src/Doc/Main/Main_Doc.thy
changeset 68484 59793df7f853
parent 68364 5c579bb9adb1
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68483:087d32a40129 68484:59793df7f853
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    78 \section*{Lattices}
    78 \section*{Lattices}
    79 
    79 
    80 Classes semilattice, lattice, distributive lattice and complete lattice (the
    80 Classes semilattice, lattice, distributive lattice and complete lattice (the
    81 latter in theory @{theory Set}).
    81 latter in theory @{theory HOL.Set}).
    82 
    82 
    83 \begin{tabular}{@ {} l @ {~::~} l @ {}}
    83 \begin{tabular}{@ {} l @ {~::~} l @ {}}
    84 @{const Lattices.inf} & @{typeof Lattices.inf}\\
    84 @{const Lattices.inf} & @{typeof Lattices.inf}\\
    85 @{const Lattices.sup} & @{typeof Lattices.sup}\\
    85 @{const Lattices.sup} & @{typeof Lattices.sup}\\
    86 @{const Complete_Lattices.Inf} & @{term_type_only Complete_Lattices.Inf "'a set \<Rightarrow> 'a::Inf"}\\
    86 @{const Complete_Lattices.Inf} & @{term_type_only Complete_Lattices.Inf "'a set \<Rightarrow> 'a::Inf"}\\
   180 @{term inv} & @{term[source]"inv_into UNIV"}
   180 @{term inv} & @{term[source]"inv_into UNIV"}
   181 \end{tabular}
   181 \end{tabular}
   182 
   182 
   183 \section*{Fixed Points}
   183 \section*{Fixed Points}
   184 
   184 
   185 Theory: @{theory Inductive}.
   185 Theory: @{theory HOL.Inductive}.
   186 
   186 
   187 Least and greatest fixed points in a complete lattice @{typ 'a}:
   187 Least and greatest fixed points in a complete lattice @{typ 'a}:
   188 
   188 
   189 \begin{tabular}{@ {} l @ {~::~} l @ {}}
   189 \begin{tabular}{@ {} l @ {~::~} l @ {}}
   190 @{const Inductive.lfp} & @{typeof Inductive.lfp}\\
   190 @{const Inductive.lfp} & @{typeof Inductive.lfp}\\
   301 \end{tabular}
   301 \end{tabular}
   302 
   302 
   303 
   303 
   304 \section*{Algebra}
   304 \section*{Algebra}
   305 
   305 
   306 Theories @{theory Groups}, @{theory Rings}, @{theory Fields} and @{theory
   306 Theories @{theory HOL.Groups}, @{theory HOL.Rings}, @{theory HOL.Fields} and @{theory
   307 Divides} define a large collection of classes describing common algebraic
   307 HOL.Divides} define a large collection of classes describing common algebraic
   308 structures from semigroups up to fields. Everything is done in terms of
   308 structures from semigroups up to fields. Everything is done in terms of
   309 overloaded operators:
   309 overloaded operators:
   310 
   310 
   311 \begin{supertabular}{@ {} l @ {~::~} l l @ {}}
   311 \begin{supertabular}{@ {} l @ {~::~} l l @ {}}
   312 \<open>0\<close> & @{typeof zero}\\
   312 \<open>0\<close> & @{typeof zero}\\
   452 @{const Wellfounded.less_than} & @{term_type_only Wellfounded.less_than "(nat*nat)set"}\\
   452 @{const Wellfounded.less_than} & @{term_type_only Wellfounded.less_than "(nat*nat)set"}\\
   453 @{const Wellfounded.pred_nat} & @{term_type_only Wellfounded.pred_nat "(nat*nat)set"}\\
   453 @{const Wellfounded.pred_nat} & @{term_type_only Wellfounded.pred_nat "(nat*nat)set"}\\
   454 \end{supertabular}
   454 \end{supertabular}
   455 
   455 
   456 
   456 
   457 \section*{Set\_Interval} % @{theory Set_Interval}
   457 \section*{Set\_Interval} % @{theory HOL.Set_Interval}
   458 
   458 
   459 \begin{supertabular}{@ {} l @ {~::~} l @ {}}
   459 \begin{supertabular}{@ {} l @ {~::~} l @ {}}
   460 @{const lessThan} & @{term_type_only lessThan "'a::ord \<Rightarrow> 'a set"}\\
   460 @{const lessThan} & @{term_type_only lessThan "'a::ord \<Rightarrow> 'a set"}\\
   461 @{const atMost} & @{term_type_only atMost "'a::ord \<Rightarrow> 'a set"}\\
   461 @{const atMost} & @{term_type_only atMost "'a::ord \<Rightarrow> 'a set"}\\
   462 @{const greaterThan} & @{term_type_only greaterThan "'a::ord \<Rightarrow> 'a set"}\\
   462 @{const greaterThan} & @{term_type_only greaterThan "'a::ord \<Rightarrow> 'a set"}\\