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