(* Title: HOLCF/Tools/fixrec_package.ML
Author: Amber Telfer and Brian Huffman
Recursive function definition package for HOLCF.
*)
signature FIXREC_PACKAGE =
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
val add_fixpat_i: (binding * attribute list) * term list -> theory -> theory
val add_matchers: (string * string) list -> theory -> theory
val setup: theory -> theory
end;
structure FixrecPackage: FIXREC_PACKAGE =
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);
fun legacy_infer_prop thy t = legacy_infer_term thy (TypeInfer.constrain propT t);
val fix_eq2 = @{thm fix_eq2};
val def_fix_ind = @{thm def_fix_ind};
fun fixrec_err s = error ("fixrec definition error:\n" ^ s);
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 *)
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;
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;
(* splits a cterm into the right and lefthand sides of equality *)
fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t);
(* similar to Thm.head_of, but for continuous application *)
fun chead_of (Const(@{const_name Rep_CFun},_)$f$t) = chead_of f
| chead_of u = u;
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 =
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 (Free("unit", HOLogic.unitT)) rhs
| lambda_ctuple (v::[]) rhs = big_lambda v rhs
| lambda_ctuple (v::vs) rhs =
mk_csplit (big_lambda v (lambda_ctuple vs rhs));
(* builds the expression <v1,v2,..,vn> *)
fun mk_ctuple [] = @{term "UU::unit"}
| mk_ctuple (t::[]) = t
| 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 ************)
(*************************************************************************)
fun add_fixdefs eqs thy =
let
val (lhss,rhss) = ListPair.unzip (map dest_eqs eqs);
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 (mk_cfst r) :: defs ls (mk_csnd r);
val (names, fixdefs) = ListPair.unzip (defs lhss fixpoint);
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 = 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]);
val ctuple_induct_thm =
(space_implode "_" names ^ "_induct", ctuple_fixdef_thm RS def_fix_ind);
fun unfolds [] thm = []
| unfolds (n::[]) thm = [(n^"_unfold", thm)]
| unfolds (n::ns) thm = let
val thmL = thm RS @{thm cpair_eqD1};
val thmR = thm RS @{thm cpair_eqD2};
in (n^"_unfold", thmL) :: unfolds ns thmR end;
val unfold_thms = unfolds names ctuple_unfold_thm;
val thms = ctuple_induct_thm :: unfold_thms;
val (_, thy'') = PureThy.add_thms (map (Thm.no_attributes o apfst Binding.name) thms) thy';
in
(thy'', names, fixdef_thms, map snd unfold_thms)
end;
(*************************************************************************)
(*********** monadic notation and pattern matching compilation ***********)
(*************************************************************************)
structure FixrecMatchData = TheoryDataFun (
type T = string Symtab.table;
val empty = Symtab.empty;
val copy = I;
val extend = I;
fun merge _ tabs : T = Symtab.merge (K true) tabs;
);
(* associate match functions with pattern constants *)
fun add_matchers ms = FixrecMatchData.map (fold Symtab.update ms);
fun add_names (Const(a,_), bs) = insert (op =) (Sign.base_name a) bs
| add_names (Free(a,_) , bs) = insert (op =) a bs
| add_names (f $ u , bs) = add_names (f, add_names(u, bs))
| add_names (Abs(a,_,t), bs) = add_names (t, insert (op =) a bs)
| add_names (_ , bs) = bs;
fun add_terms ts xs = foldr add_names xs ts;
(* builds a monadic term for matching a constructor pattern *)
fun pre_build match_name pat rhs vs taken =
case pat of
Const(@{const_name Rep_CFun},_)$f$(v as Free(n,T)) =>
pre_build match_name f rhs (v::vs) taken
| Const(@{const_name Rep_CFun},_)$f$x =>
let val (rhs', v, taken') = pre_build match_name x rhs [] taken;
in pre_build match_name f rhs' (v::vs) taken' end
| Const(c,T) =>
let
val n = Name.variant taken "v";
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 = Const(match_name c, matchT T);
val k = lambda_ctuple vs rhs;
in
(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";
(* builds a monadic term for matching a function definition pattern *)
(* returns (name, arity, matcher) *)
fun building match_name pat rhs vs taken =
case pat of
Const(@{const_name Rep_CFun}, _)$f$(v as Free(n,T)) =>
building match_name f rhs (v::vs) taken
| 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,_) => (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 (mk_return rhs) []
(add_terms [eq] [])
end;
(* returns the sum (using +++) of the terms in ms *)
(* 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 (_$Abs(_,_,t)) = unLAM (n-1) t
| unLAM _ _ = fixrec_err "fatbar: internal error, not enough LAMs";
fun reLAM ([], U) t = t
| reLAM (T::Ts, U) t = reLAM (Ts, T ->> U) (cabs_const(T,U)$Abs("",T,t));
val msum = foldr1 mk_mplus (map (unLAM arity) ms);
val (Ts, U) = LAM_Ts arity (hd ms)
in
reLAM (rev Ts, dest_maybeT U) (mk_run msum)
end;
fun unzip3 [] = ([],[],[])
| unzip3 ((x,y,z)::ts) =
let val (xs,ys,zs) = unzip3 ts
