(* Title: HOL/Code_Evaluation.thy
Author: Florian Haftmann, TU Muenchen
*)
section \<open>Term evaluation using the generic code generator\<close>
theory Code_Evaluation
imports Typerep Limited_Sequence
keywords "value" :: diag
begin
subsection \<open>Term representation\<close>
subsubsection \<open>Terms and class \<open>term_of\<close>\<close>
datatype (plugins only: extraction) "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"
definition Free :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
"Free _ _ = dummy_term"
code_datatype Const App Abs Free
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 \<open>Syntax\<close>
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 \<open>Tools setup and evaluation\<close>
context
begin
qualified definition TERM_OF :: "'a::term_of itself"
where
"TERM_OF = snd (Code_Evaluation.term_of :: 'a \<Rightarrow> _, TYPE('a))"
qualified definition TERM_OF_EQUAL :: "'a::term_of itself"
where
"TERM_OF_EQUAL = snd (\<lambda>(a::'a). (Code_Evaluation.term_of a, HOL.eq a), TYPE('a))"
end
lemma eq_eq_TrueD:
fixes x y :: "'a::{}"
assumes "(x \<equiv> y) \<equiv> Trueprop True"
shows "x \<equiv> y"
using assms by simp
code_printing
type_constructor "term" \<rightharpoonup> (Eval) "Term.term"
| constant Const \<rightharpoonup> (Eval) "Term.Const/ ((_), (_))"
| constant App \<rightharpoonup> (Eval) "Term.$/ ((_), (_))"
| constant Abs \<rightharpoonup> (Eval) "Term.Abs/ ((_), (_), (_))"
| constant Free \<rightharpoonup> (Eval) "Term.Free/ ((_), (_))"
ML_file "Tools/code_evaluation.ML"
code_reserved Eval Code_Evaluation
ML_file "~~/src/HOL/Tools/value_command.ML"
subsection \<open>\<open>term_of\<close> instances\<close>
instantiation "fun" :: (typerep, typerep) term_of
begin
definition
"term_of (f :: 'a \<Rightarrow> 'b) =
Const (STR ''Pure.dummy_pattern'')
(Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
instance ..
end
declare [[code drop: rec_term case_term
"term_of :: typerep \<Rightarrow> _" "term_of :: term \<Rightarrow> _" "term_of :: String.literal \<Rightarrow> _"
"term_of :: _ Predicate.pred \<Rightarrow> term" "term_of :: _ Predicate.seq \<Rightarrow> term"]]
definition case_char :: "'a \<Rightarrow> (num \<Rightarrow> 'a) \<Rightarrow> char \<Rightarrow> 'a"
where "case_char f g c = (if c = 0 then f else g (num_of_nat (nat_of_char c)))"
lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_num_def, code]:
"term_of =
case_char (Const (STR ''Groups.zero_class.zero'') (TYPEREP(char)))
(\<lambda>k. App (Const (STR ''String.Char'') (TYPEREP(num \<Rightarrow> char))) (term_of k))"
by (rule ext) (rule term_of_anything [THEN meta_eq_to_obj_eq])
lemma term_of_string [code]:
"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))"
by (subst term_of_anything) rule
code_printing
constant "term_of :: integer \<Rightarrow> term" \<rightharpoonup> (Eval) "HOLogic.mk'_number/ HOLogic.code'_integerT"
| constant "term_of :: String.literal \<Rightarrow> term" \<rightharpoonup> (Eval) "HOLogic.mk'_literal"
declare [[code drop: "term_of :: integer \<Rightarrow> _"]]
lemma term_of_integer [unfolded typerep_fun_def typerep_num_def typerep_integer_def, code]:
"term_of (i :: integer) =
(if i > 0 then
App (Const (STR ''Num.numeral_class.numeral'') (TYPEREP(num \<Rightarrow> integer)))
(term_of (num_of_integer i))
else if i = 0 then Const (STR ''Groups.zero_class.zero'') TYPEREP(integer)
else
App (Const (STR ''Groups.uminus_class.uminus'') TYPEREP(integer \<Rightarrow> integer))
(term_of (- i)))"
by (rule term_of_anything [THEN meta_eq_to_obj_eq])
code_reserved Eval HOLogic
subsection \<open>Generic reification\<close>
ML_file "~~/src/HOL/Tools/reification.ML"
subsection \<open>Diagnostic\<close>
definition tracing :: "String.literal \<Rightarrow> 'a \<Rightarrow> 'a" where
[code del]: "tracing s x = x"
code_printing
constant "tracing :: String.literal => 'a => 'a" \<rightharpoonup> (Eval) "Code'_Evaluation.tracing"
hide_const dummy_term valapp
hide_const (open) Const App Abs Free termify valtermify term_of tracing
end