src/HOL/Code_Evaluation.thy
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(*  Title:      HOL/Code_Evaluation.thy
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    Author:     Florian Haftmann, TU Muenchen
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*)
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header {* Term evaluation using the generic code generator *}
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theory Code_Evaluation
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imports Plain Typerep Code_Numeral Predicate
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begin
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subsection {* Term representation *}
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subsubsection {* Terms and class @{text term_of} *}
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datatype "term" = dummy_term
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definition Const :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
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  "Const _ _ = dummy_term"
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definition App :: "term \<Rightarrow> term \<Rightarrow> term" where
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  "App _ _ = dummy_term"
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definition Abs :: "String.literal \<Rightarrow> typerep \<Rightarrow> term \<Rightarrow> term" where
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  "Abs _ _ _ = dummy_term"
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definition Free :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
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  "Free _ _ = dummy_term"
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code_datatype Const App Abs Free
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class term_of = typerep +
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  fixes term_of :: "'a \<Rightarrow> term"
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lemma term_of_anything: "term_of x \<equiv> t"
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  by (rule eq_reflection) (cases "term_of x", cases t, simp)
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definition valapp :: "('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)
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  \<Rightarrow> 'a \<times> (unit \<Rightarrow> term) \<Rightarrow> 'b \<times> (unit \<Rightarrow> term)" where
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  "valapp f x = (fst f (fst x), \<lambda>u. App (snd f ()) (snd x ()))"
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lemma valapp_code [code, code_unfold]:
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  "valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"
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  by (simp only: valapp_def fst_conv snd_conv)
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subsubsection {* Syntax *}
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definition termify :: "'a \<Rightarrow> term" where
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  [code del]: "termify x = dummy_term"
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abbreviation valtermify :: "'a \<Rightarrow> 'a \<times> (unit \<Rightarrow> term)" where
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  "valtermify x \<equiv> (x, \<lambda>u. termify x)"
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locale term_syntax
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begin
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notation App (infixl "<\<cdot>>" 70)
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  and valapp (infixl "{\<cdot>}" 70)
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end
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interpretation term_syntax .
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no_notation App (infixl "<\<cdot>>" 70)
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  and valapp (infixl "{\<cdot>}" 70)
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subsection {* Tools setup and evaluation *}
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lemma eq_eq_TrueD:
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  assumes "(x \<equiv> y) \<equiv> Trueprop True"
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  shows "x \<equiv> y"
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  using assms by simp
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ML_file "Tools/code_evaluation.ML"
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code_reserved Eval Code_Evaluation
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setup {* Code_Evaluation.setup *}
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subsection {* @{text term_of} instances *}
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instantiation "fun" :: (typerep, typerep) term_of
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begin
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definition
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  "term_of (f \<Colon> 'a \<Rightarrow> 'b) = Const (STR ''dummy_pattern'') (Typerep.Typerep (STR ''fun'')
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     [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
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instance ..
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end
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instantiation String.literal :: term_of
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begin
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definition
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  "term_of s = App (Const (STR ''STR'')
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    (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''list'') [Typerep.Typerep (STR ''char'') []],
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      Typerep.Typerep (STR ''String.literal'') []])) (term_of (String.explode s))"
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instance ..
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end
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subsubsection {* Code generator setup *}
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lemmas [code del] = term.recs term.cases term.size
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lemma [code, code del]: "HOL.equal (t1\<Colon>term) t2 \<longleftrightarrow> HOL.equal t1 t2" ..
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lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..
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lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
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lemma [code, code del]: "(term_of \<Colon> String.literal \<Rightarrow> term) = term_of" ..
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lemma [code, code del]: "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Evaluation.term)
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  = Code_Evaluation.term_of" ..
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lemma [code, code del]: "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Evaluation.term)
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  = Code_Evaluation.term_of" ..
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lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]:
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  "Code_Evaluation.term_of c =
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    (let (n, m) = nibble_pair_of_char c
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  in Code_Evaluation.App (Code_Evaluation.App
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    (Code_Evaluation.Const (STR ''String.char.Char'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))
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      (Code_Evaluation.term_of n)) (Code_Evaluation.term_of m))"
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  by (subst term_of_anything) rule 
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code_type "term"
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  (Eval "Term.term")
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code_const Const and App and Abs and Free
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  (Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))" and "Term.Abs/ ((_), (_), (_))"
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     and "Term.Free/ ((_), (_))")
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code_const "term_of \<Colon> String.literal \<Rightarrow> term"
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  (Eval "HOLogic.mk'_literal")
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code_reserved Eval HOLogic
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subsubsection {* Numeric types *}
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definition term_of_num_semiring :: "'a\<Colon>semiring_div \<Rightarrow> 'a \<Rightarrow> term" where
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  "term_of_num_semiring two = (\<lambda>_. dummy_term)"
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lemma (in term_syntax) term_of_num_semiring_code [code]:
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  "term_of_num_semiring two k = (
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    if k = 1 then termify Num.One
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    else (if k mod two = 0
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      then termify Num.Bit0 <\<cdot>> term_of_num_semiring two (k div two)
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      else termify Num.Bit1 <\<cdot>> term_of_num_semiring two (k div two)))"
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  by (auto simp add: term_of_anything Const_def App_def term_of_num_semiring_def)
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lemma (in term_syntax) term_of_nat_code [code]:
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  "term_of (n::nat) = (
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    if n = 0 then termify (0 :: nat)
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    else termify (numeral :: num \<Rightarrow> nat) <\<cdot>> term_of_num_semiring (2::nat) n)"
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  by (simp only: term_of_anything)
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lemma (in term_syntax) term_of_code_numeral_code [code]:
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  "term_of (k::code_numeral) = (
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    if k = 0 then termify (0 :: code_numeral)
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    else termify (numeral :: num \<Rightarrow> code_numeral) <\<cdot>> term_of_num_semiring (2::code_numeral) k)"
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  by (simp only: term_of_anything)
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lemma (in term_syntax) term_of_int_code [code]:
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  "term_of (k::int) = (if k = 0 then termify (0 :: int)
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    else if k < 0 then termify (neg_numeral :: num \<Rightarrow> int) <\<cdot>> term_of_num_semiring (2::int) (- k)
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    else termify (numeral :: num \<Rightarrow> int) <\<cdot>> term_of_num_semiring (2::int) k)"
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  by (simp only: term_of_anything)
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subsubsection {* Obfuscation *}
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print_translation {*
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let
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  val term = Const ("<TERM>", dummyT);
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  fun tr1' [_, _] = term;
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  fun tr2' [] = term;
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in
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  [(@{const_syntax Const}, tr1'),
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    (@{const_syntax App}, tr1'),
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    (@{const_syntax dummy_term}, tr2')]
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end
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*}
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subsection {* Diagnostic *}
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definition tracing :: "String.literal \<Rightarrow> 'a \<Rightarrow> 'a" where
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  [code del]: "tracing s x = x"
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code_const "tracing :: String.literal => 'a => 'a"
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  (Eval "Code'_Evaluation.tracing")
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hide_const dummy_term valapp
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hide_const (open) Const App Abs Free termify valtermify term_of term_of_num_semiring tracing
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end