author | huffman |
Mon, 22 Mar 2010 14:44:37 -0700 | |
changeset 35903 | 0b43ff2d2e91 |
parent 35780 | 98fd7910f70a |
child 36628 | 1a251f69e96b |
permissions | -rw-r--r-- |
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(* Title: HOLCF/Tools/fixrec.ML |
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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 = |
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sig |
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val add_fixrec: bool -> (binding * typ option * mixfix) list |
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-> (Attrib.binding * term) list -> local_theory -> local_theory |
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val add_fixrec_cmd: bool -> (binding * string option * mixfix) list |
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-> (Attrib.binding * string) list -> local_theory -> local_theory |
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val add_fixpat: Thm.binding * term list -> theory -> theory |
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val add_fixpat_cmd: Attrib.binding * string list -> theory -> theory |
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val add_matchers: (string * string) list -> theory -> theory |
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val fixrec_simp_add: attribute |
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val fixrec_simp_del: attribute |
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val fixrec_simp_tac: Proof.context -> int -> tactic |
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val setup: theory -> theory |
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end; |
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structure Fixrec :> FIXREC = |
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struct |
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open HOLCF_Library; |
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infixr 6 ->>; |
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infix -->>; |
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infix 9 `; |
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val def_cont_fix_eq = @{thm def_cont_fix_eq}; |
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val def_cont_fix_ind = @{thm def_cont_fix_ind}; |
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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 (Syntax.string_of_term_global thy eq)); |
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(*************************************************************************) |
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(***************************** building types ****************************) |
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(*************************************************************************) |
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local |
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fun binder_cfun (Type(@{type_name cfun},[T, U])) = T :: binder_cfun U |
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| binder_cfun (Type(@{type_name "fun"},[T, U])) = T :: binder_cfun U |
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| binder_cfun _ = []; |
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fun body_cfun (Type(@{type_name cfun},[T, U])) = body_cfun U |
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| body_cfun (Type(@{type_name "fun"},[T, U])) = body_cfun U |
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| body_cfun T = T; |
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fun strip_cfun T : typ list * typ = |
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(binder_cfun T, body_cfun T); |
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fun matcherT (T, U) = |
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body_cfun T ->> (binder_cfun T -->> U) ->> U; |
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end |
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(*************************************************************************) |
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(***************************** building terms ****************************) |
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(*************************************************************************) |
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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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(* similar to Thm.head_of, but for continuous application *) |
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fun chead_of (Const(@{const_name Rep_CFun},_)$f$t) = chead_of f |
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| chead_of u = u; |
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infix 0 ==; val (op ==) = Logic.mk_equals; |
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infix 1 ===; val (op ===) = HOLogic.mk_eq; |
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fun mk_mplus (t, u) = |
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let val mT = Term.fastype_of t |
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in Const(@{const_name Fixrec.mplus}, mT ->> mT ->> mT) ` t ` u end; |
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fun mk_run t = |
