(* 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
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_unfold]:
"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 *}
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
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
|> Class.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.datatype_interpretation ensure_term_of
#> Code.abstype_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_global o Logic.varify_global)
(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_global
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.datatype_interpretation ensure_term_of_code
end
*}
setup {*
let
fun mk_term_of_eq thy ty vs tyco abs ty_rep proj =
let
val arg = Var (("x", 0), ty);
val rhs = Abs ("y", @{typ term}, HOLogic.reflect_term (Const (abs, ty_rep --> ty) $ Bound 0)) $
(HOLogic.mk_term_of ty_rep (Const (proj, ty --> ty_rep) $ arg))
|> Thm.cterm_of thy;
val cty = Thm.ctyp_of thy ty;
in
@{thm term_of_anything}
|> Drule.instantiate' [SOME cty] [SOME (Thm.cterm_of thy arg), SOME rhs]
|> Thm.varifyT_global
end;
fun add_term_of_code tyco raw_vs abs raw_ty_rep proj 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 ty_rep = map_atyps
(fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_ty_rep;
val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
val eq = mk_term_of_eq thy ty vs tyco abs ty_rep proj;
in
thy
|> Code.del_eqns const
|> Code.add_eqn eq
end;
fun ensure_term_of_code (tyco, (raw_vs, ((abs, ty), (proj, _)))) 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 abs ty proj thy else thy end;
in
Code.abstype_interpretation ensure_term_of_code
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
(Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))")
code_const "term_of \<Colon> String.literal \<Rightarrow> term"
(Eval "HOLogic.mk'_literal")
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
*}
subsection {* Evaluation setup *}
ML {*
signature CODE_EVALUATION =
sig
val eval_term: theory -> term -> term
val put_term: (unit -> term) -> Proof.context -> Proof.context
val tracing: string -> 'a -> 'a
end;
structure Code_Evaluation : CODE_EVALUATION =
struct
structure Evaluation = Proof_Data (
type T = unit -> term
fun init _ () = error "Evaluation"
);
val put_term = Evaluation.put;
fun tracing s x = (Output.tracing s; x);
fun eval_term thy t = Code_Runtime.dynamic_value_strict (Evaluation.get, put_term, "Code_Evaluation.put_term")
thy NONE I (HOLogic.mk_term_of (fastype_of t) t) [];
end
*}
setup {*
Value.add_evaluator ("code", Code_Evaluation.eval_term o ProofContext.theory_of)
*}
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")
code_reserved Eval Code_Evaluation
hide_const dummy_term App valapp
hide_const (open) Const termify valtermify term_of term_of_num tracing
end