--- a/src/HOLCF/Tools/fixrec_package.ML Thu Feb 26 10:28:53 2009 -0800
+++ b/src/HOLCF/Tools/fixrec_package.ML Thu Feb 26 11:17:38 2009 -0800
@@ -8,6 +8,7 @@
sig
val legacy_infer_term: theory -> term -> term
val legacy_infer_prop: theory -> term -> term
+
val add_fixrec: bool -> (Attrib.binding * string) list list -> theory -> theory
val add_fixrec_i: bool -> ((binding * attribute list) * term) list list -> theory -> theory
val add_fixpat: Attrib.binding * string list -> theory -> theory
@@ -20,7 +21,7 @@
struct
(* legacy type inference *)
-
+(* used by the domain package *)
fun legacy_infer_term thy t =
singleton (Syntax.check_terms (ProofContext.init thy)) (Sign.intern_term thy t);
@@ -35,15 +36,41 @@
fun fixrec_eq_err thy s eq =
fixrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq));
+(*************************************************************************)
+(***************************** building types ****************************)
+(*************************************************************************)
+
(* ->> is taken from holcf_logic.ML *)
-(* TODO: fix dependencies so we can import HOLCFLogic here *)
-infixr 6 ->>;
-fun S ->> T = Type (@{type_name "->"},[S,T]);
+fun cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
+
+infixr 6 ->>; val (op ->>) = cfunT;
+
+fun dest_cfunT (Type(@{type_name "->"}, [T, U])) = (T, U)
+ | dest_cfunT T = raise TYPE ("dest_cfunT", [T], []);
+
+fun binder_cfun (Type(@{type_name "->"},[T, U])) = T :: binder_cfun U
+ | binder_cfun _ = [];
+
+fun body_cfun (Type(@{type_name "->"},[T, U])) = body_cfun U
+ | body_cfun T = T;
-(* extern_name is taken from domain/library.ML *)
-fun extern_name con = case Symbol.explode con of
- ("o"::"p"::" "::rest) => implode rest
- | _ => con;
+fun strip_cfun T : typ list * typ =
+ (binder_cfun T, body_cfun T);
+
+fun maybeT T = Type(@{type_name "maybe"}, [T]);
+
+fun dest_maybeT (Type(@{type_name "maybe"}, [T])) = T
+ | dest_maybeT T = raise TYPE ("dest_maybeT", [T], []);
+
+fun tupleT [] = @{typ "unit"}
+ | tupleT [T] = T
+ | tupleT (T :: Ts) = HOLogic.mk_prodT (T, tupleT Ts);
+
+fun matchT T = body_cfun T ->> maybeT (tupleT (binder_cfun T));
+
+(*************************************************************************)
+(***************************** building terms ****************************)
+(*************************************************************************)
val mk_trp = HOLogic.mk_Trueprop;
@@ -54,30 +81,86 @@
fun chead_of (Const(@{const_name Rep_CFun},_)$f$t) = chead_of f
| chead_of u = u;
-(* these are helpful functions copied from HOLCF/domain/library.ML *)
-fun %: s = Free(s,dummyT);
-fun %%: s = Const(s,dummyT);
-infix 0 ==; fun S == T = %%:"==" $ S $ T;
-infix 1 ===; fun S === T = %%:"op =" $ S $ T;
-infix 9 ` ; fun f ` x = %%:@{const_name Rep_CFun} $ f $ x;
+fun capply_const (S, T) =
+ Const(@{const_name Rep_CFun}, (S ->> T) --> (S --> T));
+
+fun cabs_const (S, T) =
+ Const(@{const_name Abs_CFun}, (S --> T) --> (S ->> T));
+
+fun mk_capply (t, u) =
+ let val (S, T) =
+ case Term.fastype_of t of
+ Type(@{type_name "->"}, [S, T]) => (S, T)
+ | _ => raise TERM ("mk_capply " ^ ML_Syntax.print_list ML_Syntax.print_term [t, u], [t, u]);
+ in capply_const (S, T) $ t $ u end;
+
+infix 0 ==; val (op ==) = Logic.mk_equals;