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let val mT = Term.fastype_of t |
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val T = dest_matchT mT |
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in Const(@{const_name Fixrec.run}, mT ->> T) ` t end; |
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(*************************************************************************) |
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(************* fixed-point definitions and unfolding theorems ************) |
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(*************************************************************************) |
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structure FixrecUnfoldData = Generic_Data |
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( |
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type T = thm Symtab.table; |
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val empty = Symtab.empty; |
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val extend = I; |
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fun merge data : T = Symtab.merge (K true) data; |
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); |
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local |
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fun name_of (Const (n, T)) = n |
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| name_of (Free (n, T)) = n |
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| name_of t = raise TERM ("Fixrec.add_unfold: lhs not a constant", [t]); |
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val lhs_name = |
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name_of o head_of o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of; |
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in |
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val add_unfold : attribute = |
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Thm.declaration_attribute |
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(fn th => FixrecUnfoldData.map (Symtab.insert (K true) (lhs_name th, th))); |
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end |
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fun add_fixdefs |
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(fixes : ((binding * typ) * mixfix) list) |
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(spec : (Attrib.binding * term) list) |
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(lthy : local_theory) = |
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let |
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val thy = ProofContext.theory_of lthy; |
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val names = map (Binding.name_of o fst o fst) fixes; |
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val all_names = space_implode "_" names; |
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val (lhss, rhss) = ListPair.unzip (map (dest_eqs o snd) spec); |
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val functional = lambda_tuple lhss (mk_tuple rhss); |
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val fixpoint = mk_fix (mk_cabs functional); |
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val cont_thm = |
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Goal.prove lthy [] [] (mk_trp (mk_cont functional)) |
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(K (simp_tac (simpset_of lthy) 1)); |
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fun one_def (l as Free(n,_)) r = |
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let val b = Long_Name.base_name n |
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in ((Binding.name (b^"_def"), []), 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 (mk_fst r) :: defs ls (mk_snd r); |
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val fixdefs = defs lhss fixpoint; |
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val (fixdef_thms : (term * (string * thm)) list, lthy) = lthy |
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|> fold_map Local_Theory.define (map (apfst fst) fixes ~~ fixdefs); |
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fun pair_equalI (thm1, thm2) = @{thm Pair_equalI} OF [thm1, thm2]; |
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val tuple_fixdef_thm = foldr1 pair_equalI (map (snd o snd) fixdef_thms); |
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val P = Var (("P", 0), map Term.fastype_of lhss ---> HOLogic.boolT); |
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val predicate = lambda_tuple lhss (list_comb (P, lhss)); |
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val tuple_induct_thm = (def_cont_fix_ind OF [tuple_fixdef_thm, cont_thm]) |
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|> Drule.instantiate' [] [SOME (Thm.cterm_of thy predicate)] |
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|> Local_Defs.unfold lthy @{thms split_paired_all split_conv split_strict}; |
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val tuple_unfold_thm = (def_cont_fix_eq OF [tuple_fixdef_thm, cont_thm]) |
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|> Local_Defs.unfold lthy @{thms split_conv}; |
