--- a/doc-src/Main/Docs/Main_Doc.thy Mon Aug 27 21:19:16 2012 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,596 +0,0 @@
-(*<*)
-theory Main_Doc
-imports Main
-begin
-
-setup {*
- let
- fun pretty_term_type_only ctxt (t, T) =
- (if fastype_of t = Sign.certify_typ (Proof_Context.theory_of ctxt) T then ()
- else error "term_type_only: type mismatch";
- Syntax.pretty_typ ctxt T)
- in
- Thy_Output.antiquotation @{binding term_type_only}
- (Args.term -- Args.typ_abbrev)
- (fn {source, context = ctxt, ...} => fn arg =>
- Thy_Output.output ctxt
- (Thy_Output.maybe_pretty_source pretty_term_type_only ctxt source [arg]))
- end
-*}
-setup {*
- Thy_Output.antiquotation @{binding expanded_typ} (Args.typ >> single)
- (fn {source, context, ...} => Thy_Output.output context o
- Thy_Output.maybe_pretty_source Syntax.pretty_typ context source)
-*}
-(*>*)
-text{*
-
-\begin{abstract}
-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/library/HOL/}.
-\end{abstract}
-
-\section{HOL}
-
-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"}.
-\smallskip
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const HOL.undefined} & @{typeof HOL.undefined}\\
-@{const HOL.default} & @{typeof HOL.default}\\
-\end{tabular}
-
-\subsubsection*{Syntax}
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-@{term"~(x = y)"} & @{term[source]"\<not> (x = y)"} & (\verb$~=$)\\
-@{term[source]"P \<longleftrightarrow> Q"} & @{term"P \<longleftrightarrow> Q"} \\
-@{term"If x y z"} & @{term[source]"If x y z"}\\
-@{term"Let e\<^isub>1 (%x. e\<^isub>2)"} & @{term[source]"Let e\<^isub>1 (\<lambda>x. e\<^isub>2)"}\\
-\end{supertabular}
-
-
-\section{Orderings}
-
-A collection of classes defining basic orderings:
-preorder, partial order, linear order, dense linear order and wellorder.
-\smallskip
-
-\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-@{const Orderings.less_eq} & @{typeof Orderings.less_eq} & (\verb$<=$)\\
-@{const Orderings.less} & @{typeof Orderings.less}\\
-@{const Orderings.Least} & @{typeof Orderings.Least}\\
-@{const Orderings.min} & @{typeof Orderings.min}\\
-@{const Orderings.max} & @{typeof Orderings.max}\\
-@{const[source] top} & @{typeof Orderings.top}\\
-@{const[source] bot} & @{typeof Orderings.bot}\\
-@{const Orderings.mono} & @{typeof Orderings.mono}\\
-@{const Orderings.strict_mono} & @{typeof Orderings.strict_mono}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-@{term[source]"x \<ge> y"} & @{term"x \<ge> y"} & (\verb$>=$)\\
-@{term[source]"x > y"} & @{term"x > y"}\\
-@{term"ALL x<=y. P"} & @{term[source]"\<forall>x. x \<le> y \<longrightarrow> P"}\\
-@{term"EX x<=y. P"} & @{term[source]"\<exists>x. x \<le> y \<and> P"}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for $<$, $\ge$ and $>$}\\
-@{term"LEAST x. P"} & @{term[source]"Least (\<lambda>x. P)"}\\
-\end{supertabular}
-
-
-\section{Lattices}
-
-Classes semilattice, lattice, distributive lattice and complete lattice (the
-latter in theory @{theory Set}).
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Lattices.inf} & @{typeof Lattices.inf}\\
-@{const Lattices.sup} & @{typeof Lattices.sup}\\
-@{const Complete_Lattices.Inf} & @{term_type_only Complete_Lattices.Inf "'a set \<Rightarrow> 'a::Inf"}\\
-@{const Complete_Lattices.Sup} & @{term_type_only Complete_Lattices.Sup "'a set \<Rightarrow> 'a::Sup"}\\
-\end{tabular}
-
-\subsubsection*{Syntax}
-
-Available by loading theory @{text Lattice_Syntax} in directory @{text
-Library}.
