[source] "setsum (\<lambda>x. t) {a..b}"}\\
30370
79a7491ac1fd Docs updates
nipkow
parents: 30321
diff changeset
   456
@{term "setsum (%x. t) {a..<b}"} & @{term[source] "setsum (\<lambda>x. t) {a..<b}"}\\
30386
nipkow
parents: 30384
diff changeset
   457
@{term "setsum (%x. t) {..b}"} & @{term[source] "setsum (\<lambda>x. t) {..b}"}\\
nipkow
parents: 30384
diff changeset
   458
@{term "setsum (%x. t) {..<b}"} & @{term[source] "setsum (\<lambda>x. t) {..<b}"}\\
30372
96d508968153 UN syntax fix
nipkow
parents: 30370
diff changeset
   459
\multicolumn{2}{@ {}l@ {}}{Similarly for @{text"\<Prod>"} instead of @{text"\<Sum>"}}\\
30321
nipkow
parents: 30293
diff changeset
   460
\end{supertabular}
nipkow
parents: 30293
diff changeset
   461
nipkow
parents: 30293
diff changeset
   462
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   463
\section{Power}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   464
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   465
\begin{tabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   466
@{const Power.power} & @{typeof Power.power}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   467
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   468
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   469
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   470
\section{Option}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   471
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   472
@{datatype option}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   473
\bigskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   474
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   475
\begin{tabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   476
@{const Option.the} & @{typeof Option.the}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   477
@{const Option.map} & @{typ[source]"('a \<Rightarrow> 'b) \<Rightarrow> 'a option \<Rightarrow> 'b option"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   478
@{const Option.set} & @{term_type_only Option.set "'a option \<Rightarrow> 'a set"}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   479
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   480
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   481
\section{List}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   482
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   483
@{datatype list}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   484
\bigskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   485
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   486
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   487
@{const List.append} & @{typeof List.append}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   488
@{const List.butlast} & @{typeof List.butlast}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   489
@{const List.concat} & @{typeof List.concat}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   490
@{const List.distinct} & @{typeof List.distinct}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   491
@{const List.drop} & @{typeof List.drop}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   492
@{const List.dropWhile} & @{typeof List.dropWhile}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   493
@{const List.filter} & @{typeof List.filter}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   494
@{const List.foldl} & @{typeof List.foldl}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   495
@{const List.foldr} & @{typeof List.foldr}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   496
@{const List.hd} & @{typeof List.hd}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   497
@{const List.last} & @{typeof List.last}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   498
@{const List.length} & @{typeof List.length}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   499
@{const List.lenlex} & @{term_type_only List.lenlex "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   500
@{const List.lex} & @{term_type_only List.lex "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   501
@{const List.lexn} & @{term_type_only List.lexn "('a*'a)set\<Rightarrow>nat\<Rightarrow>('a list * 'a list)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   502
@{const List.lexord} & @{term_type_only List.lexord "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   503
@{const List.listrel} & @{term_type_only List.listrel "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   504
@{const List.lists} & @{term_type_only List.lists "'a set\<Rightarrow>'a list set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   505
@{const List.listset} & @{term_type_only List.listset "'a set list \<Rightarrow> 'a list set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   506
@{const List.listsum} & @{typeof List.listsum}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   507
@{const List.list_all2} & @{typeof List.list_all2}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   508
@{const List.list_update} & @{typeof List.list_update}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   509
@{const List.map} & @{typeof List.map}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   510
@{const List.measures} & @{term_type_only List.measures "('a\<Rightarrow>nat)list\<Rightarrow>('a*'a)set"}\\
32933
ba14400f7f34 added List.nth
nipkow
parents: 32885
diff changeset
   511
@{const List.nth} & @{typeof List.nth}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   512
@{const List.remdups} & @{typeof List.remdups}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   513
@{const List.removeAll} & @{typeof List.removeAll}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   514
@{const List.remove1} & @{typeof List.remove1}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   515
@{const List.replicate} & @{typeof List.replicate}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   516
@{const List.rev} & @{typeof List.rev}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   517
@{const List.rotate} & @{typeof List.rotate}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   518
@{const List.rotate1} & @{typeof List.rotate1}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   519
