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(* Authors: Florian Haftmann, Johannes Hölzl, Tobias Nipkow *)
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theory Code_Real_Approx_By_Float
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imports Complex_Main "~~/src/HOL/Library/Code_Integer"
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begin
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text{* \textbf{WARNING} This theory implements mathematical reals by machine
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reals (floats). This is inconsistent. See the proof of False at the end of
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the theory, where an equality on mathematical reals is (incorrectly)
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disproved by mapping it to machine reals.
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The value command cannot display real results yet.
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The only legitimate use of this theory is as a tool for code generation
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purposes. *}
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code_type real
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(SML "real")
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(OCaml "float")
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code_const Ratreal
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(SML "error/ \"Bad constant: Ratreal\"")
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code_const "0 :: real"
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(SML "0.0")
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(OCaml "0.0")
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declare zero_real_code[code_unfold del]
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code_const "1 :: real"
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(SML "1.0")
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(OCaml "1.0")
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declare one_real_code[code_unfold del]
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code_const "HOL.equal :: real \<Rightarrow> real \<Rightarrow> bool"
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(SML "Real.== ((_), (_))")
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(OCaml "Pervasives.(=)")
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code_const "Orderings.less_eq :: real \<Rightarrow> real \<Rightarrow> bool"
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(SML "Real.<= ((_), (_))")
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(OCaml "Pervasives.(<=)")
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code_const "Orderings.less :: real \<Rightarrow> real \<Rightarrow> bool"
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(SML "Real.< ((_), (_))")
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(OCaml "Pervasives.(<)")
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code_const "op + :: real \<Rightarrow> real \<Rightarrow> real"
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(SML "Real.+ ((_), (_))")
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(OCaml "Pervasives.( +. )")
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code_const "op * :: real \<Rightarrow> real \<Rightarrow> real"
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(SML "Real.* ((_), (_))")
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(OCaml "Pervasives.( *. )")
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code_const "op - :: real \<Rightarrow> real \<Rightarrow> real"
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(SML "Real.- ((_), (_))")
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(OCaml "Pervasives.( -. )")
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code_const "uminus :: real \<Rightarrow> real"
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(SML "Real.~")
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(OCaml "Pervasives.( ~-. )")
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code_const "op / :: real \<Rightarrow> real \<Rightarrow> real"
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(SML "Real.'/ ((_), (_))")
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(OCaml "Pervasives.( '/. )")
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code_const "HOL.equal :: real \<Rightarrow> real \<Rightarrow> bool"
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(SML "Real.== ((_:real), (_))")
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code_const "sqrt :: real \<Rightarrow> real"
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(SML "Math.sqrt")
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(OCaml "Pervasives.sqrt")
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declare sqrt_def[code del]
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definition real_exp :: "real \<Rightarrow> real" where "real_exp = exp"
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lemma exp_eq_real_exp[code_unfold]: "exp = real_exp"
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unfolding real_exp_def ..
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code_const real_exp
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(SML "Math.exp")
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(OCaml "Pervasives.exp")
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declare real_exp_def[code del]
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declare exp_def[code del]
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hide_const (open) real_exp
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code_const ln
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(SML "Math.ln")
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(OCaml "Pervasives.ln")
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declare ln_def[code del]
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code_const cos
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(SML "Math.cos")
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(OCaml "Pervasives.cos")
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declare cos_def[code del]
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code_const sin
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(SML "Math.sin")
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(OCaml "Pervasives.sin")
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declare sin_def[code del]
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code_const pi
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(SML "Math.pi")
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(OCaml "Pervasives.pi")
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declare pi_def[code del]
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code_const arctan
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(SML "Math.atan")
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(OCaml "Pervasives.atan")
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declare arctan_def[code del]
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code_const arccos
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(SML "Math.scos")
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(OCaml "Pervasives.acos")
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declare arccos_def[code del]
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code_const arcsin
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(SML "Math.asin")
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(OCaml "Pervasives.asin")
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declare arcsin_def[code del]
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definition real_of_int :: "int \<Rightarrow> real" where
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"real_of_int \<equiv> of_int"
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code_const real_of_int
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(SML "Real.fromInt")
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(OCaml "Pervasives.float (Big'_int.int'_of'_big'_int (_))")
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lemma of_int_eq_real_of_int[code_unfold]: "of_int = real_of_int"
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unfolding real_of_int_def ..
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hide_const (open) real_of_int
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declare number_of_real_code [code_unfold del]
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lemma "False"
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proof-
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have "cos(pi/2) = 0" by(rule cos_pi_half)
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moreover have "cos(pi/2) \<noteq> 0" by eval
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ultimately show "False" by blast
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qed
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end
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