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section \<open>Lazy evaluation within the logic\<close>
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theory Lazy_Eval
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imports
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Complex_Main
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begin
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text \<open>
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This is infrastructure to lazily evaluate an expression (typically something corecursive)
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within the logic by simple rewriting. A signature of supported (co-)datatype constructures
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upon which pattern matching is allowed and a list of function equations that are used in
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rewriting must be provided.
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One can then e.\,g.\ determine whether a given pattern matches a given expression. To do this,
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the expression will be rewritten using the given function equations until enough constructors
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have been exposed to decide whether the pattern matches.
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This infrastructure was developed specifically for evaluating Multiseries expressions, but
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can, in principle, be used for other purposes as well.
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\<close>
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lemma meta_eq_TrueE: "PROP P \<equiv> Trueprop True \<Longrightarrow> PROP P" by simp
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datatype cmp_result = LT | EQ | GT
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definition COMPARE :: "real \<Rightarrow> real \<Rightarrow> cmp_result" where
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"COMPARE x y = (if x < y then LT else if x > y then GT else EQ)"
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lemma COMPARE_intros:
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"x < y \<Longrightarrow> COMPARE x y \<equiv> LT" "x > y \<Longrightarrow> COMPARE x y \<equiv> GT" "x = y \<Longrightarrow> COMPARE x y \<equiv> EQ"
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by (simp_all add: COMPARE_def)
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primrec CMP_BRANCH :: "cmp_result \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> 'a" where
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"CMP_BRANCH LT x y z = x"
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| "CMP_BRANCH EQ x y z = y"
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| "CMP_BRANCH GT x y z = z"
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ML_file \<open>lazy_eval.ML\<close>
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end |