Quot/Examples/AbsRepTest.thy
author Christian Urban <urbanc@in.tum.de>
Tue, 05 Jan 2010 14:09:04 +0100
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theory AbsRepTest
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imports "../QuotMain" "../QuotList" "../QuotOption" "../QuotSum" "../QuotProd" List
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begin
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ML {* open Quotient_Term *}
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ML {*
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fun test_funs flag ctxt (rty, qty) =
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  (absrep_fun_chk flag ctxt (rty, qty)
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   |> Syntax.string_of_term ctxt
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   |> writeln;
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   equiv_relation_chk ctxt (rty, qty) 
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   |> Syntax.string_of_term ctxt
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   |> writeln;
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   new_equiv_relation_chk ctxt (rty, qty) 
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   |> Syntax.string_of_term ctxt
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   |> writeln)
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*}
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definition
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  erel1 (infixl "\<approx>1" 50)
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where
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  "erel1 \<equiv> \<lambda>xs ys. \<forall>e. e \<in> set xs \<longleftrightarrow> e \<in> set ys"
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quotient_type 
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  'a fset = "'a list" / erel1
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  apply(rule equivpI)
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  unfolding erel1_def reflp_def symp_def transp_def
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  by auto
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definition
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  erel2 (infixl "\<approx>2" 50)
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where
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  "erel2 \<equiv> \<lambda>(xs::('a * 'a) list) ys. \<forall>e. e \<in> set xs \<longleftrightarrow> e \<in> set ys"
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quotient_type 
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  'a foo = "('a * 'a) list" / erel2
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  apply(rule equivpI)
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  unfolding erel2_def reflp_def symp_def transp_def
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  by auto
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definition
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  erel3 (infixl "\<approx>3" 50)
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where
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  "erel3 \<equiv> \<lambda>(xs::('a * int) list) ys. \<forall>e. e \<in> set xs \<longleftrightarrow> e \<in> set ys"
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quotient_type 
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  'a bar = "('a * int) list" / "erel3"
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  apply(rule equivpI)
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  unfolding erel3_def reflp_def symp_def transp_def
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  by auto
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fun
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  intrel :: "(nat \<times> nat) \<Rightarrow> (nat \<times> nat) \<Rightarrow> bool" (infixl "\<approx>4" 50)
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where
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  "intrel (x, y) (u, v) = (x + v = u + y)"
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quotient_type myint = "nat \<times> nat" / intrel
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  by (auto simp add: equivp_def expand_fun_eq)
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ML {*
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test_funs absF @{context} 
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     (@{typ "nat \<times> nat"}, 
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      @{typ "myint"})
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*}
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ML {*
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test_funs absF @{context} 
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     (@{typ "('a * 'a) list"}, 
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      @{typ "'a foo"})
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*}
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ML {*
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test_funs repF @{context} 
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     (@{typ "(('a * 'a) list * 'b)"}, 
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      @{typ "('a foo * 'b)"})
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*}
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ML {*
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test_funs absF @{context} 
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     (@{typ "(('a list) * int) list"}, 
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      @{typ "('a fset) bar"})
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*}
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ML {*
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test_funs absF @{context} 
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     (@{typ "('a list)"}, 
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      @{typ "('a fset)"})
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*}
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ML {*
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test_funs absF @{context} 
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     (@{typ "('a list) list"}, 
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      @{typ "('a fset) fset"})
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*}
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ML {*
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test_funs absF @{context} 
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     (@{typ "(('a * 'a) list) list"}, 
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      @{typ "(('a * 'a) fset) fset"})
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*}
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ML {*
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test_funs absF @{context} 
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      (@{typ "(nat * nat) list"}, 
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       @{typ "myint fset"})
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*}
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ML {*
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test_funs absF @{context} 
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     (@{typ "('a list) list \<Rightarrow> 'a list"}, 
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      @{typ "('a fset) fset \<Rightarrow> 'a fset"})
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*}
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end