+infix 1 ===; val (op ===) = HOLogic.mk_eq;
+infix 9 ` ; val (op `) = mk_capply;
+
+
+fun mk_cpair (t, u) =
+ let val T = Term.fastype_of t
+ val U = Term.fastype_of u
+ val cpairT = T ->> U ->> HOLogic.mk_prodT (T, U)
+ in Const(@{const_name cpair}, cpairT) ` t ` u end;
+
+fun mk_cfst t =
+ let val T = Term.fastype_of t;
+ val (U, _) = HOLogic.dest_prodT T;
+ in Const(@{const_name cfst}, T ->> U) ` t end;
+
+fun mk_csnd t =
+ let val T = Term.fastype_of t;
+ val (_, U) = HOLogic.dest_prodT T;
+ in Const(@{const_name csnd}, T ->> U) ` t end;
+
+fun mk_csplit t =
+ let val (S, TU) = dest_cfunT (Term.fastype_of t);
+ val (T, U) = dest_cfunT TU;
+ val csplitT = (S ->> T ->> U) ->> HOLogic.mk_prodT (S, T) ->> U;
+ in Const(@{const_name csplit}, csplitT) ` t end;
(* builds the expression (LAM v. rhs) *)
-fun big_lambda v rhs = %%:@{const_name Abs_CFun}$(Term.lambda v rhs);
+fun big_lambda v rhs =
+ cabs_const (Term.fastype_of v, Term.fastype_of rhs) $ Term.lambda v rhs;
(* builds the expression (LAM v1 v2 .. vn. rhs) *)
fun big_lambdas [] rhs = rhs
| big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs);
(* builds the expression (LAM <v1,v2,..,vn>. rhs) *)
-fun lambda_ctuple [] rhs = big_lambda (%:"unit") rhs
+fun lambda_ctuple [] rhs = big_lambda (Free("unit", HOLogic.unitT)) rhs
| lambda_ctuple (v::[]) rhs = big_lambda v rhs
| lambda_ctuple (v::vs) rhs =
- %%:@{const_name csplit}`(big_lambda v (lambda_ctuple vs rhs));
+ mk_csplit (big_lambda v (lambda_ctuple vs rhs));
(* builds the expression <v1,v2,..,vn> *)
-fun mk_ctuple [] = %%:"UU"
+fun mk_ctuple [] = @{term "UU::unit"}
| mk_ctuple (t::[]) = t
-| mk_ctuple (t::ts) = %%:@{const_name cpair}`t`(mk_ctuple ts);
+| mk_ctuple (t::ts) = mk_cpair (t, mk_ctuple ts);
+
+fun mk_return t =
+ let val T = Term.fastype_of t
+ in Const(@{const_name Fixrec.return}, T ->> maybeT T) ` t end;
+
+fun mk_bind (t, u) =
+ let val (T, mU) = dest_cfunT (Term.fastype_of u);
+ val bindT = maybeT T ->> (T ->> mU) ->> mU;
+ in Const(@{const_name Fixrec.bind}, bindT) ` t ` u end;
+
+fun mk_mplus (t, u) =
+ let val mT = Term.fastype_of t
+ in Const(@{const_name Fixrec.mplus}, mT ->> mT ->> mT) ` t ` u end;
+
+fun mk_run t =
+ let val mT = Term.fastype_of t
+ val T = dest_maybeT mT
+ in Const(@{const_name Fixrec.run}, mT ->> T) ` t end;
+
+fun mk_fix t =
+ let val (T, _) = dest_cfunT (Term.fastype_of t)
+ in Const(@{const_name fix}, (T ->> T) ->> T) ` t end;
(*************************************************************************)
(************* fixed-point definitions and unfolding theorems ************)
@@ -86,22 +169,21 @@
fun add_fixdefs eqs thy =
let
val (lhss,rhss) = ListPair.unzip (map dest_eqs eqs);
- val fixpoint = %%:@{const_name fix}`lambda_ctuple lhss (mk_ctuple rhss);
+ val fixpoint = mk_fix (lambda_ctuple lhss (mk_ctuple rhss));
fun one_def (l as Const(n,T)) r =
let val b = Sign.base_name n in (b, (b^"_def", l == r)) end
| one_def _ _ = fixrec_err "fixdefs: lhs not of correct form";
fun defs [] _ = []
| defs (l::[]) r = [one_def l r]
- | defs (l::ls) r = one_def l (%%:@{const_name cfst}`r) :: defs ls (%%:@{const_name csnd}`r);
- val (names, pre_fixdefs) = ListPair.unzip (defs lhss fixpoint);
+ | defs (l::ls) r = one_def l (mk_cfst r) :: defs ls (mk_csnd r);
