renamed Binding.name_pos to Binding.make, renamed Binding.base_name to Binding.name_of, renamed Binding.map_base to Binding.map_name, added mandatory flag to Binding.qualify;
minor tuning;
(* 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 -> (binding * string option * mixfix) list
-> (Attrib.binding * string) list -> local_theory -> local_theory
val add_fixrec_i: bool -> (binding * typ option * mixfix) list
-> (Attrib.binding * term) list -> local_theory -> local_theory
val add_fixpat: Attrib.binding * string list -> theory -> theory
val add_fixpat_i: Thm.binding * 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
(fixes : ((binding * typ) * mixfix) list)
(spec : (Attrib.binding * term) list)
(lthy : local_theory) =
let
val names = map (Binding.name_of o fst o fst) fixes;
val all_names = space_implode "_" names;
val (lhss,rhss) = ListPair.unzip (map (dest_eqs o snd) spec);
val fixpoint = mk_fix (lambda_ctuple lhss (mk_ctuple rhss));
fun one_def (l as Free(n,_)) r =
let val b = Sign.base_name n
in ((Binding.name (b^"_def"), []), 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 fixdefs = defs lhss fixpoint;
val define_all = fold_map (LocalTheory.define Thm.definitionK);
val (fixdef_thms : (term * (string * thm)) list, lthy') = lthy
|> define_all (map (apfst fst) fixes ~~ fixdefs);
fun cpair_equalI (thm1, thm2) = @{thm cpair_equalI} OF [thm1, thm2];
val ctuple_fixdef_thm = foldr1 cpair_equalI (map (snd o snd) fixdef_thms);
val ctuple_induct_thm = ctuple_fixdef_thm RS def_fix_ind;
val ctuple_unfold_thm =
Goal.prove lthy' [] [] (mk_trp (mk_ctuple lhss === mk_ctuple rhss))
(fn _ => EVERY [rtac (ctuple_fixdef_thm RS fix_eq2 RS trans) 1,
simp_tac (local_simpset_of lthy') 1]);
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;
fun mk_note (n, thm) = ((Binding.name n, []), [thm]);
val (thmss, lthy'') = lthy'
|> fold_map (LocalTheory.note Thm.theoremK o mk_note)
((all_names ^ "_induct", ctuple_induct_thm) :: unfold_thms);
in
(lthy'', 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 taken_names (t : term) : bstring list =
let
fun taken (Const(a,_), bs) = insert (op =) (Sign.base_name a) bs
| taken (Free(a,_) , bs) = insert (op =) a bs
| taken (f $ u , bs) = taken (f, taken (u, bs))
| taken (Abs(a,_,t), bs) = taken (t, insert (op =) a bs)
| taken (_ , bs) = bs;
in
taken (t, [])
end;
(* 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
| Free(_,_) => ((pat, length vs), big_lambdas vs rhs)
| Const(_,_) => ((pat, length vs), big_lambdas vs rhs)
| _ => fixrec_err ("function is not declared as constant in theory: "
^ ML_Syntax.print_term pat);
fun strip_alls t =
if Logic.is_all t then strip_alls (snd (Logic.dest_all t)) else t;
fun match_eq match_name eq =
let
val (lhs,rhs) = dest_eqs (Logic.strip_imp_concl (strip_alls eq));
in
building match_name lhs (mk_return rhs) [] (taken_names 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;
(* this is the pattern-matching compiler function *)
fun compile_pats match_name eqs =
let
val (((n::names),(a::arities)),mats) =
apfst ListPair.unzip (ListPair.unzip (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 lthy (unfold_thm, eqns : (Attrib.binding * term) list) =
let
val tacs =
[rtac (unfold_thm RS @{thm ssubst_lhs}) 1,
asm_simp_tac (local_simpset_of lthy) 1];
fun prove_term t = Goal.prove lthy [] [] t (K (EVERY tacs));
fun prove_eqn (bind, eqn_t) = (bind, prove_term eqn_t);
in
map prove_eqn eqns
end;
(*************************************************************************)
(************************* Main fixrec function **************************)
