(* Title: HOLCF/Tools/fixrec_package.ML ID: $Id: fixrec_package.ML,v 1.7 2007/10/21 12:21:53 wenzelm Exp $ 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 -> ((string * Attrib.src list) * string) list list -> theory -> theory val add_fixrec_i: bool -> ((string * attribute list) * term) list list -> theory -> theory val add_fixpat: (string * Attrib.src list) * string list -> theory -> theory val add_fixpat_i: (string * attribute list) * term list -> theory -> theory end; structure FixrecPackage: FIXREC_PACKAGE = struct (* legacy type inference *) 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 (Sign.string_of_term thy eq)); (* ->> is taken from holcf_logic.ML *) (* TODO: fix dependencies so we can import HOLCFLogic here *) infixr 6 ->>; fun S ->> T = Type ("Cfun.->",[S,T]); (* extern_name is taken from domain/library.ML *) fun extern_name con = case Symbol.explode con of ("o"::"p"::" "::rest) => implode rest | _ => con; 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("Cfun.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 = %%:"Cfun.Rep_CFun" $ f $ x; (* builds the expression (LAM v. rhs) *) fun big_lambda v rhs = %%:"Cfun.Abs_CFun"$(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 | lambda_ctuple (v::[]) rhs = big_lambda v rhs | lambda_ctuple (v::vs) rhs = %%:"Cprod.csplit"`(big_lambda v (lambda_ctuple vs rhs)); (* builds the expression <v1,v2,..,vn> *) fun mk_ctuple [] = %%:"UU" | mk_ctuple (t::[]) = t | mk_ctuple (t::ts) = %%:"Cprod.cpair"`t`(mk_ctuple ts); (*************************************************************************) (************* fixed-point definitions and unfolding theorems ************) (*************************************************************************) fun add_fixdefs eqs thy = let val (lhss,rhss) = ListPair.unzip (map dest_eqs eqs); val fixpoint = %%:"Fix.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 (%%:"Cprod.cfst"`r) :: defs ls (%%:"Cprod.csnd"`r); val (names, pre_fixdefs) = ListPair.unzip (defs lhss fixpoint); val fixdefs = map (apsnd (legacy_infer_prop thy)) pre_fixdefs; val (fixdef_thms, thy') = PureThy.add_defs_i false (map Thm.no_attributes 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_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 thms) thy'; in (thy'', names, fixdef_thms, map snd unfold_thms) end; (*************************************************************************) (*********** monadic notation and pattern matching compilation ***********) (*************************************************************************) 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 pat rhs vs taken = case pat of Const("Cfun.Rep_CFun",_)$f$(v as Free(n,T)) => pre_build f rhs (v::vs) taken | Const("Cfun.Rep_CFun",_)$f$x => let val (rhs', v, taken') = pre_build x rhs [] taken; in pre_build f rhs' (v::vs) taken' end | Const(c,T) => let val n = Name.variant taken "v"; fun result_type (Type("Cfun.->",[_,T])) (x::xs) = result_type T xs | result_type T _ = T; val v = Free(n, result_type T vs); val m = "match_"^(extern_name(Sign.base_name c)); val k = lambda_ctuple vs rhs; in (%%:"Fixrec.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 pat rhs vs taken = case pat of Const("Cfun.Rep_CFun", _)$f$(v as Free(n,T)) => building f rhs (v::vs) taken | Const("Cfun.Rep_CFun", _)$f$x => let val (rhs', v, taken') = pre_build x rhs [] taken; in building f rhs' (v::vs) taken' end | Const(name,_) => (name, length vs, big_lambdas vs rhs) | _ => fixrec_err "function is not declared as constant in theory"; fun match_eq eq = let val (lhs,rhs) = dest_eqs eq; in building lhs (%%:"Fixrec.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 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) (%%:"Cfun.Abs_CFun" $ Abs("",dummyT,t)); fun mplus (x,y) = %%:"Fixrec.mplus"`x`y; val msum = foldr1 mplus (map (unLAM arity) ms); in reLAM arity (%%:"Fixrec.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 eqs = let val ((n::names),(a::arities),mats) = unzip3 (map match_eq 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 ((names, srcss), strings) = apfst split_list (split_list eqns); 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') = PrimrecPackage.unify_consts thy rec_ts eqn_ts; fun unconcat [] _ = [] | unconcat (n::ns) xs = List.take (xs,n) :: unconcat ns (List.drop (xs,n)); val pattern_blocks = unconcat lengths (map Logic.strip_imp_concl eqn_ts'); val compiled_ts = map (legacy_infer_term thy o compile_pats) 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 = List.concat (map (make_simps thy') (unfold_thms ~~ eqn_blocks)); val (simp_thms, thy'') = PureThy.add_thms 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 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 (Name (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; end;