(* Title: HOL/Code_Eval.thy
Author: Florian Haftmann, TU Muenchen
*)
header {* Term evaluation using the generic code generator *}
theory Code_Eval
imports Plain Typerep Code_Numeral
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"
code_datatype Const App
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 inline]:
"valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"
by (simp only: valapp_def fst_conv snd_conv)
subsubsection {* @{text term_of} instances *}
setup {*
let
fun add_term_of tyco raw_vs thy =
let
val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;
val ty = Type (tyco, map TFree vs);
val lhs = Const (@{const_name term_of}, ty --> @{typ term})
$ Free ("x", ty);
val rhs = @{term "undefined \<Colon> term"};
val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst
o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv";
in
thy
|> TheoryTarget.instantiation ([tyco], vs, @{sort term_of})
|> `(fn lthy => Syntax.check_term lthy eq)
|-> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq)))
|> snd
|> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
end;
fun ensure_term_of (tyco, (raw_vs, _)) thy =
let
val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of})
andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep};
in if need_inst then add_term_of tyco raw_vs thy else thy end;
in
Code.type_interpretation ensure_term_of
end
*}
setup {*
let
fun mk_term_of_eq thy ty vs tyco (c, tys) =
let
val t = list_comb (Const (c, tys ---> ty),
map Free (Name.names Name.context "a" tys));
val (arg, rhs) = pairself (Thm.cterm_of thy o map_types Logic.unvarifyT o Logic.varify)
(t, (map_aterms (fn t as Free (v, ty) => HOLogic.mk_term_of ty t | t => t) o HOLogic.reflect_term) t)
val cty = Thm.ctyp_of thy ty;
in
@{thm term_of_anything}
|> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]
|> Thm.varifyT
end;
fun add_term_of_code tyco raw_vs raw_cs thy =
let
val algebra = Sign.classes_of thy;
val vs = map (fn (v, sort) =>
(v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) raw_vs;
val ty = Type (tyco, map TFree vs);
val cs = (map o apsnd o map o map_atyps)
(fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs;
val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
val eqs = map (mk_term_of_eq thy ty vs tyco) cs;
in
thy
|> Code.del_eqns const
|> fold Code.add_eqn eqs
end;
fun ensure_term_of_code (tyco, (raw_vs, cs)) thy =
let
val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};
in if has_inst then add_term_of_code tyco raw_vs cs thy else thy end;
in
Code.type_interpretation ensure_term_of_code
end
*}
subsubsection {* Code generator setup *}
lemmas [code del] = term.recs term.cases term.size
lemma [code, code del]: "eq_class.eq (t1\<Colon>term) t2 \<longleftrightarrow> eq_class.eq 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_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
lemma [code, code del]:
"(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]: "Code_Eval.term_of c =
(let (n, m) = nibble_pair_of_char c
in Code_Eval.App (Code_Eval.App (Code_Eval.Const (STR ''Pair'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))
(Code_Eval.term_of n)) (Code_Eval.term_of m))"
by (subst term_of_anything) rule
code_type "term"
(Eval "Term.term")
code_const Const and App
(Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))")
code_const "term_of \<Colon> String.literal \<Rightarrow> term"
(Eval "HOLogic.mk'_message'_string")
code_reserved Eval HOLogic
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)"
setup {*
let
fun map_default f xs =
let val ys = map f xs
in if exists is_some ys
then SOME (map2 the_default xs ys)
else NONE
end;
fun subst_termify_app (Const (@{const_name termify}, T), [t]) =
if not (Term.has_abs t)
then if fold_aterms (fn Const _ => I | _ => K false) t true
then SOME (HOLogic.reflect_term t)
else error "Cannot termify expression containing variables"
else error "Cannot termify expression containing abstraction"
| subst_termify_app (t, ts) = case map_default subst_termify ts
of SOME ts' => SOME (list_comb (t, ts'))
| NONE => NONE
and subst_termify (Abs (v, T, t)) = (case subst_termify t
of SOME t' => SOME (Abs (v, T, t'))
| NONE => NONE)
| subst_termify t = subst_termify_app (strip_comb t)
fun check_termify ts ctxt = map_default subst_termify ts
|> Option.map (rpair ctxt)
in
Context.theory_map (Syntax.add_term_check 0 "termify" check_termify)
end;
*}
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 {* Numeric types *}
definition term_of_num :: "'a\<Colon>{semiring_div} \<Rightarrow> 'a\<Colon>{semiring_div} \<Rightarrow> term" where
"term_of_num two = (\<lambda>_. dummy_term)"
lemma (in term_syntax) term_of_num_code [code]:
"term_of_num two k = (if k = 0 then termify Int.Pls
else (if k mod two = 0
then termify Int.Bit0 <\<cdot>> term_of_num two (k div two)
else termify Int.Bit1 <\<cdot>> term_of_num two (k div two)))"
by (auto simp add: term_of_anything Const_def App_def term_of_num_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 (2::nat) n"
by (simp only: term_of_anything)
lemma (in term_syntax) term_of_int_code [code]:
"term_of (k::int) = (if k = 0 then termify (0 :: int)
else if k > 0 then termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) k
else termify (uminus :: int \<Rightarrow> int) <\<cdot>> (termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) (- k)))"
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 (2::code_numeral) k"
by (simp only: term_of_anything)
subsection {* Obfuscate *}
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
*}
hide const dummy_term App valapp
hide (open) const Const termify valtermify term_of term_of_num
subsection {* Evaluation setup *}
ML {*
signature EVAL =
sig
val eval_ref: (unit -> term) option ref
val eval_term: theory -> term -> term
end;
structure Eval : EVAL =
struct
val eval_ref = ref (NONE : (unit -> term) option);
fun eval_term thy t =
Code_ML.eval NONE ("Eval.eval_ref", eval_ref) I thy (HOLogic.mk_term_of (fastype_of t) t) [];
end;
*}
setup {*
Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)
*}
end