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fun unfolds [] thm = [] |
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| unfolds (n::[]) thm = [(n, thm)] |
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| unfolds (n::ns) thm = let |
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val thmL = thm RS @{thm Pair_eqD1}; |
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val thmR = thm RS @{thm Pair_eqD2}; |
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in (n, thmL) :: unfolds ns thmR end; |
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val unfold_thms = unfolds names tuple_unfold_thm; |
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val induct_note : Attrib.binding * Thm.thm list = |
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let |
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val thm_name = Binding.qualify true all_names (Binding.name "induct"); |
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in |
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((thm_name, []), [tuple_induct_thm]) |
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end; |
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fun unfold_note (name, thm) : Attrib.binding * Thm.thm list = |
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let |
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val thm_name = Binding.qualify true name (Binding.name "unfold"); |
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val src = Attrib.internal (K add_unfold); |
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in |
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((thm_name, [src]), [thm]) |
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end; |
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val (thmss, lthy) = lthy |
33671 | 173 |
|> fold_map Local_Theory.note (induct_note :: map unfold_note unfold_thms); |
23152 | 174 |
in |
35772 | 175 |
(lthy, names, fixdef_thms, map snd unfold_thms) |
23152 | 176 |
end; |
177 |
||
178 |
(*************************************************************************) |
|
179 |
(*********** monadic notation and pattern matching compilation ***********) |
|
180 |
(*************************************************************************) |
|
181 |
||
33522 | 182 |
structure FixrecMatchData = Theory_Data |
183 |
( |
|
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type T = string Symtab.table; |
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val empty = Symtab.empty; |
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val extend = I; |
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fun merge data = Symtab.merge (K true) data; |
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); |
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189 |
|
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(* associate match functions with pattern constants *) |
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fun add_matchers ms = FixrecMatchData.map (fold Symtab.update ms); |
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192 |
|
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fun taken_names (t : term) : bstring list = |
194 |
let |
|
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fun taken (Const(a,_), bs) = insert (op =) (Long_Name.base_name a) bs |
30157 | 196 |
| taken (Free(a,_) , bs) = insert (op =) a bs |
197 |
| taken (f $ u , bs) = taken (f, taken (u, bs)) |
|
198 |
| taken (Abs(a,_,t), bs) = taken (t, insert (op =) a bs) |
|
199 |
| taken (_ , bs) = bs; |
|
200 |
in |
|
201 |
taken (t, []) |
|
202 |
end; |
|
23152 | 203 |
|
204 |
(* builds a monadic term for matching a constructor pattern *) |
|
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fun pre_build match_name pat rhs vs taken = |
23152 | 206 |
case pat of |
26045 | 207 |
Const(@{const_name Rep_CFun},_)$f$(v as Free(n,T)) => |
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pre_build match_name f rhs (v::vs) taken |
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| Const(@{const_name Rep_CFun},_)$f$x => |
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let val (rhs', v, taken') = pre_build match_name x rhs [] taken; |
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in pre_build match_name f rhs' (v::vs) taken' end |
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212 |
| f$(v as Free(n,T)) => |
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pre_build match_name f rhs (v::vs) taken |
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214 |
| f$x => |
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let val (rhs', v, taken') = pre_build match_name x rhs [] taken; |
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216 |
in pre_build match_name f rhs' (v::vs) taken' end |
23152 | 217 |
| Const(c,T) => |
218 |
let |
|
219 |
val n = Name.variant taken "v"; |
|
35525 | 220 |
fun result_type (Type(@{type_name cfun},[_,T])) (x::xs) = result_type T xs |
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| result_type (Type (@{type_name "fun"},[_,T])) (x::xs) = result_type T xs |
23152 | 222 |
| result_type T _ = T; |
223 |
val v = Free(n, result_type T vs); |
|
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val m = Const(match_name c, matcherT (T, fastype_of rhs)); |