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{text[source]"x \<sqsubseteq> y"} & @{term"x \<le> y"}\\
-@{text[source]"x \<sqsubset> y"} & @{term"x < y"}\\
-@{text[source]"x \<sqinter> y"} & @{term"inf x y"}\\
-@{text[source]"x \<squnion> y"} & @{term"sup x y"}\\
-@{text[source]"\<Sqinter> A"} & @{term"Sup A"}\\
-@{text[source]"\<Squnion> A"} & @{term"Inf A"}\\
-@{text[source]"\<top>"} & @{term[source] top}\\
-@{text[source]"\<bottom>"} & @{term[source] bot}\\
-\end{supertabular}
-
-
-\section{Set}
-
-%Sets are predicates: @{text[source]"'a set = 'a \<Rightarrow> bool"}
-%\bigskip
-
-\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-@{const Set.empty} & @{term_type_only "Set.empty" "'a set"}\\
-@{const Set.insert} & @{term_type_only insert "'a\<Rightarrow>'a set\<Rightarrow>'a set"}\\
-@{const Collect} & @{term_type_only Collect "('a\<Rightarrow>bool)\<Rightarrow>'a set"}\\
-@{const Set.member} & @{term_type_only Set.member "'a\<Rightarrow>'a set\<Rightarrow>bool"} & (\texttt{:})\\
-@{const Set.union} & @{term_type_only Set.union "'a set\<Rightarrow>'a set \<Rightarrow> 'a set"} & (\texttt{Un})\\
-@{const Set.inter} & @{term_type_only Set.inter "'a set\<Rightarrow>'a set \<Rightarrow> 'a set"} & (\texttt{Int})\\
-@{const UNION} & @{term_type_only UNION "'a set\<Rightarrow>('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"}\\
-@{const INTER} & @{term_type_only INTER "'a set\<Rightarrow>('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"}\\
-@{const Union} & @{term_type_only Union "'a set set\<Rightarrow>'a set"}\\
-@{const Inter} & @{term_type_only Inter "'a set set\<Rightarrow>'a set"}\\
-@{const Pow} & @{term_type_only Pow "'a set \<Rightarrow>'a set set"}\\
-@{const UNIV} & @{term_type_only UNIV "'a set"}\\
-@{const image} & @{term_type_only image "('a\<Rightarrow>'b)\<Rightarrow>'a set\<Rightarrow>'b set"}\\
-@{const Ball} & @{term_type_only Ball "'a set\<Rightarrow>('a\<Rightarrow>bool)\<Rightarrow>bool"}\\
-@{const Bex} & @{term_type_only Bex "'a set\<Rightarrow>('a\<Rightarrow>bool)\<Rightarrow>bool"}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-@{text"{x\<^isub>1,\<dots>,x\<^isub>n}"} & @{text"insert x\<^isub>1 (\<dots> (insert x\<^isub>n {})\<dots>)"}\\
-@{term"x ~: A"} & @{term[source]"\<not>(x \<in> A)"}\\
-@{term"A \<subseteq> B"} & @{term[source]"A \<le> B"}\\
-@{term"A \<subset> B"} & @{term[source]"A < B"}\\
-@{term[source]"A \<supseteq> B"} & @{term[source]"B \<le> A"}\\
-@{term[source]"A \<supset> B"} & @{term[source]"B < A"}\\
-@{term"{x. P}"} & @{term[source]"Collect (\<lambda>x. P)"}\\
-@{term[mode=xsymbols]"UN x:I. A"} & @{term[source]"UNION I (\<lambda>x. A)"} & (\texttt{UN})\\
-@{term[mode=xsymbols]"UN x. A"} & @{term[source]"UNION UNIV (\<lambda>x. A)"}\\
-@{term[mode=xsymbols]"INT x:I. A"} & @{term[source]"INTER I (\<lambda>x. A)"} & (\texttt{INT})\\
-@{term[mode=xsymbols]"INT x. A"} & @{term[source]"INTER UNIV (\<lambda>x. A)"}\\
-@{term"ALL x:A. P"} & @{term[source]"Ball A (\<lambda>x. P)"}\\
-@{term"EX x:A. P"} & @{term[source]"Bex A (\<lambda>x. P)"}\\
