equal
deleted
inserted
replaced
76 |
76 |
77 |
77 |
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"}\\ |