author | wenzelm |
Fri, 10 Mar 2000 01:13:37 +0100 | |
changeset 8404 | 4b39358f9810 |
parent 8324 | df7dccddc3de |
child 8435 | 51a040fd2200 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/datatype_aux.ML |
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ID: $Id$ |
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Author: Stefan Berghofer |
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Copyright 1998 TU Muenchen |
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Auxiliary functions for defining datatypes |
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*) |
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signature DATATYPE_AUX = |
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sig |
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val quiet_mode : bool ref |
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val message : string -> unit |
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val foldl1 : ('a * 'a -> 'a) -> 'a list -> 'a |
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val add_path : bool -> string -> theory -> theory |
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val parent_path : bool -> theory -> theory |
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val store_thmss : string -> string list -> thm list list -> theory -> theory |
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val store_thms : string -> string list -> thm list -> theory -> theory |
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val split_conj_thm : thm -> thm list |
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val mk_conj : term list -> term |
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val mk_disj : term list -> term |
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val indtac : thm -> int -> tactic |
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val exh_tac : (string -> thm) -> int -> tactic |
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datatype simproc_dist = QuickAndDirty |
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| FewConstrs of thm list |
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| ManyConstrs of thm * simpset; |
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datatype dtyp = |
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DtTFree of string |
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| DtType of string * (dtyp list) |
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| DtRec of int; |
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type descr |
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type datatype_info |
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exception Datatype |
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val dtyp_of_typ : (string * string list) list -> typ -> dtyp |
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val mk_Free : string -> typ -> int -> term |
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val is_rec_type : dtyp -> bool |
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val typ_of_dtyp : (int * (string * dtyp list * |
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(string * dtyp list) list)) list -> (string * sort) list -> dtyp -> typ |
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val dest_DtTFree : dtyp -> string |
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val dest_DtRec : dtyp -> int |
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val dest_TFree : typ -> string |
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val get_nonrec_types : (int * (string * dtyp list * |
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(string * dtyp list) list)) list -> (string * sort) list -> typ list |
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val get_branching_types : (int * (string * dtyp list * |
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(string * dtyp list) list)) list -> (string * sort) list -> typ list |
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val get_rec_types : (int * (string * dtyp list * |
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(string * dtyp list) list)) list -> (string * sort) list -> typ list |
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val check_nonempty : (int * (string * dtyp list * |
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(string * dtyp list) list)) list list -> unit |
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val unfold_datatypes : |
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Sign.sg -> (int * (string * dtyp list * (string * dtyp list) list)) list -> |
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(string * sort) list -> datatype_info Symtab.table -> |
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(int * (string * dtyp list * (string * dtyp list) list)) list -> int -> |
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(int * (string * dtyp list * |
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(string * dtyp list) list)) list list * int |
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end; |
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structure DatatypeAux : DATATYPE_AUX = |
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struct |
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val quiet_mode = ref false; |
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fun message s = if !quiet_mode then () else writeln s; |
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(* FIXME: move to library ? *) |
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fun foldl1 f (x::xs) = foldl f (x, xs); |
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fun add_path flat_names s = if flat_names then I else Theory.add_path s; |
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fun parent_path flat_names = if flat_names then I else Theory.parent_path; |
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(* store theorems in theory *) |
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fun store_thmss label tnames thmss thy = |
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foldr (fn ((tname, thms), thy') => thy' |> |
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Theory.add_path tname |> |
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PureThy.add_thmss [((label, thms), [])] |> |
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Theory.parent_path) |
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(tnames ~~ thmss, thy); |
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fun store_thms label tnames thms thy = |
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foldr (fn ((tname, thm), thy') => thy' |> |
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Theory.add_path tname |> |
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PureThy.add_thms [((label, thm), [])] |> |
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Theory.parent_path) |
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(tnames ~~ thms, thy); |
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(* split theorem thm_1 & ... & thm_n into n theorems *) |
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fun split_conj_thm th = |
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((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle THM _ => [th]; |
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val mk_conj = foldr1 (HOLogic.mk_binop "op &"); |
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val mk_disj = foldr1 (HOLogic.mk_binop "op |"); |
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(* instantiate induction rule *) |
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fun indtac indrule i st = |
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let |
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val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule)); |
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val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop |
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(Logic.strip_imp_concl (nth_elem (i - 1, prems_of st)))); |