-@{term"range f"} & @{term[source]"f ` UNIV"}\\
-\end{supertabular}
-
-
-\section{Fun}
-
-\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-@{const "Fun.id"} & @{typeof Fun.id}\\
-@{const "Fun.comp"} & @{typeof Fun.comp} & (\texttt{o})\\
-@{const "Fun.inj_on"} & @{term_type_only Fun.inj_on "('a\<Rightarrow>'b)\<Rightarrow>'a set\<Rightarrow>bool"}\\
-@{const "Fun.inj"} & @{typeof Fun.inj}\\
-@{const "Fun.surj"} & @{typeof Fun.surj}\\
-@{const "Fun.bij"} & @{typeof Fun.bij}\\
-@{const "Fun.bij_betw"} & @{term_type_only Fun.bij_betw "('a\<Rightarrow>'b)\<Rightarrow>'a set\<Rightarrow>'b set\<Rightarrow>bool"}\\
-@{const "Fun.fun_upd"} & @{typeof Fun.fun_upd}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term"fun_upd f x y"} & @{term[source]"fun_upd f x y"}\\
-@{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)"}\\
-\end{tabular}
-
-
-\section{Hilbert\_Choice}
-
-Hilbert's selection ($\varepsilon$) operator: @{term"SOME x. P"}.
-\smallskip
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Hilbert_Choice.inv_into} & @{term_type_only Hilbert_Choice.inv_into "'a set \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> ('b \<Rightarrow> 'a)"}
-\end{tabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term inv} & @{term[source]"inv_into UNIV"}
-\end{tabular}
-
-\section{Fixed Points}
-
-Theory: @{theory Inductive}.
-
-Least and greatest fixed points in a complete lattice @{typ 'a}:
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Inductive.lfp} & @{typeof Inductive.lfp}\\
-@{const Inductive.gfp} & @{typeof Inductive.gfp}\\
-\end{tabular}
-
-Note that in particular sets (@{typ"'a \<Rightarrow> bool"}) are complete lattices.
-
-\section{Sum\_Type}
-
-Type constructor @{text"+"}.
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Sum_Type.Inl} & @{typeof Sum_Type.Inl}\\
-@{const Sum_Type.Inr} & @{typeof Sum_Type.Inr}\\
-@{const Sum_Type.Plus} & @{term_type_only Sum_Type.Plus "'a set\<Rightarrow>'b set\<Rightarrow>('a+'b)set"}
-\end{tabular}
-
-
-\section{Product\_Type}
-
-Types @{typ unit} and @{text"\<times>"}.
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const Product_Type.Unity} & @{typeof Product_Type.Unity}\\
-@{const Pair} & @{typeof Pair}\\
-@{const fst} & @{typeof fst}\\
-@{const snd} & @{typeof snd}\\
-@{const split} & @{typeof split}\\
-@{const curry} & @{typeof curry}\\
-@{const Product_Type.Sigma} & @{term_type_only Product_Type.Sigma "'a set\<Rightarrow>('a\<Rightarrow>'b set)\<Rightarrow>('a*'b)set"}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} ll @ {}}
-@{term"Pair a b"} & @{term[source]"Pair a b"}\\
-@{term"split (\<lambda>x y. t)"} & @{term[source]"split (\<lambda>x y. t)"}\\
-@{term"A <*> B"} & @{text"Sigma A (\<lambda>\<^raw:\_>. B)"} & (\verb$<*>$)
-\end{tabular}
-
-Pairs may be nested. Nesting to the right is printed as a tuple,
-e.g.\ \mbox{@{term"(a,b,c)"}} is really \mbox{@{text"(a, (b, c))"}.}
-Pattern matching with pairs and tuples extends to all binders,
-e.g.\ \mbox{@{prop"ALL (x,y):A. P"},} @{term"{(x,y). P}"}, etc.