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val k = big_lambdas vs rhs; |
23152 | 226 |
in |
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(m`v`k, v, n::taken) |
23152 | 228 |
end |
229 |
| Free(n,_) => fixrec_err ("expected constructor, found free variable " ^ quote n) |
|
230 |
| _ => fixrec_err "pre_build: invalid pattern"; |
|
231 |
||
232 |
(* builds a monadic term for matching a function definition pattern *) |
|
233 |
(* returns (name, arity, matcher) *) |
|
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fun building match_name pat rhs vs taken = |
23152 | 235 |
case pat of |
26045 | 236 |
Const(@{const_name Rep_CFun}, _)$f$(v as Free(n,T)) => |
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237 |
building match_name f rhs (v::vs) taken |
26045 | 238 |
| Const(@{const_name Rep_CFun}, _)$f$x => |
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239 |
let val (rhs', v, taken') = pre_build match_name x rhs [] taken; |
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in building match_name f rhs' (v::vs) taken' end |
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| Free(_,_) => ((pat, length vs), big_lambdas vs rhs) |
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| Const(_,_) => ((pat, length vs), big_lambdas vs rhs) |
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| _ => fixrec_err ("function is not declared as constant in theory: " |
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^ ML_Syntax.print_term pat); |
23152 | 245 |
|
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246 |
fun strip_alls t = |
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if Logic.is_all t then strip_alls (snd (Logic.dest_all t)) else t; |
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248 |
|
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249 |
fun match_eq match_name eq = |
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250 |
let |
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251 |
val (lhs,rhs) = dest_eqs (Logic.strip_imp_concl (strip_alls eq)); |
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252 |
in |
30157 | 253 |
building match_name lhs (mk_return rhs) [] (taken_names eq) |
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254 |
end; |
23152 | 255 |
|
256 |
(* returns the sum (using +++) of the terms in ms *) |
|
257 |
(* also applies "run" to the result! *) |
|
258 |
fun fatbar arity ms = |
|
259 |
let |
|
30132 | 260 |
fun LAM_Ts 0 t = ([], Term.fastype_of t) |
261 |
| LAM_Ts n (_ $ Abs(_,T,t)) = |
|
262 |
let val (Ts, U) = LAM_Ts (n-1) t in (T::Ts, U) end |
|
263 |
| LAM_Ts _ _ = fixrec_err "fatbar: internal error, not enough LAMs"; |
|
23152 | 264 |
fun unLAM 0 t = t |
265 |
| unLAM n (_$Abs(_,_,t)) = unLAM (n-1) t |
|
266 |
| unLAM _ _ = fixrec_err "fatbar: internal error, not enough LAMs"; |
|
30132 | 267 |
fun reLAM ([], U) t = t |
268 |
| reLAM (T::Ts, U) t = reLAM (Ts, T ->> U) (cabs_const(T,U)$Abs("",T,t)); |
|
269 |
val msum = foldr1 mk_mplus (map (unLAM arity) ms); |
|
270 |
val (Ts, U) = LAM_Ts arity (hd ms) |
|
23152 | 271 |
in |
35527 | 272 |
reLAM (rev Ts, dest_matchT U) (mk_run msum) |
23152 | 273 |
end; |
274 |
||
275 |
(* this is the pattern-matching compiler function *) |
|
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|
276 |
fun compile_pats match_name eqs = |
23152 | 277 |
let |
35903 | 278 |
val ((names, arities), mats) = |
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279 |
apfst ListPair.unzip (ListPair.unzip (map (match_eq match_name) eqs)); |
35903 | 280 |
val cname = |
281 |
case distinct (op =) names of |
|
282 |
[n] => n |
|
283 |
| _ => fixrec_err "all equations in block must define the same function"; |
|
284 |
val arity = |
|
285 |
case distinct (op =) arities of |
|
286 |
[a] => a |
|
287 |
| _ => fixrec_err "all equations in block must have the same arity"; |
|
23152 | 288 |
val rhs = fatbar arity mats; |
289 |
in |
|
30132 | 290 |
mk_trp (cname === rhs) |
23152 | 291 |
end; |
292 |
||
293 |
(*************************************************************************) |
|
294 |
(********************** Proving associated theorems **********************) |
|
295 |
(*************************************************************************) |
|
296 |
||
33519 | 297 |
structure FixrecSimpData = Generic_Data |
298 |
( |
|
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299 |
type T = simpset; |
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300 |
val empty = |
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|
301 |
HOL_basic_ss |
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|
302 |
addsimps simp_thms |
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|
303 |
addsimps [@{thm beta_cfun}] |
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|
304 |
addsimprocs [@{simproc cont_proc}]; |
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|
305 |
val extend = I; |
33519 | 306 |
val merge = merge_ss; |
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|
307 |
); |
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|
308 |
|
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|
309 |
fun fixrec_simp_tac ctxt = |
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|
310 |
let |
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|
