(* Title: HOL/Code_Eval.thy
Author: Florian Haftmann, TU Muenchen
*)
header {* Term evaluation using the generic code generator *}
theory Code_Eval
imports Plain Typerep
begin
subsection {* Term representation *}
subsubsection {* Terms and class @{text term_of} *}
datatype "term" = dummy_term
definition Const :: "message_string \<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)
ML {*
structure Eval =
struct
fun mk_term f g (Const (c, ty)) =
@{term Const} $ HOLogic.mk_message_string c $ g ty
| mk_term f g (t1 $ t2) =
@{term App} $ mk_term f g t1 $ mk_term f g t2
| mk_term f g (Free v) = f v
| mk_term f g (Bound i) = Bound i
| mk_term f g (Abs (v, _, t)) = Abs (v, @{typ term}, mk_term f g t);
fun mk_term_of ty t = Const (@{const_name term_of}, ty --> @{typ term}) $ t;
end;
*}
subsubsection {* @{text term_of} instances *}
setup {*
let
fun add_term_of_def ty vs tyco thy =
let
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_instance (K (Class.intro_classes_tac []))
|> LocalTheory.exit_global
end;
fun interpretator ("prop", (raw_vs, _)) thy = thy
| interpretator (tyco, (raw_vs, _)) thy =
let
val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};
val constrain_sort =
curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort term_of};
val vs = (map o apsnd) constrain_sort raw_vs;
val ty = Type (tyco, map TFree vs);
in
thy
|> Typerep.perhaps_add_def tyco
|> not has_inst ? add_term_of_def ty vs tyco
end;
in
Code.type_interpretation interpretator
end
*}
setup {*
let
fun mk_term_of_eq ty vs tyco (c, tys) =
let
val t = list_comb (Const (c, tys ---> ty),
map Free (Name.names Name.context "a" tys));
in (map_aterms (fn Free (v, ty) => Var ((v, 0), ty) | t => t) t, Eval.mk_term
(fn (v, ty) => Eval.mk_term_of ty (Var ((v, 0), ty)))
(Typerep.mk (fn (v, sort) => Typerep.typerep (TFree (v, sort)))) t)
end;
fun prove_term_of_eq ty eq thy =
let
val cty = Thm.ctyp_of thy ty;
val (arg, rhs) = pairself (Thm.cterm_of thy) eq;
val thm = @{thm term_of_anything}
|> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]
|> Thm.varifyT;
in
thy
|> Code.add_eqn thm
end;
fun interpretator ("prop", (raw_vs, _)) thy = thy
| interpretator (tyco, (raw_vs, raw_cs)) thy =
let
val constrain_sort =
curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort term_of};
val vs = (map o apsnd) constrain_sort raw_vs;
val cs = (map o apsnd o map o map_atyps)
(fn TFree (v, sort) => TFree (v, constrain_sort sort)) raw_cs;
val ty = Type (tyco, map TFree vs);
val eqs = map (mk_term_of_eq ty vs tyco) cs;
val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
in
thy
|> Code.del_eqns const
|> fold (prove_term_of_eq ty) eqs
end;
in
Code.type_interpretation interpretator
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> message_string \<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> message_string \<Rightarrow> term"
(Eval "HOLogic.mk'_message'_string")
code_reserved Eval HOLogic
subsection {* Evaluation setup *}
ML {*
signature EVAL =
sig
val mk_term: ((string * typ) -> term) -> (typ -> term) -> term -> term
val mk_term_of: typ -> term -> term
val eval_ref: (unit -> term) option ref
val eval_term: theory -> term -> term
end;
structure Eval : EVAL =
struct
open Eval;
val eval_ref = ref (NONE : (unit -> term) option);
fun eval_term thy t =
t
|> Eval.mk_term_of (fastype_of t)
|> (fn t => Code_ML.eval NONE ("Eval.eval_ref", eval_ref) I thy t []);
end;
*}
setup {*
Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)
*}
subsubsection {* Syntax *}
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
hide (open) const Const App
hide (open) const term_of
end