-
-
-\section{Relation}
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Relation.converse} & @{term_type_only Relation.converse "('a * 'b)set \<Rightarrow> ('b*'a)set"}\\
-@{const Relation.relcomp} & @{term_type_only Relation.relcomp "('a*'b)set\<Rightarrow>('b*'c)set\<Rightarrow>('a*'c)set"}\\
-@{const Relation.Image} & @{term_type_only Relation.Image "('a*'b)set\<Rightarrow>'a set\<Rightarrow>'b set"}\\
-@{const Relation.inv_image} & @{term_type_only Relation.inv_image "('a*'a)set\<Rightarrow>('b\<Rightarrow>'a)\<Rightarrow>('b*'b)set"}\\
-@{const Relation.Id_on} & @{term_type_only Relation.Id_on "'a set\<Rightarrow>('a*'a)set"}\\
-@{const Relation.Id} & @{term_type_only Relation.Id "('a*'a)set"}\\
-@{const Relation.Domain} & @{term_type_only Relation.Domain "('a*'b)set\<Rightarrow>'a set"}\\
-@{const Relation.Range} & @{term_type_only Relation.Range "('a*'b)set\<Rightarrow>'b set"}\\
-@{const Relation.Field} & @{term_type_only Relation.Field "('a*'a)set\<Rightarrow>'a set"}\\
-@{const Relation.refl_on} & @{term_type_only Relation.refl_on "'a set\<Rightarrow>('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.refl} & @{term_type_only Relation.refl "('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.sym} & @{term_type_only Relation.sym "('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.antisym} & @{term_type_only Relation.antisym "('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.trans} & @{term_type_only Relation.trans "('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.irrefl} & @{term_type_only Relation.irrefl "('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.total_on} & @{term_type_only Relation.total_on "'a set\<Rightarrow>('a*'a)set\<Rightarrow>bool"}\\
-@{const Relation.total} & @{term_type_only Relation.total "('a*'a)set\<Rightarrow>bool"}\\
-\end{tabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-@{term"converse r"} & @{term[source]"converse r"} & (\verb$^-1$)
-\end{tabular}
-\medskip
-
-\noindent
-Type synonym \ @{typ"'a rel"} @{text"="} @{expanded_typ "'a rel"}
-
-\section{Equiv\_Relations}
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const Equiv_Relations.equiv} & @{term_type_only Equiv_Relations.equiv "'a set \<Rightarrow> ('a*'a)set\<Rightarrow>bool"}\\
-@{const Equiv_Relations.quotient} & @{term_type_only Equiv_Relations.quotient "'a set \<Rightarrow> ('a \<times> 'a) set \<Rightarrow> 'a set set"}\\
-@{const Equiv_Relations.congruent} & @{term_type_only Equiv_Relations.congruent "('a*'a)set\<Rightarrow>('a\<Rightarrow>'b)\<Rightarrow>bool"}\\
-@{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"}\\
-%@ {const Equiv_Relations.} & @ {term_type_only Equiv_Relations. ""}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term"congruent r f"} & @{term[source]"congruent r f"}\\
-@{term"congruent2 r r f"} & @{term[source]"congruent2 r r f"}\\
-\end{tabular}
-
-
-\section{Transitive\_Closure}
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Transitive_Closure.rtrancl} & @{term_type_only Transitive_Closure.rtrancl "('a*'a)set\<Rightarrow>('a*'a)set"}\\
-@{const Transitive_Closure.trancl} & @{term_type_only Transitive_Closure.trancl "('a*'a)set\<Rightarrow>('a*'a)set"}\\
-@{const Transitive_Closure.reflcl} & @{term_type_only Transitive_Closure.reflcl "('a*'a)set\<Rightarrow>('a*'a)set"}\\
-@{const Transitive_Closure.acyclic} & @{term_type_only Transitive_Closure.acyclic "('a*'a)set\<Rightarrow>bool"}\\