(*************************************************************************)
local
(* code adapted from HOL/Tools/primrec_package.ML *)
fun prepare_spec prep_spec ctxt raw_fixes raw_spec =
let
val ((fixes, spec), _) = prep_spec
raw_fixes (map (single o apsnd single) raw_spec) ctxt
in (fixes, map (apsnd the_single) spec) end;
fun gen_fixrec
(set_group : bool)
(prep_spec : (binding * 'a option * mixfix) list ->
(Attrib.binding * 'b list) list list ->
Proof.context ->
(((binding * typ) * mixfix) list * (Attrib.binding * term list) list)
* Proof.context
)
(strict : bool)
raw_fixes
raw_spec
(lthy : local_theory) =
let
val (fixes : ((binding * typ) * mixfix) list,
spec : (Attrib.binding * term) list) =
prepare_spec prep_spec lthy raw_fixes raw_spec;
val chead_of_spec =
chead_of o fst o dest_eqs o Logic.strip_imp_concl o strip_alls o snd;
fun name_of (Free (n, _)) = n
| name_of t = fixrec_err ("unknown term");
val all_names = map (name_of o chead_of_spec) spec;
val names = distinct (op =) all_names;
fun block_of_name n =
map_filter
(fn (m,eq) => if m = n then SOME eq else NONE)
(all_names ~~ spec);
val blocks = map block_of_name names;
val matcher_tab = FixrecMatchData.get (ProofContext.theory_of lthy);
fun match_name c =
case Symtab.lookup matcher_tab c of SOME m => m
| NONE => fixrec_err ("unknown pattern constructor: " ^ c);
val matches = map (compile_pats match_name) (map (map snd) blocks);
val spec' = map (pair Attrib.empty_binding) matches;
val (lthy', cnames, fixdef_thms, unfold_thms) =
add_fixdefs fixes spec' lthy;
in
if strict then let (* only prove simp rules if strict = true *)
val simps : (Attrib.binding * thm) list list =
map (make_simps lthy') (unfold_thms ~~ blocks);
fun mk_bind n : Attrib.binding =
(Binding.name (n ^ "_simps"),
[Attrib.internal (K Simplifier.simp_add)]);
val simps1 : (Attrib.binding * thm list) list =
map (fn (n,xs) => (mk_bind n, map snd xs)) (names ~~ simps);
val simps2 : (Attrib.binding * thm list) list =
map (apsnd (fn thm => [thm])) (List.concat simps);
val (_, lthy'') = lthy'
|> fold_map (LocalTheory.note Thm.theoremK) (simps1 @ simps2);
in
lthy''
end
else lthy'
end;
in
val add_fixrec_i = gen_fixrec false Specification.check_specification;
val add_fixrec = gen_fixrec true Specification.read_specification;
end; (* local *)
(*************************************************************************)
(******************************** 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
(* bool parser *)
val fixrec_strict = P.opt_keyword "permissive" >> not;
fun pipe_error t = P.!!! (Scan.fail_with (K
(cat_lines ["Equations must be separated by " ^ quote "|", quote t])));
(* (Attrib.binding * string) parser *)
val statement = SpecParse.opt_thm_name ":" -- P.prop --| Scan.ahead
((P.term :-- pipe_error) || Scan.succeed ("",""));
(* ((Attrib.binding * string) list) parser *)
val statements = P.enum1 "|" statement;
(* (((xstring option * bool) * (Binding.binding * string option * Mixfix.mixfix) list)
* (Attrib.binding * string) list) parser *)
val fixrec_decl =
P.opt_target -- fixrec_strict -- P.fixes --| P.$$$ "where" -- statements;
(* this builds a parser for a new keyword, fixrec, whose functionality
is defined by add_fixrec *)
val _ =
let
val desc = "define recursive functions (HOLCF)";
fun fixrec (((opt_target, strict), raw_fixes), raw_spec) =
Toplevel.local_theory opt_target (add_fixrec strict raw_fixes raw_spec);
in
OuterSyntax.command "fixrec" desc K.thy_decl (fixrec_decl >> fixrec)
end;
(* 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;