author | haftmann |
Tue, 06 Dec 2005 09:04:09 +0100 | |
changeset 18358 | 0a733e11021a |
parent 17985 | d5d576b72371 |
child 18377 | 0e1d025d57b3 |
permissions | -rw-r--r-- |
16226 | 1 |
(* Title: HOLCF/fixrec_package.ML |
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ID: $Id$ |
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Author: Amber Telfer and Brian Huffman |
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Recursive function definition package for HOLCF. |
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*) |
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signature FIXREC_PACKAGE = |
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sig |
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val add_fixrec: bool -> ((string * Attrib.src list) * string) list list |
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-> theory -> theory |
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val add_fixrec_i: bool -> ((string * theory attribute list) * term) list list |
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-> theory -> theory |
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val add_fixpat: (string * Attrib.src list) * string list |
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-> theory -> theory |
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val add_fixpat_i: (string * theory attribute list) * term list |
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-> theory -> theory |
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end; |
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structure FixrecPackage: FIXREC_PACKAGE = |
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struct |
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fun fixrec_err s = error ("fixrec definition error:\n" ^ s); |
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fun fixrec_eq_err thy s eq = |
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fixrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq)); |
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(* ->> is taken from holcf_logic.ML *) |
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(* TODO: fix dependencies so we can import HOLCFLogic here *) |
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infixr 6 ->>; |
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fun S ->> T = Type ("Cfun.->",[S,T]); |
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(* extern_name is taken from domain/library.ML *) |
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fun extern_name con = case Symbol.explode con of |
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("o"::"p"::" "::rest) => implode rest |
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| _ => con; |
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val mk_trp = HOLogic.mk_Trueprop; |
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(* splits a cterm into the right and lefthand sides of equality *) |
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fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t); |
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(* |
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fun dest_eqs (Const ("==", _)$lhs$rhs) = (lhs, rhs) |
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| dest_eqs (Const ("Trueprop", _)$(Const ("op =", _)$lhs$rhs)) = (lhs,rhs) |
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| dest_eqs t = fixrec_err (Sign.string_of_term (sign_of (the_context())) t); |
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*) |
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(* similar to Thm.head_of, but for continuous application *) |
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fun chead_of (Const("Cfun.Rep_CFun",_)$f$t) = chead_of f |
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| chead_of u = u; |
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(* these are helpful functions copied from HOLCF/domain/library.ML *) |
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fun %: s = Free(s,dummyT); |
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fun %%: s = Const(s,dummyT); |
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infix 0 ==; fun S == T = %%:"==" $ S $ T; |
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infix 1 ===; fun S === T = %%:"op =" $ S $ T; |
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infix 9 ` ; fun f ` x = %%:"Cfun.Rep_CFun" $ f $ x; |
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(* infers the type of a term *) |
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(* similar to Theory.inferT_axm, but allows any type, not just propT *) |
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fun infer sg t = |
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fst (Sign.infer_types (Sign.pp sg) sg (K NONE) (K NONE) [] true ([t],dummyT)); |
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(* Similar to Term.lambda, but also allows abstraction over constants *) |
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fun lambda' (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) |
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| lambda' (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) |
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| lambda' (v as Const (x, T)) t = Abs (Sign.base_name x, T, abstract_over (v, t)) |
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| lambda' v t = raise TERM ("lambda'", [v, t]); |
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(* builds the expression (LAM v. rhs) *) |
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fun big_lambda v rhs = %%:"Cfun.Abs_CFun"$(lambda' v rhs); |
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(* builds the expression (LAM v1 v2 .. vn. rhs) *) |
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fun big_lambdas [] rhs = rhs |
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| big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs); |
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(* builds the expression (LAM <v1,v2,..,vn>. rhs) *) |
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fun lambda_ctuple [] rhs = big_lambda (%:"unit") rhs |
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| lambda_ctuple (v::[]) rhs = big_lambda v rhs |