-@{const compower} & @{term_type_only "op ^^ :: ('a*'a)set\<Rightarrow>nat\<Rightarrow>('a*'a)set" "('a*'a)set\<Rightarrow>nat\<Rightarrow>('a*'a)set"}\\
-\end{tabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-@{term"rtrancl r"} & @{term[source]"rtrancl r"} & (\verb$^*$)\\
-@{term"trancl r"} & @{term[source]"trancl r"} & (\verb$^+$)\\
-@{term"reflcl r"} & @{term[source]"reflcl r"} & (\verb$^=$)
-\end{tabular}
-
-
-\section{Algebra}
-
-Theories @{theory Groups}, @{theory Rings}, @{theory Fields} and @{theory
-Divides} define a large collection of classes describing common algebraic
-structures from semigroups up to fields. Everything is done in terms of
-overloaded operators:
-
-\begin{supertabular}{@ {} l @ {~::~} l l @ {}}
-@{text "0"} & @{typeof zero}\\
-@{text "1"} & @{typeof one}\\
-@{const plus} & @{typeof plus}\\
-@{const minus} & @{typeof minus}\\
-@{const uminus} & @{typeof uminus} & (\verb$-$)\\
-@{const times} & @{typeof times}\\
-@{const inverse} & @{typeof inverse}\\
-@{const divide} & @{typeof divide}\\
-@{const abs} & @{typeof abs}\\
-@{const sgn} & @{typeof sgn}\\
-@{const dvd_class.dvd} & @{typeof "dvd_class.dvd"}\\
-@{const div_class.div} & @{typeof "div_class.div"}\\
-@{const div_class.mod} & @{typeof "div_class.mod"}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term"abs x"} & @{term[source]"abs x"}
-\end{tabular}
-
-
-\section{Nat}
-
-@{datatype nat}
-\bigskip
-
-\begin{tabular}{@ {} lllllll @ {}}
-@{term "op + :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
-@{term "op - :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
-@{term "op * :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
-@{term "op ^ :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
-@{term "op div :: nat \<Rightarrow> nat \<Rightarrow> nat"}&
-@{term "op mod :: nat \<Rightarrow> nat \<Rightarrow> nat"}&
-@{term "op dvd :: nat \<Rightarrow> nat \<Rightarrow> bool"}\\
-@{term "op \<le> :: nat \<Rightarrow> nat \<Rightarrow> bool"} &
-@{term "op < :: nat \<Rightarrow> nat \<Rightarrow> bool"} &
-@{term "min :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
-@{term "max :: nat \<Rightarrow> nat \<Rightarrow> nat"} &
-@{term "Min :: nat set \<Rightarrow> nat"} &
-@{term "Max :: nat set \<Rightarrow> nat"}\\
-\end{tabular}
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Nat.of_nat} & @{typeof Nat.of_nat}\\
-@{term "op ^^ :: ('a \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a"} &
- @{term_type_only "op ^^ :: ('a \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a" "('a \<Rightarrow> 'a) \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a"}
-\end{tabular}
-
-\section{Int}
-
-Type @{typ int}
-\bigskip
-
-\begin{tabular}{@ {} llllllll @ {}}
-@{term "op + :: int \<Rightarrow> int \<Rightarrow> int"} &
-@{term "op - :: int \<Rightarrow> int \<Rightarrow> int"} &
-@{term "uminus :: int \<Rightarrow> int"} &
-@{term "op * :: int \<Rightarrow> int \<Rightarrow> int"} &
-@{term "op ^ :: int \<Rightarrow> nat \<Rightarrow> int"} &
-@{term "op div :: int \<Rightarrow> int \<Rightarrow> int"}&
-@{term "op mod :: int \<Rightarrow> int \<Rightarrow> int"}&
-@{term "op dvd :: int \<Rightarrow> int \<Rightarrow> bool"}\\
-@{term "op \<le> :: int \<Rightarrow> int \<Rightarrow> bool"} &
-@{term "op < :: int \<Rightarrow> int \<Rightarrow> bool"} &
-@{term "min :: int \<Rightarrow> int \<Rightarrow> int"} &
-@{term "max :: int \<Rightarrow> int \<Rightarrow> int"} &
-@{term "Min :: int set \<Rightarrow> int"} &
