src/HOL/Code_Evaluation.thy
author kuncar
Fri Dec 09 18:07:04 2011 +0100 (2011-12-09)
changeset 45802 b16f976db515
parent 42979 5b9e16259341
child 46635 cde737f9c911
permissions -rw-r--r--
Quotient_Info stores only relation maps
     1 (*  Title:      HOL/Code_Evaluation.thy
     2     Author:     Florian Haftmann, TU Muenchen
     3 *)
     4 
     5 header {* Term evaluation using the generic code generator *}
     6 
     7 theory Code_Evaluation
     8 imports Plain Typerep Code_Numeral
     9 uses ("Tools/code_evaluation.ML")
    10 begin
    11 
    12 subsection {* Term representation *}
    13 
    14 subsubsection {* Terms and class @{text term_of} *}
    15 
    16 datatype "term" = dummy_term
    17 
    18 definition Const :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
    19   "Const _ _ = dummy_term"
    20 
    21 definition App :: "term \<Rightarrow> term \<Rightarrow> term" where
    22   "App _ _ = dummy_term"
    23 
    24 definition Abs :: "String.literal \<Rightarrow> typerep \<Rightarrow> term \<Rightarrow> term" where
    25   "Abs _ _ _ = dummy_term"
    26 
    27 definition Free :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
    28   "Free _ _ = dummy_term"
    29 
    30 code_datatype Const App Abs Free
    31 
    32 class term_of = typerep +
    33   fixes term_of :: "'a \<Rightarrow> term"
    34 
    35 lemma term_of_anything: "term_of x \<equiv> t"
    36   by (rule eq_reflection) (cases "term_of x", cases t, simp)
    37 
    38 definition valapp :: "('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)
    39   \<Rightarrow> 'a \<times> (unit \<Rightarrow> term) \<Rightarrow> 'b \<times> (unit \<Rightarrow> term)" where
    40   "valapp f x = (fst f (fst x), \<lambda>u. App (snd f ()) (snd x ()))"
    41 
    42 lemma valapp_code [code, code_unfold]:
    43   "valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"
    44   by (simp only: valapp_def fst_conv snd_conv)
    45 
    46 
    47 subsubsection {* Syntax *}
    48 
    49 definition termify :: "'a \<Rightarrow> term" where
    50   [code del]: "termify x = dummy_term"
    51 
    52 abbreviation valtermify :: "'a \<Rightarrow> 'a \<times> (unit \<Rightarrow> term)" where
    53   "valtermify x \<equiv> (x, \<lambda>u. termify x)"
    54 
    55 locale term_syntax
    56 begin
    57 
    58 notation App (infixl "<\<cdot>>" 70)
    59   and valapp (infixl "{\<cdot>}" 70)
    60 
    61 end
    62 
    63 interpretation term_syntax .
    64 
    65 no_notation App (infixl "<\<cdot>>" 70)
    66   and valapp (infixl "{\<cdot>}" 70)
    67 
    68 
    69 subsection {* Tools setup and evaluation *}
    70 
    71 lemma eq_eq_TrueD:
    72   assumes "(x \<equiv> y) \<equiv> Trueprop True"
    73   shows "x \<equiv> y"
    74   using assms by simp
    75 
    76 use "Tools/code_evaluation.ML"
    77 
    78 code_reserved Eval Code_Evaluation
    79 
    80 setup {* Code_Evaluation.setup *}
    81 
    82 
    83 subsection {* @{text term_of} instances *}
    84 
    85 instantiation "fun" :: (typerep, typerep) term_of
    86 begin
    87 
    88 definition
    89   "term_of (f \<Colon> 'a \<Rightarrow> 'b) = Const (STR ''dummy_pattern'') (Typerep.Typerep (STR ''fun'')
    90      [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
    91 
    92 instance ..
    93 
    94 end
    95 
    96 instantiation String.literal :: term_of
    97 begin
    98 
    99 definition
   100   "term_of s = App (Const (STR ''STR'')
   101     (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''list'') [Typerep.Typerep (STR ''char'') []],
   102       Typerep.Typerep (STR ''String.literal'') []])) (term_of (String.explode s))"
   103 
   104 instance ..
   105 
   106 end
   107 
   108 
   109 subsubsection {* Code generator setup *}
   110 
   111 lemmas [code del] = term.recs term.cases term.size
   112 lemma [code, code del]: "HOL.equal (t1\<Colon>term) t2 \<longleftrightarrow> HOL.equal t1 t2" ..
   113 
   114 lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..