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| lambda_ctuple (v::vs) rhs = |
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%%:"Cprod.csplit"`(big_lambda v (lambda_ctuple vs rhs)); |
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(* builds the expression <v1,v2,..,vn> *) |
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fun mk_ctuple [] = %%:"UU" |
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| mk_ctuple (t::[]) = t |
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| mk_ctuple (t::ts) = %%:"Cprod.cpair"`t`(mk_ctuple ts); |
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(*************************************************************************) |
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(************* fixed-point definitions and unfolding theorems ************) |
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(*************************************************************************) |
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fun add_fixdefs eqs thy = |
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let |
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val (lhss,rhss) = ListPair.unzip (map dest_eqs eqs); |
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val fixpoint = %%:"Fix.fix"`lambda_ctuple lhss (mk_ctuple rhss); |
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fun one_def (l as Const(n,T)) r = |
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let val b = Sign.base_name n in (b, (b^"_def", l == r)) end |
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| one_def _ _ = fixrec_err "fixdefs: lhs not of correct form"; |
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fun defs [] _ = [] |
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| defs (l::[]) r = [one_def l r] |
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| defs (l::ls) r = one_def l (%%:"Cprod.cfst"`r) :: defs ls (%%:"Cprod.csnd"`r); |
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val (names, pre_fixdefs) = ListPair.unzip (defs lhss fixpoint); |
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val fixdefs = map (inferT_axm thy) pre_fixdefs; |
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val (fixdef_thms, thy') = |
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PureThy.add_defs_i false (map Thm.no_attributes fixdefs) thy; |
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val ctuple_fixdef_thm = foldr1 (fn (x,y) => cpair_equalI OF [x,y]) fixdef_thms; |
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val ctuple_unfold = infer thy' (mk_trp (mk_ctuple lhss === mk_ctuple rhss)); |
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val ctuple_unfold_thm = standard (Goal.prove thy' [] [] ctuple_unfold |
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(fn _ => EVERY [rtac (ctuple_fixdef_thm RS fix_eq2 RS trans) 1, |
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simp_tac (simpset_of thy') 1])); |
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val ctuple_induct_thm = |
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(space_implode "_" names ^ "_induct", ctuple_fixdef_thm RS def_fix_ind); |
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fun unfolds [] thm = [] |
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| unfolds (n::[]) thm = [(n^"_unfold", thm)] |
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| unfolds (n::ns) thm = let |
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val thmL = thm RS cpair_eqD1; |
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val thmR = thm RS cpair_eqD2; |
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in (n^"_unfold", thmL) :: unfolds ns thmR end; |
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val unfold_thms = unfolds names ctuple_unfold_thm; |
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val thms = ctuple_induct_thm :: unfold_thms; |
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val (thy'', _) = PureThy.add_thms (map Thm.no_attributes thms) thy'; |
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in |
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(thy'', names, fixdef_thms, map snd unfold_thms) |
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end; |
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(*************************************************************************) |
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(*********** monadic notation and pattern matching compilation ***********) |
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(*************************************************************************) |
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fun add_names (Const(a,_), bs) = Sign.base_name a ins_string bs |
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| add_names (Free(a,_) , bs) = a ins_string bs |
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| add_names (f $ u , bs) = add_names (f, add_names(u, bs)) |
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| add_names (Abs(a,_,t), bs) = add_names (t, a ins_string bs) |
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| add_names (_ , bs) = bs; |
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fun add_terms ts xs = foldr add_names xs ts; |
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(* builds a monadic term for matching a constructor pattern *) |
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fun pre_build pat rhs vs taken = |
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case pat of |
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Const("Cfun.Rep_CFun",_)$f$(v as Free(n,T)) => |
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pre_build f rhs (v::vs) taken |
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| Const("Cfun.Rep_CFun",_)$f$x => |
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let val (rhs', v, taken') = pre_build x rhs [] taken; |
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in pre_build f rhs' (v::vs) taken' end |
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| Const(c,T) => |
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let |
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val n = variant taken "v"; |