-@{term "Max :: int set \<Rightarrow> int"}\\
-@{term "abs :: int \<Rightarrow> int"} &
-@{term "sgn :: int \<Rightarrow> int"}\\
-\end{tabular}
-
-\begin{tabular}{@ {} l @ {~::~} l l @ {}}
-@{const Int.nat} & @{typeof Int.nat}\\
-@{const Int.of_int} & @{typeof Int.of_int}\\
-@{const Int.Ints} & @{term_type_only Int.Ints "'a::ring_1 set"} & (\verb$Ints$)
-\end{tabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term"of_nat::nat\<Rightarrow>int"} & @{term[source]"of_nat"}\\
-\end{tabular}
-
-
-\section{Finite\_Set}
-
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const Finite_Set.finite} & @{term_type_only Finite_Set.finite "'a set\<Rightarrow>bool"}\\
-@{const Finite_Set.card} & @{term_type_only Finite_Set.card "'a set => nat"}\\
-@{const Finite_Set.fold} & @{term_type_only Finite_Set.fold "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> 'b \<Rightarrow> 'a set \<Rightarrow> 'b"}\\
-@{const Finite_Set.fold_image} & @{typ "('b \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'b \<Rightarrow> 'a set \<Rightarrow> 'b"}\\
-@{const Big_Operators.setsum} & @{term_type_only Big_Operators.setsum "('a => 'b) => 'a set => 'b::comm_monoid_add"}\\
-@{const Big_Operators.setprod} & @{term_type_only Big_Operators.setprod "('a => 'b) => 'a set => 'b::comm_monoid_mult"}\\
-\end{supertabular}
-
-
-\subsubsection*{Syntax}
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l l @ {}}
-@{term"setsum (%x. x) A"} & @{term[source]"setsum (\<lambda>x. x) A"} & (\verb$SUM$)\\
-@{term"setsum (%x. t) A"} & @{term[source]"setsum (\<lambda>x. t) A"}\\
-@{term[source]"\<Sum>x|P. t"} & @{term"\<Sum>x|P. t"}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for @{text"\<Prod>"} instead of @{text"\<Sum>"}} & (\verb$PROD$)\\
-\end{supertabular}
-
-
-\section{Wellfounded}
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const Wellfounded.wf} & @{term_type_only Wellfounded.wf "('a*'a)set\<Rightarrow>bool"}\\
-@{const Wellfounded.acc} & @{term_type_only Wellfounded.acc "('a*'a)set\<Rightarrow>'a set"}\\
-@{const Wellfounded.measure} & @{term_type_only Wellfounded.measure "('a\<Rightarrow>nat)\<Rightarrow>('a*'a)set"}\\
-@{const Wellfounded.lex_prod} & @{term_type_only Wellfounded.lex_prod "('a*'a)set\<Rightarrow>('b*'b)set\<Rightarrow>(('a*'b)*('a*'b))set"}\\
-@{const Wellfounded.mlex_prod} & @{term_type_only Wellfounded.mlex_prod "('a\<Rightarrow>nat)\<Rightarrow>('a*'a)set\<Rightarrow>('a*'a)set"}\\
-@{const Wellfounded.less_than} & @{term_type_only Wellfounded.less_than "(nat*nat)set"}\\
-@{const Wellfounded.pred_nat} & @{term_type_only Wellfounded.pred_nat "(nat*nat)set"}\\
-\end{supertabular}
-
-
-\section{SetInterval}
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const lessThan} & @{term_type_only lessThan "'a::ord \<Rightarrow> 'a set"}\\
-@{const atMost} & @{term_type_only atMost "'a::ord \<Rightarrow> 'a set"}\\
-@{const greaterThan} & @{term_type_only greaterThan "'a::ord \<Rightarrow> 'a set"}\\
-@{const atLeast} & @{term_type_only atLeast "'a::ord \<Rightarrow> 'a set"}\\
-@{const greaterThanLessThan} & @{term_type_only greaterThanLessThan "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
-@{const atLeastLessThan} & @{term_type_only atLeastLessThan "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
-@{const greaterThanAtMost} & @{term_type_only greaterThanAtMost "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