311 |
val tab = FixrecUnfoldData.get (Context.Proof ctxt); |
35780
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|
312 |
val ss = Simplifier.context ctxt (FixrecSimpData.get (Context.Proof ctxt)); |
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|
313 |
fun concl t = |
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|
314 |
if Logic.is_all t then concl (snd (Logic.dest_all t)) |
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|
315 |
else HOLogic.dest_Trueprop (Logic.strip_imp_concl t); |
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|
316 |
fun tac (t, i) = |
33430 | 317 |
let |
35903 | 318 |
val (c, T) = |
319 |
(dest_Const o head_of o chead_of o fst o HOLogic.dest_eq o concl) t; |
|
33430 | 320 |
val unfold_thm = the (Symtab.lookup tab c); |
321 |
val rule = unfold_thm RS @{thm ssubst_lhs}; |
|
322 |
in |
|
323 |
CHANGED (rtac rule i THEN asm_simp_tac ss i) |
|
324 |
end |
|
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|
325 |
in |
33505 | 326 |
SUBGOAL (fn ti => the_default no_tac (try tac ti)) |
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|
327 |
end; |
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|
328 |
|
33442 | 329 |
val fixrec_simp_add : attribute = |
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|
330 |
Thm.declaration_attribute |
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|
331 |
(fn th => FixrecSimpData.map (fn ss => ss addsimps [th])); |
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|
332 |
|
33442 | 333 |
val fixrec_simp_del : attribute = |
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|
334 |
Thm.declaration_attribute |
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|
335 |
(fn th => FixrecSimpData.map (fn ss => ss delsimps [th])); |
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|
336 |
|
23152 | 337 |
(* proves a block of pattern matching equations as theorems, using unfold *) |
32149
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|
338 |
fun make_simps ctxt (unfold_thm, eqns : (Attrib.binding * term) list) = |
23152 | 339 |
let |
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|
340 |
val tacs = |
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|
341 |
[rtac (unfold_thm RS @{thm ssubst_lhs}) 1, |
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|
342 |
asm_simp_tac (simpset_of ctxt) 1]; |
ef59550a55d3
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|
343 |
fun prove_term t = Goal.prove ctxt [] [] t (K (EVERY tacs)); |
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|
344 |
fun prove_eqn (bind, eqn_t) = (bind, prove_term eqn_t); |
23152 | 345 |
in |
346 |
map prove_eqn eqns |
|
347 |
end; |
|
348 |
||
349 |
(*************************************************************************) |
|
350 |
(************************* Main fixrec function **************************) |
|
351 |
(*************************************************************************) |
|
352 |
||
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|
353 |
local |
31738
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|
354 |
(* code adapted from HOL/Tools/primrec.ML *) |
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|
355 |
|
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|
356 |
fun gen_fixrec |
30485 | 357 |
prep_spec |
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|
358 |
(strict : bool) |
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|
359 |
raw_fixes |
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|
360 |
raw_spec |
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|
361 |
(lthy : local_theory) = |
23152 | 362 |
let |
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|
363 |
val (fixes : ((binding * typ) * mixfix) list, |
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|
364 |
spec : (Attrib.binding * term) list) = |
30485 | 365 |
fst (prep_spec raw_fixes raw_spec lthy); |
30158
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|
366 |
val chead_of_spec = |
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|
367 |
chead_of o fst o dest_eqs o Logic.strip_imp_concl o strip_alls o snd; |
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|
368 |
fun name_of (Free (n, _)) = n |
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|
369 |
| name_of t = fixrec_err ("unknown term"); |
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|
370 |
val all_names = map (name_of o chead_of_spec) spec; |
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val names = distinct (op =) all_names; |
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372 |
fun block_of_name n = |
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373 |
map_filter |
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(fn (m,eq) => if m = n then SOME eq else NONE) |
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(all_names ~~ spec); |
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val blocks = map block_of_name names; |
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377 |
|
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378 |
val matcher_tab = FixrecMatchData.get (ProofContext.theory_of lthy); |
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fun match_name c = |