in (x::xs, y::ys, z::zs) end;
(* this is the pattern-matching compiler function *)
fun compile_pats match_name eqs =
let
val ((n::names),(a::arities),mats) = unzip3 (map (match_eq match_name) eqs);
val cname = if forall (fn x => n=x) names then n
else fixrec_err "all equations in block must define the same function";
val arity = if forall (fn x => a=x) arities then a
else fixrec_err "all equations in block must have the same arity";
val rhs = fatbar arity mats;
in
mk_trp (cname === rhs)
end;
(*************************************************************************)
(********************** Proving associated theorems **********************)
(*************************************************************************)
(* proves a block of pattern matching equations as theorems, using unfold *)
fun make_simps thy (unfold_thm, eqns) =
let
val tacs = [rtac (unfold_thm RS @{thm ssubst_lhs}) 1, asm_simp_tac (simpset_of thy) 1];
fun prove_term t = Goal.prove_global thy [] [] t (K (EVERY tacs));
fun prove_eqn ((name, eqn_t), atts) = ((name, prove_term eqn_t), atts);
in
map prove_eqn eqns
end;
(*************************************************************************)
(************************* Main fixrec function **************************)
(*************************************************************************)
fun gen_add_fixrec prep_prop prep_attrib strict blocks thy =
let
val eqns = List.concat blocks;
val lengths = map length blocks;
val ((bindings, srcss), strings) = apfst split_list (split_list eqns);
val names = map Binding.base_name bindings;
val atts = map (map (prep_attrib thy)) srcss;
val eqn_ts = map (prep_prop thy) strings;
val rec_ts = map (fn eq => chead_of (fst (dest_eqs (Logic.strip_imp_concl eq)))
handle TERM _ => fixrec_eq_err thy "not a proper equation" eq) eqn_ts;
val (_, eqn_ts') = OldPrimrecPackage.unify_consts thy rec_ts eqn_ts;
fun unconcat [] _ = []
| unconcat (n::ns) xs = List.take (xs,n) :: unconcat ns (List.drop (xs,n));
val matcher_tab = FixrecMatchData.get thy;
fun match_name c =
case Symtab.lookup matcher_tab c of SOME m => m
| NONE => fixrec_err ("unknown pattern constructor: " ^ c);
val pattern_blocks = unconcat lengths (map Logic.strip_imp_concl eqn_ts');
val compiled_ts =
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 *)
val eqn_blocks = unconcat lengths ((names ~~ eqn_ts') ~~ atts);
val simps = maps (make_simps thy') (unfold_thms ~~ eqn_blocks);
val (simp_thms, thy'') = PureThy.add_thms ((map o apfst o apfst) Binding.name simps) thy';
val simp_names = map (fn name => name^"_simps") cnames;
val simp_attribute = rpair [Simplifier.simp_add];
val simps' = map simp_attribute (simp_names ~~ unconcat lengths simp_thms);
in
(snd o PureThy.add_thmss ((map o apfst o apfst) Binding.name simps')) thy''
end
else thy'
end;
val add_fixrec = gen_add_fixrec Syntax.read_prop_global Attrib.attribute;
val add_fixrec_i = gen_add_fixrec Sign.cert_prop (K I);
(*************************************************************************)
(******************************** Fixpat *********************************)
(*************************************************************************)
fun fix_pat thy t =
let
val T = fastype_of t;
val eq = mk_trp (HOLogic.eq_const T $ t $ Var (("x",0),T));
val cname = case chead_of t of Const(c,_) => c | _ =>
fixrec_err "function is not declared as constant in theory";
val unfold_thm = PureThy.get_thm thy (cname^"_unfold");
val simp = Goal.prove_global thy [] [] eq
(fn _ => EVERY [stac unfold_thm 1, simp_tac (simpset_of thy) 1]);
in simp end;
fun gen_add_fixpat prep_term prep_attrib ((name, srcs), strings) thy =
let
val atts = map (prep_attrib thy) srcs;
val ts = map (prep_term thy) strings;
val simps = map (fix_pat thy) ts;
in
(snd o PureThy.add_thmss [((name, simps), atts)]) thy
end;
val add_fixpat = gen_add_fixpat Syntax.read_term_global Attrib.attribute;
val add_fixpat_i = gen_add_fixpat Sign.cert_term (K I);
(*************************************************************************)
(******************************** Parsers ********************************)
(*************************************************************************)
local structure P = OuterParse and K = OuterKeyword in
val fixrec_eqn = SpecParse.opt_thm_name ":" -- P.prop;
val fixrec_strict = P.opt_keyword "permissive" >> not;
val fixrec_decl = fixrec_strict -- P.and_list1 (Scan.repeat1 fixrec_eqn);
(* this builds a parser for a new keyword, fixrec, whose functionality
is defined by add_fixrec *)
val _ =
OuterSyntax.command "fixrec" "define recursive functions (HOLCF)" K.thy_decl
(fixrec_decl >> (Toplevel.theory o uncurry add_fixrec));
(* fixpat parser *)
val fixpat_decl = SpecParse.opt_thm_name ":" -- Scan.repeat1 P.prop;
val _ =
OuterSyntax.command "fixpat" "define rewrites for fixrec functions" K.thy_decl
(fixpat_decl >> (Toplevel.theory o add_fixpat));
end; (* local structure *)
val setup = FixrecMatchData.init;
end;