-@{const atLeastAtMost} & @{term_type_only atLeastAtMost "'a::ord \<Rightarrow> 'a \<Rightarrow> 'a set"}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term "lessThan y"} & @{term[source] "lessThan y"}\\
-@{term "atMost y"} & @{term[source] "atMost y"}\\
-@{term "greaterThan x"} & @{term[source] "greaterThan x"}\\
-@{term "atLeast x"} & @{term[source] "atLeast x"}\\
-@{term "greaterThanLessThan x y"} & @{term[source] "greaterThanLessThan x y"}\\
-@{term "atLeastLessThan x y"} & @{term[source] "atLeastLessThan x y"}\\
-@{term "greaterThanAtMost x y"} & @{term[source] "greaterThanAtMost x y"}\\
-@{term "atLeastAtMost x y"} & @{term[source] "atLeastAtMost x y"}\\
-@{term[mode=xsymbols] "UN i:{..n}. A"} & @{term[source] "\<Union> i \<in> {..n}. A"}\\
-@{term[mode=xsymbols] "UN i:{..<n}. A"} & @{term[source] "\<Union> i \<in> {..<n}. A"}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for @{text"\<Inter>"} instead of @{text"\<Union>"}}\\
-@{term "setsum (%x. t) {a..b}"} & @{term[source] "setsum (\<lambda>x. t) {a..b}"}\\
-@{term "setsum (%x. t) {a..<b}"} & @{term[source] "setsum (\<lambda>x. t) {a..<b}"}\\
-@{term "setsum (%x. t) {..b}"} & @{term[source] "setsum (\<lambda>x. t) {..b}"}\\
-@{term "setsum (%x. t) {..<b}"} & @{term[source] "setsum (\<lambda>x. t) {..<b}"}\\
-\multicolumn{2}{@ {}l@ {}}{Similarly for @{text"\<Prod>"} instead of @{text"\<Sum>"}}\\
-\end{supertabular}
-
-
-\section{Power}
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Power.power} & @{typeof Power.power}
-\end{tabular}
-
-
-\section{Option}
-
-@{datatype option}
-\bigskip
-
-\begin{tabular}{@ {} l @ {~::~} l @ {}}
-@{const Option.the} & @{typeof Option.the}\\
-@{const Option.map} & @{typ[source]"('a \<Rightarrow> 'b) \<Rightarrow> 'a option \<Rightarrow> 'b option"}\\
-@{const Option.set} & @{term_type_only Option.set "'a option \<Rightarrow> 'a set"}\\
-@{const Option.bind} & @{term_type_only Option.bind "'a option \<Rightarrow> ('a \<Rightarrow> 'b option) \<Rightarrow> 'b option"}
-\end{tabular}
-
-\section{List}
-
-@{datatype list}
-\bigskip
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const List.append} & @{typeof List.append}\\
-@{const List.butlast} & @{typeof List.butlast}\\
-@{const List.concat} & @{typeof List.concat}\\
-@{const List.distinct} & @{typeof List.distinct}\\
-@{const List.drop} & @{typeof List.drop}\\
-@{const List.dropWhile} & @{typeof List.dropWhile}\\
-@{const List.filter} & @{typeof List.filter}\\
-@{const List.find} & @{typeof List.find}\\
-@{const List.fold} & @{typeof List.fold}\\
-@{const List.foldr} & @{typeof List.foldr}\\
-@{const List.foldl} & @{typeof List.foldl}\\
-@{const List.hd} & @{typeof List.hd}\\
-@{const List.last} & @{typeof List.last}\\
-@{const List.length} & @{typeof List.length}\\
-@{const List.lenlex} & @{term_type_only List.lenlex "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
-@{const List.lex} & @{term_type_only List.lex "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
-@{const List.lexn} & @{term_type_only List.lexn "('a*'a)set\<Rightarrow>nat\<Rightarrow>('a list * 'a list)set"}\\
-@{const List.lexord} & @{term_type_only List.lexord "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
-@{const List.listrel} & @{term_type_only List.listrel "('a*'b)set\<Rightarrow>('a list * 'b list)set"}\\
-@{const List.listrel1} & @{term_type_only List.listrel1 "('a*'a)set\<Rightarrow>('a list * 'a list)set"}\\
-@{const List.lists} & @{term_type_only List.lists "'a set\<Rightarrow>'a list set"}\\
