src/HOL/ex/IArray_Examples.thy
author haftmann
Thu Mar 14 09:46:04 2019 +0100 (5 weeks ago)
changeset 69908 1bd74a0944b3
parent 66453 cc19f7ca2ed6
permissions -rw-r--r--
slightly more complete check of code generation for immutable arrays
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theory IArray_Examples
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imports "HOL-Library.IArray" "HOL-Library.Code_Target_Numeral"
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begin
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lemma "IArray [True,False] !! 1 = False"
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by eval
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lemma "IArray.length (IArray [[],[]]) = 2"
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by eval
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lemma "IArray.list_of (IArray [1,3::int]) = [1,3]"
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by eval
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lemma "IArray.list_of (IArray.of_fun (%n. n*n) 5) = [0,1,4,9,16]"
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by eval
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lemma "\<not> IArray.all (\<lambda>x. x > 2) (IArray [1,3::int])"
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by eval
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lemma "IArray.exists (\<lambda>x. x > 2) (IArray [1,3::int])"
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by eval
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fun sum2 :: "'a::monoid_add iarray \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a" where
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"sum2 A n s = (if n=0 then s else sum2 A (n - 1) (s + A!!(n - 1)))"
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definition sum :: "'a::monoid_add iarray \<Rightarrow> 'a" where
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"sum A = sum2 A (IArray.length A) 0"
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lemma "sum (IArray [1,2,3,4,5,6,7,8,9::int]) = 45"
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by eval
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definition partial_geometric_sum :: "'a::comm_ring_1 list \<Rightarrow> 'a"
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  where "partial_geometric_sum xs = (let
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    values = IArray xs;
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    coefficients = IArray.of_fun of_nat (length xs)
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  in sum_list (map (\<lambda>i. values !! i * coefficients !! i) [0..<IArray.length values]))"
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export_code partial_geometric_sum checking SML OCaml? Haskell? Scala
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end
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