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val getP = if can HOLogic.dest_imp (hd ts) then |
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(apfst Some) o HOLogic.dest_imp else pair None; |
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fun abstr (t1, t2) = (case t1 of |
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None => let val [Free (s, T)] = add_term_frees (t2, []) |
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in absfree (s, T, t2) end |
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| Some (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2))) |
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val cert = cterm_of (Thm.sign_of_thm st); |
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val Ps = map (cert o head_of o snd o getP) ts; |
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val indrule' = cterm_instantiate (Ps ~~ |
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(map (cert o abstr o getP) ts')) indrule |
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in |
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rtac indrule' i st |
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end; |
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(* perform exhaustive case analysis on last parameter of subgoal i *) |
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fun exh_tac exh_thm_of i state = |
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let |
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val sg = Thm.sign_of_thm state; |
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val prem = nth_elem (i - 1, prems_of state); |
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val params = Logic.strip_params prem; |
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val (_, Type (tname, _)) = hd (rev params); |
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val exhaustion = lift_rule (state, i) (exh_thm_of tname); |
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val prem' = hd (prems_of exhaustion); |
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val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem')); |
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val exhaustion' = cterm_instantiate [(cterm_of sg (head_of lhs), |
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cterm_of sg (foldr (fn ((_, T), t) => Abs ("z", T, t)) |
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(params, Bound 0)))] exhaustion |
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in compose_tac (false, exhaustion', nprems_of exhaustion) i state |
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end; |
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(* handling of distinctness theorems *) |
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datatype simproc_dist = QuickAndDirty |
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| FewConstrs of thm list |
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| ManyConstrs of thm * simpset; |
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(********************** Internal description of datatypes *********************) |
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datatype dtyp = |
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DtTFree of string |
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| DtType of string * (dtyp list) |
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| DtRec of int; |
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(* information about datatypes *) |
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type descr = (int * (string * dtyp list * (string * dtyp list) list)) list; |
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type datatype_info = |
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{index : int, |
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descr : descr, |
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rec_names : string list, |
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rec_rewrites : thm list, |
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case_name : string, |
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case_rewrites : thm list, |
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induction : thm, |
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exhaustion : thm, |
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distinct : simproc_dist, |
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inject : thm list, |
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nchotomy : thm, |
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case_cong : thm}; |
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fun mk_Free s T i = Free (s ^ (string_of_int i), T); |
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fun subst_DtTFree _ substs (T as (DtTFree name)) = |
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(case assoc (substs, name) of |
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None => T |
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| Some U => U) |
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| subst_DtTFree i substs (DtType (name, ts)) = |
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DtType (name, map (subst_DtTFree i substs) ts) |
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| subst_DtTFree i _ (DtRec j) = DtRec (i + j); |
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exception Datatype; |
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fun dest_DtTFree (DtTFree a) = a |
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| dest_DtTFree _ = raise Datatype; |
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fun dest_DtRec (DtRec i) = i |
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| dest_DtRec _ = raise Datatype; |
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fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts |
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| is_rec_type (DtRec _) = true |
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| is_rec_type _ = false; |
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fun dest_TFree (TFree (n, _)) = n; |
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fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n |
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| dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)" |
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| dtyp_of_typ new_dts (Type (tname, Ts)) = |
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(case assoc (new_dts, tname) of |
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None => DtType (tname, map (dtyp_of_typ new_dts) Ts) |
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| Some vs => if map (try dest_TFree) Ts = map Some vs then |
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DtRec (find_index (curry op = tname o fst) new_dts) |
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else error ("Illegal occurence of recursive type " ^ tname)); |
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fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, the (assoc (sorts, a))) |
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| typ_of_dtyp descr sorts (DtRec i) = |
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let val (s, ds, _) = the (assoc (descr, i)) |
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in Type (s, map (typ_of_dtyp descr sorts) ds) end |
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| typ_of_dtyp descr sorts (DtType (s, ds)) = |
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Type (s, map (typ_of_dtyp descr sorts) ds); |
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(* find all non-recursive types in datatype description *) |
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fun get_nonrec_types descr sorts = |
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let fun add (Ts, T as DtTFree _) = T ins Ts |