-@{const List.listset} & @{term_type_only List.listset "'a set list \<Rightarrow> 'a list set"}\\
-@{const List.listsum} & @{typeof List.listsum}\\
-@{const List.list_all2} & @{typeof List.list_all2}\\
-@{const List.list_update} & @{typeof List.list_update}\\
-@{const List.map} & @{typeof List.map}\\
-@{const List.measures} & @{term_type_only List.measures "('a\<Rightarrow>nat)list\<Rightarrow>('a*'a)set"}\\
-@{const List.nth} & @{typeof List.nth}\\
-@{const List.remdups} & @{typeof List.remdups}\\
-@{const List.removeAll} & @{typeof List.removeAll}\\
-@{const List.remove1} & @{typeof List.remove1}\\
-@{const List.replicate} & @{typeof List.replicate}\\
-@{const List.rev} & @{typeof List.rev}\\
-@{const List.rotate} & @{typeof List.rotate}\\
-@{const List.rotate1} & @{typeof List.rotate1}\\
-@{const List.set} & @{term_type_only List.set "'a list \<Rightarrow> 'a set"}\\
-@{const List.sort} & @{typeof List.sort}\\
-@{const List.sorted} & @{typeof List.sorted}\\
-@{const List.splice} & @{typeof List.splice}\\
-@{const List.sublist} & @{typeof List.sublist}\\
-@{const List.take} & @{typeof List.take}\\
-@{const List.takeWhile} & @{typeof List.takeWhile}\\
-@{const List.tl} & @{typeof List.tl}\\
-@{const List.upt} & @{typeof List.upt}\\
-@{const List.upto} & @{typeof List.upto}\\
-@{const List.zip} & @{typeof List.zip}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{supertabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{text"[x\<^isub>1,\<dots>,x\<^isub>n]"} & @{text"x\<^isub>1 # \<dots> # x\<^isub>n # []"}\\
-@{term"[m..<n]"} & @{term[source]"upt m n"}\\
-@{term"[i..j]"} & @{term[source]"upto i j"}\\
-@{text"[e. x \<leftarrow> xs]"} & @{term"map (%x. e) xs"}\\
-@{term"[x \<leftarrow> xs. b]"} & @{term[source]"filter (\<lambda>x. b) xs"} \\
-@{term"xs[n := x]"} & @{term[source]"list_update xs n x"}\\
-@{term"\<Sum>x\<leftarrow>xs. e"} & @{term[source]"listsum (map (\<lambda>x. e) xs)"}\\
-\end{supertabular}
-\medskip
-
-List comprehension: @{text"[e. q\<^isub>1, \<dots>, q\<^isub>n]"} where each
-qualifier @{text q\<^isub>i} is either a generator \mbox{@{text"pat \<leftarrow> e"}} or a
-guard, i.e.\ boolean expression.
-
-\section{Map}
-
-Maps model partial functions and are often used as finite tables. However,
-the domain of a map may be infinite.
-
-\begin{supertabular}{@ {} l @ {~::~} l @ {}}
-@{const Map.empty} & @{typeof Map.empty}\\
-@{const Map.map_add} & @{typeof Map.map_add}\\
-@{const Map.map_comp} & @{typeof Map.map_comp}\\
-@{const Map.restrict_map} & @{term_type_only Map.restrict_map "('a\<Rightarrow>'b option)\<Rightarrow>'a set\<Rightarrow>('a\<Rightarrow>'b option)"}\\
-@{const Map.dom} & @{term_type_only Map.dom "('a\<Rightarrow>'b option)\<Rightarrow>'a set"}\\
-@{const Map.ran} & @{term_type_only Map.ran "('a\<Rightarrow>'b option)\<Rightarrow>'b set"}\\
-@{const Map.map_le} & @{typeof Map.map_le}\\
-@{const Map.map_of} & @{typeof Map.map_of}\\
-@{const Map.map_upds} & @{typeof Map.map_upds}\\
-\end{supertabular}
-
-\subsubsection*{Syntax}
-
-\begin{tabular}{@ {} l @ {\quad$\equiv$\quad} l @ {}}
-@{term"Map.empty"} & @{term"\<lambda>x. None"}\\
-@{term"m(x:=Some y)"} & @{term[source]"m(x:=Some y)"}\\
-@{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)"}\\
-@{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)"}\\
-@{term"map_upds m xs ys"} & @{term[source]"map_upds m xs ys"}\\
-\end{tabular}
-
-*}
-(*<*)
-end
-(*>*)
\ No newline at end of file