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fun result_type (Type("Cfun.->",[_,T])) (x::xs) = result_type T xs |
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| result_type T _ = T; |
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val v = Free(n, result_type T vs); |
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val m = "match_"^(extern_name(Sign.base_name c)); |
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val k = lambda_ctuple vs rhs; |
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in |
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(%%:"Fixrec.bind"`(%%:m`v)`k, v, n::taken) |
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end |
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| Free(n,_) => fixrec_err ("expected constructor, found free variable " ^ quote n) |
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| _ => fixrec_err "pre_build: invalid pattern"; |
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(* builds a monadic term for matching a function definition pattern *) |
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(* returns (name, arity, matcher) *) |
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fun building pat rhs vs taken = |
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case pat of |
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Const("Cfun.Rep_CFun", _)$f$(v as Free(n,T)) => |
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building f rhs (v::vs) taken |
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| Const("Cfun.Rep_CFun", _)$f$x => |
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let val (rhs', v, taken') = pre_build x rhs [] taken; |
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in building f rhs' (v::vs) taken' end |
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| Const(name,_) => (name, length vs, big_lambdas vs rhs) |
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| _ => fixrec_err "function is not declared as constant in theory"; |
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fun match_eq eq = |
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let val (lhs,rhs) = dest_eqs eq; |
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in building lhs (%%:"Fixrec.return"`rhs) [] (add_terms [eq] []) end; |
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(* returns the sum (using +++) of the terms in ms *) |
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(* also applies "run" to the result! *) |
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fun fatbar arity ms = |
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let |
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fun unLAM 0 t = t |
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| unLAM n (_$Abs(_,_,t)) = unLAM (n-1) t |
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| unLAM _ _ = fixrec_err "fatbar: internal error, not enough LAMs"; |
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fun reLAM 0 t = t |
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| reLAM n t = reLAM (n-1) (%%:"Cfun.Abs_CFun" $ Abs("",dummyT,t)); |
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fun mplus (x,y) = %%:"Fixrec.mplus"`x`y; |
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val msum = foldr1 mplus (map (unLAM arity) ms); |
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in |
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reLAM arity (%%:"Fixrec.run"`msum) |
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end; |
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fun unzip3 [] = ([],[],[]) |
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| unzip3 ((x,y,z)::ts) = |
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let val (xs,ys,zs) = unzip3 ts |
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in (x::xs, y::ys, z::zs) end; |
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(* this is the pattern-matching compiler function *) |
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fun compile_pats eqs = |
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let |
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val ((n::names),(a::arities),mats) = unzip3 (map match_eq eqs); |
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val cname = if forall (fn x => n=x) names then n |
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else fixrec_err "all equations in block must define the same function"; |
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val arity = if forall (fn x => a=x) arities then a |
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else fixrec_err "all equations in block must have the same arity"; |
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val rhs = fatbar arity mats; |
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in |
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mk_trp (%%:cname === rhs) |
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end; |
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(*************************************************************************) |
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(********************** Proving associated theorems **********************) |
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(*************************************************************************) |
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(* proves a block of pattern matching equations as theorems, using unfold *) |
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fun make_simps thy (unfold_thm, eqns) = |
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let |
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val tacs = [rtac (unfold_thm RS ssubst_lhs) 1, asm_simp_tac (simpset_of thy) 1]; |
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fun prove_term t = standard (Goal.prove thy [] [] t (K (EVERY tacs))); |
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fun prove_eqn ((name, eqn_t), atts) = ((name, prove_term eqn_t), atts); |
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221 |
in |
16552 | 222 |
map prove_eqn eqns |
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end; |
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|
