added verification framework for the HeapMonad and quicksort as example for this framework
(* Title: HOL/Library/Eval.thy
ID: $Id$
Author: Florian Haftmann, TU Muenchen
*)
header {* A simple term evaluation mechanism *}
theory Eval
imports
Plain
RType
Code_Index (* this theory is just imported for a term_of setup *)
begin
subsection {* Term representation *}
subsubsection {* Terms and class @{text term_of} *}
datatype "term" = dummy_term
definition
Const :: "message_string \<Rightarrow> rtype \<Rightarrow> term"
where
"Const _ _ = dummy_term"
definition
App :: "term \<Rightarrow> term \<Rightarrow> term"
where
"App _ _ = dummy_term"
code_datatype Const App
class term_of = rtype +
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} $ Message_String.mk 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));
in
thy
|> TheoryTarget.instantiation ([tyco], vs, @{sort term_of})
|> `(fn lthy => Syntax.check_term lthy eq)
|-> (fn eq => Specification.definition (NONE, (("", []), eq)))
|> snd
|> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
|> LocalTheory.exit
|> ProofContext.theory_of
end;
fun 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
|> RType.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)))
(RType.mk (fn (v, sort) => RType.rtype (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_func thm
end;
fun 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_funcs const
|> fold (prove_term_of_eq ty) eqs
end;
in
Code.type_interpretation interpretator
end
*}
subsubsection {* Code generator setup *}
lemmas [code func del] = term.recs term.cases term.size
lemma [code func, code func del]: "(t1\<Colon>term) = t2 \<longleftrightarrow> t1 = t2" ..
lemma [code func, code func del]: "(term_of \<Colon> rtype \<Rightarrow> term) = term_of" ..
lemma [code func, code func del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
lemma [code func, code func del]: "(term_of \<Colon> index \<Rightarrow> term) = term_of" ..
lemma [code func, code func del]: "(term_of \<Colon> message_string \<Rightarrow> term) = term_of" ..
code_type "term"
(SML "Term.term")
code_const Const and App
(SML "Term.Const/ (_, _)" and "Term.$/ (_, _)")
code_const "term_of \<Colon> index \<Rightarrow> term"
(SML "HOLogic.mk'_number/ HOLogic.indexT")
code_const "term_of \<Colon> message_string \<Rightarrow> term"
(SML "Message'_String.mk")
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
*}
setup {*
Sign.declare_const [] ("rterm_of", @{typ "'a \<Rightarrow> 'b"}, NoSyn)
#> snd
*}
notation (output)
rterm_of ("\<guillemotleft>_\<guillemotright>")
locale (open) rterm_syntax =
fixes rterm_of_syntax :: "'a \<Rightarrow> 'b" ("\<guillemotleft>_\<guillemotright>")
parse_translation {*
let
fun rterm_of_tr [t] = Lexicon.const @{const_name rterm_of} $ t
| rterm_of_tr ts = raise TERM ("rterm_of_tr", ts);
in
[(Syntax.fixedN ^ "rterm_of_syntax", rterm_of_tr)]
end
*}
setup {*
let
val subst_rterm_of = Eval.mk_term
(fn (v, _) => error ("illegal free variable in term quotation: " ^ quote v))
(RType.mk (fn (v, sort) => RType.rtype (TFree (v, sort))));
fun subst_rterm_of' (Const (@{const_name rterm_of}, _), [t]) = subst_rterm_of t
| subst_rterm_of' (Const (@{const_name rterm_of}, _), _) =
error ("illegal number of arguments for " ^ quote @{const_name rterm_of})
| subst_rterm_of' (t, ts) = list_comb (t, map (subst_rterm_of' o strip_comb) ts);
fun subst_rterm_of'' t =
let
val t' = subst_rterm_of' (strip_comb t);
in if t aconv t'
then NONE
else SOME t'
end;
fun check_rterm_of ts ctxt =
let
val ts' = map subst_rterm_of'' ts;
in if exists is_some ts'
then SOME (map2 the_default ts ts', ctxt)
else NONE
end;
in
Context.theory_map (Syntax.add_term_check 0 "rterm_of" check_rterm_of)
end;
*}
hide const dummy_term
hide (open) const Const App
hide (open) const term_of
subsection {* Evaluation setup *}
ML {*
signature EVAL =
sig
val mk_term: ((string * typ) -> term) -> (typ -> term) -> term -> term
val eval_ref: (unit -> term) option ref
val eval_term: theory -> term -> term
val evaluate: Proof.context -> term -> unit
val evaluate': string -> Proof.context -> term -> unit
val evaluate_cmd: string option -> string -> Toplevel.state -> unit
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 => CodeTarget.eval_term ("Eval.eval_ref", eval_ref) thy t [])
|> Code.postprocess_term thy;
val evaluators = [
("code", eval_term),
("SML", Codegen.eval_term),
("normal_form", Nbe.norm_term)
];
fun gen_evaluate evaluators ctxt t =
let
val thy = ProofContext.theory_of ctxt;
val (evls, evl) = split_last evaluators;
val t' = case get_first (fn f => try (f thy) t) evls
of SOME t' => t'
| NONE => evl thy t;
val ty' = Term.type_of t';
val p = Pretty.block [Pretty.quote (Syntax.pretty_term ctxt t'),
Pretty.fbrk, Pretty.str "::", Pretty.brk 1,
Pretty.quote (Syntax.pretty_typ ctxt ty')];
in Pretty.writeln p end;
val evaluate = gen_evaluate (map snd evaluators);
fun evaluate' name = gen_evaluate
[(the o AList.lookup (op =) evaluators) name];
fun evaluate_cmd some_name raw_t state =
let
val ctxt = Toplevel.context_of state;
val t = Syntax.read_term ctxt raw_t;
in case some_name
of NONE => evaluate ctxt t
| SOME name => evaluate' name ctxt t
end;
end;
*}
ML {*
OuterSyntax.improper_command "value" "read, evaluate and print term" OuterKeyword.diag
(Scan.option (OuterParse.$$$ "(" |-- OuterParse.name --| OuterParse.$$$ ")")
-- OuterParse.term
>> (fn (some_name, t) => Toplevel.no_timing o Toplevel.keep
(Eval.evaluate_cmd some_name t)));
*}
end