@{const List.set} & @{term_type_only List.set "'a list \<Rightarrow> 'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   520
@{const List.sort} & @{typeof List.sort}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   521
@{const List.sorted} & @{typeof List.sorted}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   522
@{const List.splice} & @{typeof List.splice}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   523
@{const List.sublist} & @{typeof List.sublist}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   524
@{const List.take} & @{typeof List.take}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   525
@{const List.takeWhile} & @{typeof List.takeWhile}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   526
@{const List.tl} & @{typeof List.tl}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   527
@{const List.upt} & @{typeof List.upt}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   528
@{const List.upto} & @{typeof List.upto}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   529
@{const List.zip} & @{typeof List.zip}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   530
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   531
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   532
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   533
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   534
\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   535
@{text"[x\<^isub>1,\<dots>,x\<^isub>n]"} & @{text"x\<^isub>1 # \<dots> # x\<^isub>n # []"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   536
@{term"[m..<n]"} & @{term[source]"upt m n"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   537
@{term"[i..j]"} & @{term[source]"upto i j"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   538
@{text"[e. x \<leftarrow> xs]"} & @{term"map (%x. e) xs"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   539
@{term"[x \<leftarrow> xs. b]"} & @{term[source]"filter (\<lambda>x. b) xs"} \\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   540
@{term"xs[n := x]"} & @{term[source]"list_update xs n x"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   541
@{term"\<Sum>x\<leftarrow>xs. e"} & @{term[source]"listsum (map (\<lambda>x. e) xs)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   542
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   543
\medskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   544
30440
nipkow
parents: 30425
diff changeset
   545
List comprehension: @{text"[e. q\<^isub>1, \<dots>, q\<^isub>n]"} where each
nipkow
parents: 30425
diff changeset
   546
qualifier @{text q\<^isub>i} is either a generator \mbox{@{text"pat \<leftarrow> e"}} or a
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   547
guard, i.e.\ boolean expression.
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   548
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   549
\section{Map}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   550
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   551
Maps model partial functions and are often used as finite tables. However,
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   552
the domain of a map may be infinite.
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   553
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   554
@{text"'a \<rightharpoonup> 'b  =  'a \<Rightarrow> 'b option"}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   555
\bigskip
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   556
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   557
\begin{supertabular}{@ {} l @ {~::~} l @ {}}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   558
@{const Map.empty} & @{typeof Map.empty}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   559
@{const Map.map_add} & @{typeof Map.map_add}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   560
@{const Map.map_comp} & @{typeof Map.map_comp}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   561
@{const Map.restrict_map} & @{term_type_only Map.restrict_map "('a\<Rightarrow>'b option)\<Rightarrow>'a set\<Rightarrow>('a\<Rightarrow>'b option)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   562
@{const Map.dom} & @{term_type_only Map.dom "('a\<Rightarrow>'b option)\<Rightarrow>'a set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   563
@{const Map.ran} & @{term_type_only Map.ran "('a\<Rightarrow>'b option)\<Rightarrow>'b set"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   564
@{const Map.map_le} & @{typeof Map.map_le}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   565
@{const Map.map_of} & @{typeof Map.map_of}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   566
@{const Map.map_upds} & @{typeof Map.map_upds}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   567
\end{supertabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   568
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   569
\subsubsection*{Syntax}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   570
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   571
\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
30403
nipkow
parents: 30402
diff changeset
   572
@{term"Map.empty"} & @{term"\<lambda>x. None"}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   573
@{term"m(x:=Some y)"} & @{term[source]"m(x:=Some y)"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   574
@{text"m(x\<^isub>1\<mapsto>y\<^isub>1,\<dots>,x\<^isub>n\<mapsto>y\<^isub>n)"} & @{text[source]"m(x\<^isub>1\<mapsto>y\<^isub>1)\<dots>(x\<^isub>n\<mapsto>y\<^isub>n)"}\\
30440
nipkow
parents: 30425
diff changeset
   575
@{text"[x\<^isub>1\<mapsto>y\<^isub>1,\<dots>,x\<^isub>n\<mapsto>y\<^isub>n]"} & @{text[source]"Map.empty(x\<^isub>1\<mapsto>y\<^isub>1,\<dots>,x\<^isub>n\<mapsto>y\<^isub>n)"}\\
30293
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   576
@{term"map_upds m xs ys"} & @{term[source]"map_upds m xs ys"}\\
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   577
\end{tabular}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   578
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   579
*}
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   580
(*<*)
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   581
end
cf57f2acb94c Added Docs
nipkow
parents:
diff changeset
   582
(*>*)