src/HOL/Code_Evaluation.thy
author paulson <lp15@cam.ac.uk>
Mon May 23 15:33:24 2016 +0100 (2016-05-23)
changeset 63114 27afe7af7379
parent 62958 b41c1cb5e251
child 63161 2660ba498798
permissions -rw-r--r--
Lots of new material for multivariate analysis
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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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section \<open>Term evaluation using the generic code generator\<close>
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theory Code_Evaluation
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imports Typerep Limited_Sequence
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keywords "value" :: diag
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begin
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subsection \<open>Term representation\<close>
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subsubsection \<open>Terms and class \<open>term_of\<close>\<close>
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datatype (plugins only: code extraction) "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 \<open>Syntax\<close>
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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 \<open>Tools setup and evaluation\<close>
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lemma eq_eq_TrueD:
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  fixes x y :: "'a::{}"
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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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code_printing
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  type_constructor "term" \<rightharpoonup> (Eval) "Term.term"
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| constant Const \<rightharpoonup> (Eval) "Term.Const/ ((_), (_))"
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| constant App \<rightharpoonup> (Eval) "Term.$/ ((_), (_))"
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| constant Abs \<rightharpoonup> (Eval) "Term.Abs/ ((_), (_), (_))"
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| constant Free \<rightharpoonup> (Eval) "Term.Free/ ((_), (_))"
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ML_file "Tools/code_evaluation.ML"
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code_reserved Eval Code_Evaluation
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ML_file "~~/src/HOL/Tools/value.ML"
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subsection \<open>\<open>term_of\<close> instances\<close>
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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 :: 'a \<Rightarrow> 'b) =
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    Const (STR ''Pure.dummy_pattern'')
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      (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
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instance ..
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end
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declare [[code drop: rec_term case_term "HOL.equal :: term \<Rightarrow> _"
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  "term_of :: typerep \<Rightarrow> _" "term_of :: term \<Rightarrow> _" "term_of :: String.literal \<Rightarrow> _"
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  "term_of :: _ Predicate.pred \<Rightarrow> term" "term_of :: _ Predicate.seq \<Rightarrow> term"]]
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definition case_char :: "'a \<Rightarrow> (num \<Rightarrow> 'a) \<Rightarrow> char \<Rightarrow> 'a"
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  where "case_char f g c = (if c = 0 then f else g (num_of_nat (nat_of_char c)))"
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lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_num_def, code]:
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  "term_of =
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    case_char (Const (STR ''Groups.zero_class.zero'') (TYPEREP(char)))
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    (\<lambda>k. App (Const (STR ''String.Char'') (TYPEREP(num \<Rightarrow> char))) (term_of k))"
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  by (rule ext) (rule term_of_anything [THEN meta_eq_to_obj_eq])
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lemma term_of_string [code]:
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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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  by (subst term_of_anything) rule 
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code_printing
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  constant "term_of :: integer \<Rightarrow> term" \<rightharpoonup> (Eval) "HOLogic.mk'_number/ HOLogic.code'_integerT"
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| constant "term_of :: String.literal \<Rightarrow> term" \<rightharpoonup> (Eval) "HOLogic.mk'_literal"
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declare [[code drop: "term_of :: integer \<Rightarrow> _"]]
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lemma term_of_integer [unfolded typerep_fun_def typerep_num_def typerep_integer_def, code]:
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  "term_of (i :: integer) =
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  (if i > 0 then 
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     App (Const (STR ''Num.numeral_class.numeral'') (TYPEREP(num \<Rightarrow> integer)))
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      (term_of (num_of_integer i))
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   else if i = 0 then Const (STR ''Groups.zero_class.zero'') TYPEREP(integer)
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   else
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     App (Const (STR ''Groups.uminus_class.uminus'') TYPEREP(integer \<Rightarrow> integer))
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       (term_of (- i)))"
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  by (rule term_of_anything [THEN meta_eq_to_obj_eq])
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code_reserved Eval HOLogic
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subsection \<open>Generic reification\<close>
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ML_file "~~/src/HOL/Tools/reification.ML"
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subsection \<open>Diagnostic\<close>
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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_printing
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  constant "tracing :: String.literal => 'a => 'a" \<rightharpoonup> (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 tracing
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end
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