+ val (names, fixdefs) = ListPair.unzip (defs lhss fixpoint);
- val fixdefs = map (apsnd (legacy_infer_prop thy)) pre_fixdefs;
val (fixdef_thms, thy') =
PureThy.add_defs false (map (Thm.no_attributes o apfst Binding.name) fixdefs) thy;
val ctuple_fixdef_thm = foldr1 (fn (x,y) => @{thm cpair_equalI} OF [x,y]) fixdef_thms;
- val ctuple_unfold = legacy_infer_term thy' (mk_trp (mk_ctuple lhss === mk_ctuple rhss));
+ val ctuple_unfold = mk_trp (mk_ctuple lhss === mk_ctuple rhss);
val ctuple_unfold_thm = Goal.prove_global thy' [] [] ctuple_unfold
(fn _ => EVERY [rtac (ctuple_fixdef_thm RS fix_eq2 RS trans) 1,
simp_tac (simpset_of thy') 1]);
@@ -158,10 +240,10 @@
fun result_type (Type(@{type_name "->"},[_,T])) (x::xs) = result_type T xs
| result_type T _ = T;
val v = Free(n, result_type T vs);
- val m = match_name c;
+ val m = Const(match_name c, matchT T);
val k = lambda_ctuple vs rhs;
in
- (%%:@{const_name Fixrec.bind}`(%%:m`v)`k, v, n::taken)
+ (mk_bind (m`v, k), v, n::taken)
end
| Free(n,_) => fixrec_err ("expected constructor, found free variable " ^ quote n)
| _ => fixrec_err "pre_build: invalid pattern";
@@ -175,13 +257,13 @@
| Const(@{const_name Rep_CFun}, _)$f$x =>
let val (rhs', v, taken') = pre_build match_name x rhs [] taken;
in building match_name f rhs' (v::vs) taken' end
- | Const(name,_) => (name, length vs, big_lambdas vs rhs)
+ | Const(name,_) => (pat, length vs, big_lambdas vs rhs)
| _ => fixrec_err "function is not declared as constant in theory";
fun match_eq match_name eq =
let val (lhs,rhs) = dest_eqs eq;
in
- building match_name lhs (%%:@{const_name Fixrec.return}`rhs) []
+ building match_name lhs (mk_return rhs) []
(add_terms [eq] [])
end;
@@ -189,15 +271,19 @@
(* also applies "run" to the result! *)
fun fatbar arity ms =
let
+ fun LAM_Ts 0 t = ([], Term.fastype_of t)
+ | LAM_Ts n (_ $ Abs(_,T,t)) =
+ let val (Ts, U) = LAM_Ts (n-1) t in (T::Ts, U) end
+ | LAM_Ts _ _ = fixrec_err "fatbar: internal error, not enough LAMs";
fun unLAM 0 t = t
| unLAM n (_$Abs(_,_,t)) = unLAM (n-1) t
| unLAM _ _ = fixrec_err "fatbar: internal error, not enough LAMs";
- fun reLAM 0 t = t
- | reLAM n t = reLAM (n-1) (%%:@{const_name Abs_CFun} $ Abs("",dummyT,t));
- fun mplus (x,y) = %%:@{const_name Fixrec.mplus}`x`y;
- val msum = foldr1 mplus (map (unLAM arity) ms);
+ fun reLAM ([], U) t = t
+ | reLAM (T::Ts, U) t = reLAM (Ts, T ->> U) (cabs_const(T,U)$Abs("",T,t));
+ val msum = foldr1 mk_mplus (map (unLAM arity) ms);
+ val (Ts, U) = LAM_Ts arity (hd ms)
in
- reLAM arity (%%:@{const_name Fixrec.run}`msum)
+ reLAM (rev Ts, dest_maybeT U) (mk_run msum)
end;
fun unzip3 [] = ([],[],[])
@@ -215,7 +301,7 @@
else fixrec_err "all equations in block must have the same arity";
val rhs = fatbar arity mats;
in
- mk_trp (%%:cname === rhs)
+ mk_trp (cname === rhs)
end;
(*************************************************************************)
@@ -258,7 +344,7 @@
val pattern_blocks = unconcat lengths (map Logic.strip_imp_concl eqn_ts');
val compiled_ts =
- map (legacy_infer_term thy o compile_pats match_name) pattern_blocks;
+ map (compile_pats match_name) pattern_blocks;
val (thy', cnames, fixdef_thms, unfold_thms) = add_fixdefs compiled_ts thy;
in
if strict then let (* only prove simp rules if strict = true *)