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case Symtab.lookup matcher_tab c of SOME m => m |
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| NONE => fixrec_err ("unknown pattern constructor: " ^ c); |
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382 |
|
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383 |
val matches = map (compile_pats match_name) (map (map snd) blocks); |
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384 |
val spec' = map (pair Attrib.empty_binding) matches; |
35772 | 385 |
val (lthy, cnames, fixdef_thms, unfold_thms) = |
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386 |
add_fixdefs fixes spec' lthy; |
23152 | 387 |
in |
388 |
if strict then let (* only prove simp rules if strict = true *) |
|
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389 |
val simps : (Attrib.binding * thm) list list = |
35772 | 390 |
map (make_simps lthy) (unfold_thms ~~ blocks); |
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fun mk_bind n : Attrib.binding = |
35769 | 392 |
(Binding.qualify true n (Binding.name "simps"), |
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[Attrib.internal (K Simplifier.simp_add)]); |
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val simps1 : (Attrib.binding * thm list) list = |
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map (fn (n,xs) => (mk_bind n, map snd xs)) (names ~~ simps); |
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396 |
val simps2 : (Attrib.binding * thm list) list = |
32952 | 397 |
map (apsnd (fn thm => [thm])) (flat simps); |
35772 | 398 |
val (_, lthy) = lthy |
33671 | 399 |
|> fold_map Local_Theory.note (simps1 @ simps2); |
23152 | 400 |
in |
35772 | 401 |
lthy |
23152 | 402 |
end |
35772 | 403 |
else lthy |
23152 | 404 |
end; |
405 |
||
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406 |
in |
23152 | 407 |
|
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408 |
val add_fixrec = gen_fixrec Specification.check_spec; |
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val add_fixrec_cmd = gen_fixrec Specification.read_spec; |
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410 |
|
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411 |
end; (* local *) |
23152 | 412 |
|
413 |
(*************************************************************************) |
|
414 |
(******************************** Fixpat *********************************) |
|
415 |
(*************************************************************************) |
|
416 |
||
417 |
fun fix_pat thy t = |
|
418 |
let |
|
419 |
val T = fastype_of t; |
|
420 |
val eq = mk_trp (HOLogic.eq_const T $ t $ Var (("x",0),T)); |
|
421 |
val cname = case chead_of t of Const(c,_) => c | _ => |
|
422 |
fixrec_err "function is not declared as constant in theory"; |
|
35769 | 423 |
val unfold_thm = PureThy.get_thm thy (cname^".unfold"); |
23152 | 424 |
val simp = Goal.prove_global thy [] [] eq |
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425 |
(fn _ => EVERY [stac unfold_thm 1, simp_tac (global_simpset_of thy) 1]); |
23152 | 426 |
in simp end; |
427 |
||
428 |
fun gen_add_fixpat prep_term prep_attrib ((name, srcs), strings) thy = |
|
429 |
let |
|
35779 | 430 |
val _ = legacy_feature "\"fixpat\"; prefer \"fixrec_simp\" method instead"; |
23152 | 431 |
val atts = map (prep_attrib thy) srcs; |
432 |
val ts = map (prep_term thy) strings; |
|
433 |
val simps = map (fix_pat thy) ts; |
|
434 |
in |
|
29585 | 435 |
(snd o PureThy.add_thmss [((name, simps), atts)]) thy |
23152 | 436 |
end; |
437 |
||
30485 | 438 |
val add_fixpat = gen_add_fixpat Sign.cert_term (K I); |
439 |
val add_fixpat_cmd = gen_add_fixpat Syntax.read_term_global Attrib.attribute; |
|
23152 | 440 |
|
441 |
||
442 |
(*************************************************************************) |
|
443 |
(******************************** Parsers ********************************) |
|
444 |
(*************************************************************************) |
|
445 |
||
446 |
local structure P = OuterParse and K = OuterKeyword in |
|
447 |
||
30485 | 448 |
val _ = OuterSyntax.local_theory "fixrec" "define recursive functions (HOLCF)" K.thy_decl |
449 |
((P.opt_keyword "permissive" >> not) -- P.fixes -- SpecParse.where_alt_specs |
|
450 |
>> (fn ((strict, fixes), specs) => add_fixrec_cmd strict fixes specs)); |
|
23152 | 451 |
|
30485 | 452 |
val _ = OuterSyntax.command "fixpat" "define rewrites for fixrec functions" K.thy_decl |
453 |
(SpecParse.specs >> (Toplevel.theory o add_fixpat_cmd)); |
|
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454 |
|
30485 | 455 |
end; |
23152 | 456 |
|
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|
457 |
val setup = |
33522 | 458 |
Attrib.setup @{binding fixrec_simp} |
33427 | 459 |
(Attrib.add_del fixrec_simp_add fixrec_simp_del) |
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460 |
"declaration of fixrec simp rule" |
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461 |
#> Method.setup @{binding fixrec_simp} |
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462 |
(Scan.succeed (SIMPLE_METHOD' o fixrec_simp_tac)) |
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|
463 |
"pattern prover for fixrec constants"; |
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464 |
|
24867 | 465 |
end; |