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| add (Ts, T as DtType ("fun", [_, DtRec _])) = Ts |
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| add (Ts, T as DtType _) = T ins Ts |
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| add (Ts, _) = Ts |
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in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) => |
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foldl (fn (Ts', (_, cargs)) => |
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foldl add (Ts', cargs)) (Ts, constrs)) ([], descr)) |
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end; |
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(* get all recursive types in datatype description *) |
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fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) => |
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Type (s, map (typ_of_dtyp descr sorts) ds)) descr; |
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(* get all branching types *) |
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fun get_branching_types descr sorts = |
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let fun add (Ts, DtType ("fun", [T, DtRec _])) = T ins Ts |
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| add (Ts, _) = Ts |
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in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) => |
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foldl (fn (Ts', (_, cargs)) => |
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foldl add (Ts', cargs)) (Ts, constrs)) ([], descr)) |
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end; |
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(* nonemptiness check for datatypes *) |
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fun check_nonempty descr = |
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let |
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val descr' = flat descr; |
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fun is_nonempty_dt is i = |
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let |
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val (_, _, constrs) = the (assoc (descr', i)); |
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fun arg_nonempty (DtRec i) = if i mem is then false |
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else is_nonempty_dt (i::is) i |
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| arg_nonempty (DtType ("fun", [_, T])) = arg_nonempty T |
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| arg_nonempty _ = true; |
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in exists ((forall arg_nonempty) o snd) constrs |
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end |
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in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr) |
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(fn (_, (s, _, _)) => "Nonemptiness check failed for datatype " ^ s) |
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end; |
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(* unfold a list of mutually recursive datatype specifications *) |
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(* all types of the form DtType (dt_name, [..., DtRec _, ...]) *) |
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(* need to be unfolded *) |
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fun unfold_datatypes sign orig_descr sorts (dt_info : datatype_info Symtab.table) descr i = |
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let |
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fun typ_error T msg = error ("Non-admissible type expression\n" ^ |
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Sign.string_of_typ sign (typ_of_dtyp (orig_descr @ descr) sorts T) ^ "\n" ^ msg); |
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fun get_dt_descr T i tname dts = |
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(case Symtab.lookup (dt_info, tname) of |
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None => typ_error T (tname ^ " is not a datatype - can't use it in\ |
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\ nested recursion") |
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| (Some {index, descr, ...}) => |
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let val (_, vars, _) = the (assoc (descr, index)); |
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val subst = ((map dest_DtTFree vars) ~~ dts) handle LIST _ => |
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typ_error T ("Type constructor " ^ tname ^ " used with wrong\ |
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\ number of arguments") |
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in (i + index, map (fn (j, (tn, args, cs)) => (i + j, |
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(tn, map (subst_DtTFree i subst) args, |
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map (apsnd (map (subst_DtTFree i subst))) cs))) descr) |
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end); |
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(* unfold a single constructor argument *) |
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fun unfold_arg ((i, Ts, descrs), T as (DtType (tname, dts))) = |
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if is_rec_type T then |
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if tname = "fun" then |
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if is_rec_type (hd dts) then |
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typ_error T "Non-strictly positive recursive occurrence of type" |
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else |
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(case hd (tl dts) of |
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DtType ("fun", _) => typ_error T "Curried function types not allowed" |
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| T' => let val (i', [T''], descrs') = unfold_arg ((i, [], descrs), T') |
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in (i', Ts @ [DtType (tname, [hd dts, T''])], descrs') end) |
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let val (index, descr) = get_dt_descr T i tname dts; |
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val (descr', i') = unfold_datatypes sign orig_descr sorts dt_info descr (i + length descr) |
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in (i', Ts @ [DtRec index], descrs @ descr') end |
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else (i, Ts @ [T], descrs) |
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| unfold_arg ((i, Ts, descrs), T) = (i, Ts @ [T], descrs); |
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(* unfold a constructor *) |
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fun unfold_constr ((i, constrs, descrs), (cname, cargs)) = |
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let val (i', cargs', descrs') = foldl unfold_arg ((i, [], descrs), cargs) |
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in (i', constrs @ [(cname, cargs')], descrs') end; |
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(* unfold a single datatype *) |
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fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) = |
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let val (i', constrs', descrs') = |
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foldl unfold_constr ((i, [], descrs), constrs) |
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in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs') |
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end; |
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val (i', descr', descrs) = foldl unfold_datatype ((i, [],[]), descr); |
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in (descr' :: descrs, i') end; |
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end; |