   115 lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
   116 lemma [code, code del]: "(term_of \<Colon> String.literal \<Rightarrow> term) = term_of" ..
   117 lemma [code, code del]: "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Evaluation.term)
   118   = Code_Evaluation.term_of" ..
   119 lemma [code, code del]: "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Evaluation.term)
   120   = Code_Evaluation.term_of" ..
   121 
   122 lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]:
   123   "Code_Evaluation.term_of c =
   124     (let (n, m) = nibble_pair_of_char c
   125   in Code_Evaluation.App (Code_Evaluation.App
   126     (Code_Evaluation.Const (STR ''String.char.Char'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))
   127       (Code_Evaluation.term_of n)) (Code_Evaluation.term_of m))"
   128   by (subst term_of_anything) rule 
   129 
   130 code_type "term"
   131   (Eval "Term.term")
   132 
   133 code_const Const and App and Abs and Free
   134   (Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))" and "Term.Abs/ ((_), (_), (_))"
   135      and "Term.Free/ ((_), (_))")
   136 
   137 code_const "term_of \<Colon> String.literal \<Rightarrow> term"
   138   (Eval "HOLogic.mk'_literal")
   139 
   140 code_reserved Eval HOLogic
   141 
   142 
   143 subsubsection {* Numeric types *}
   144 
   145 definition term_of_num_semiring :: "'a\<Colon>semiring_div \<Rightarrow> 'a \<Rightarrow> term" where
   146   "term_of_num_semiring two = (\<lambda>_. dummy_term)"
   147 
   148 lemma (in term_syntax) term_of_num_semiring_code [code]:
   149   "term_of_num_semiring two k = (if k = 0 then termify Int.Pls
   150     else (if k mod two = 0
   151       then termify Int.Bit0 <\<cdot>> term_of_num_semiring two (k div two)
   152       else termify Int.Bit1 <\<cdot>> term_of_num_semiring two (k div two)))"
   153   by (auto simp add: term_of_anything Const_def App_def term_of_num_semiring_def Let_def)
   154 
   155 lemma (in term_syntax) term_of_nat_code [code]:
   156   "term_of (n::nat) = termify (number_of :: int \<Rightarrow> nat) <\<cdot>> term_of_num_semiring (2::nat) n"
   157   by (simp only: term_of_anything)
   158 
   159 lemma (in term_syntax) term_of_code_numeral_code [code]:
   160   "term_of (k::code_numeral) = termify (number_of :: int \<Rightarrow> code_numeral) <\<cdot>> term_of_num_semiring (2::code_numeral) k"
   161   by (simp only: term_of_anything)
   162 
   163 definition term_of_num_ring :: "'a\<Colon>ring_div \<Rightarrow> 'a \<Rightarrow> term" where
   164   "term_of_num_ring two = (\<lambda>_. dummy_term)"
   165 
   166 lemma (in term_syntax) term_of_num_ring_code [code]:
   167   "term_of_num_ring two k = (if k = 0 then termify Int.Pls
   168     else if k = -1 then termify Int.Min
   169     else if k mod two = 0 then termify Int.Bit0 <\<cdot>> term_of_num_ring two (k div two)
   170     else termify Int.Bit1 <\<cdot>> term_of_num_ring two (k div two))"
   171   by (auto simp add: term_of_anything Const_def App_def term_of_num_ring_def Let_def)
   172 
   173 lemma (in term_syntax) term_of_int_code [code]:
   174   "term_of (k::int) = (if k = 0 then termify (0 :: int)
   175     else termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num_ring (2::int) k)"
   176   by (simp only: term_of_anything)
   177 
   178 
   179 subsubsection {* Obfuscation *}
   180 
   181 print_translation {*
   182 let
   183   val term = Const ("<TERM>", dummyT);
   184   fun tr1' [_, _] = term;
   185   fun tr2' [] = term;
   186 in
   187   [(@{const_syntax Const}, tr1'),
   188     (@{const_syntax App}, tr1'),
   189     (@{const_syntax dummy_term}, tr2')]
   190 end
   191 *}
   192 
   193 
   194 subsection {* Diagnostic *}
   195 
   196 definition tracing :: "String.literal \<Rightarrow> 'a \<Rightarrow> 'a" where
   197   [code del]: "tracing s x = x"
   198 
   199 code_const "tracing :: String.literal => 'a => 'a"
   200   (Eval "Code'_Evaluation.tracing")
   201 
   202 
   203 hide_const dummy_term valapp
   204 hide_const (open) Const App Abs Free termify valtermify term_of term_of_num_semiring term_of_num_ring tracing
   205 
   206 end