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(*************************************************************************) |
226 |
(************************* Main fixrec function **************************) |
|
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(*************************************************************************) |
|
16226 | 228 |
|
16552 | 229 |
fun gen_add_fixrec prep_prop prep_attrib strict blocks thy = |
16226 | 230 |
let |
16552 | 231 |
val eqns = List.concat blocks; |
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val lengths = map length blocks; |
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||
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val ((names, srcss), strings) = apfst split_list (split_list eqns); |
|
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val atts = map (map (prep_attrib thy)) srcss; |
|
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val eqn_ts = map (prep_prop thy) strings; |
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val rec_ts = map (fn eq => chead_of (fst (dest_eqs (Logic.strip_imp_concl eq))) |
|
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handle TERM _ => fixrec_eq_err thy "not a proper equation" eq) eqn_ts; |
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val (_, eqn_ts') = InductivePackage.unify_consts thy rec_ts eqn_ts; |
|
16552 | 240 |
|
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fun unconcat [] _ = [] |
|
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| unconcat (n::ns) xs = List.take (xs,n) :: unconcat ns (List.drop (xs,n)); |
|
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val pattern_blocks = unconcat lengths (map Logic.strip_imp_concl eqn_ts'); |
|
16628 | 244 |
val compiled_ts = map (infer thy o compile_pats) pattern_blocks; |
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val (thy', cnames, fixdef_thms, unfold_thms) = add_fixdefs compiled_ts thy; |
16226 | 246 |
in |
16552 | 247 |
if strict then let (* only prove simp rules if strict = true *) |
248 |
val eqn_blocks = unconcat lengths ((names ~~ eqn_ts') ~~ atts); |
|
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val simps = List.concat (map (make_simps thy') (unfold_thms ~~ eqn_blocks)); |
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val (thy'', simp_thms) = PureThy.add_thms simps thy'; |
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||
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val simp_names = map (fn name => name^"_simps") cnames; |
|
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val simp_attribute = rpair [Simplifier.simp_add_global]; |
|
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val simps' = map simp_attribute (simp_names ~~ unconcat lengths simp_thms); |
|
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in |
|
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(#1 o PureThy.add_thmss simps') thy'' |
|
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end |
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else thy' |
|
16226 | 259 |
end; |
260 |
||
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val add_fixrec = gen_add_fixrec Sign.read_prop Attrib.global_attribute; |
262 |
val add_fixrec_i = gen_add_fixrec Sign.cert_prop (K I); |
|
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||
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||
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(*************************************************************************) |
266 |
(******************************** Fixpat *********************************) |
|
267 |
(*************************************************************************) |
|
16226 | 268 |
|
16552 | 269 |
fun fix_pat thy t = |
16226 | 270 |
let |
16387 | 271 |
val T = fastype_of t; |
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val eq = mk_trp (HOLogic.eq_const T $ t $ Var (("x",0),T)); |
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val cname = case chead_of t of Const(c,_) => c | _ => |
16552 | 274 |
fixrec_err "function is not declared as constant in theory"; |
16488 | 275 |
val unfold_thm = PureThy.get_thm thy (Name (cname^"_unfold")); |
17985 | 276 |
val simp = standard (Goal.prove thy [] [] eq |
277 |
(fn _ => EVERY [stac unfold_thm 1, simp_tac (simpset_of thy) 1])); |
|
16552 | 278 |
in simp end; |
16226 | 279 |
|
16552 | 280 |
fun gen_add_fixpat prep_term prep_attrib ((name, srcs), strings) thy = |
16402 | 281 |
let |
16552 | 282 |
val atts = map (prep_attrib thy) srcs; |
283 |
val ts = map (prep_term thy) strings; |
|
284 |
val simps = map (fix_pat thy) ts; |
|
285 |
in |
|
286 |
(#1 o PureThy.add_thmss [((name, simps), atts)]) thy |
|
287 |
end; |
|
16226 | 288 |
|
16488 | 289 |
val add_fixpat = gen_add_fixpat Sign.read_term Attrib.global_attribute; |
290 |
val add_fixpat_i = gen_add_fixpat Sign.cert_term (K I); |
|
291 |
||
292 |
||
16387 | 293 |
(*************************************************************************) |
294 |
(******************************** Parsers ********************************) |
|
295 |
(*************************************************************************) |
|
16226 | 296 |
|
17057 | 297 |
local structure P = OuterParse and K = OuterKeyword in |
16226 | 298 |
|
16552 | 299 |
val fixrec_eqn = P.opt_thm_name ":" -- P.prop; |
300 |
||
16628 | 301 |
val fixrec_strict = P.opt_keyword "permissive" >> not; |
16552 | 302 |
|
303 |
val fixrec_decl = fixrec_strict -- P.and_list1 (Scan.repeat1 fixrec_eqn); |
|
16226 | 304 |
|
305 |
(* this builds a parser for a new keyword, fixrec, whose functionality |
|
306 |
is defined by add_fixrec *) |
|
307 |
val fixrecP = |
|
16402 | 308 |
OuterSyntax.command "fixrec" "define recursive functions (HOLCF)" K.thy_decl |
16552 | 309 |
(fixrec_decl >> (Toplevel.theory o uncurry add_fixrec)); |
16226 | 310 |
|
311 |
(* fixpat parser *) |
|
16552 | 312 |
val fixpat_decl = P.opt_thm_name ":" -- Scan.repeat1 P.prop; |
16226 | 313 |
|
314 |
val fixpatP = |
|
16402 | 315 |
OuterSyntax.command "fixpat" "define rewrites for fixrec functions" K.thy_decl |
16226 | 316 |
(fixpat_decl >> (Toplevel.theory o add_fixpat)); |
317 |
||
16552 | 318 |
val _ = OuterSyntax.add_parsers [fixrecP, fixpatP]; |
16226 | 319 |
|
320 |
end; (* local structure *) |
|
321 |
||
322 |
end; (* struct *) |