ZF/Inductive.thy,.ML: renamed from "inductive" to allow re-building without
the keyword "inductive" making the theory file fail
ZF/Makefile: now has Inductive.thy,.ML
ZF/Datatype,Finite,Zorn: depend upon Inductive
ZF/intr_elim: now checks that the inductive name does not clash with
existing theory names
ZF/ind_section: deleted things replicated in Pure/section_utils.ML
ZF/ROOT: now loads Pure/section_utils
(* Title: ZF/ind-syntax.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Abstract Syntax functions for Inductive Definitions
*)
(*The structure protects these items from redeclaration (somewhat!). The
datatype definitions in theory files refer to these items by name!
*)
structure Ind_Syntax =
struct
(** Abstract syntax definitions for FOL and ZF **)
val iT = Type("i",[])
and oT = Type("o",[]);
(*Given u expecting arguments of types [T1,...,Tn], create term of
type T1*...*Tn => i using split*)
fun ap_split split u [ ] = Abs("null", iT, u)
| ap_split split u [_] = u
| ap_split split u [_,_] = split $ u
| ap_split split u (T::Ts) =
split $ (Abs("v", T, ap_split split (u $ Bound(length Ts - 2)) Ts));
val conj = Const("op &", [oT,oT]--->oT)
and disj = Const("op |", [oT,oT]--->oT)
and imp = Const("op -->", [oT,oT]--->oT);
val eq_const = Const("op =", [iT,iT]--->oT);
val mem_const = Const("op :", [iT,iT]--->oT);
val exists_const = Const("Ex", [iT-->oT]--->oT);
fun mk_exists (Free(x,T),P) = exists_const $ (absfree (x,T,P));
val all_const = Const("All", [iT-->oT]--->oT);
fun mk_all (Free(x,T),P) = all_const $ (absfree (x,T,P));
(*Creates All(%v.v:A --> P(v)) rather than Ball(A,P) *)
fun mk_all_imp (A,P) =
all_const $ Abs("v", iT, imp $ (mem_const $ Bound 0 $ A) $ (P $ Bound 0));
val Part_const = Const("Part", [iT,iT-->iT]--->iT);
val Collect_const = Const("Collect", [iT,iT-->oT]--->iT);
fun mk_Collect (a,D,t) = Collect_const $ D $ absfree(a, iT, t);
val Trueprop = Const("Trueprop",oT-->propT);
fun mk_tprop P = Trueprop $ P;
(*simple error-checking in the premises of an inductive definition*)
fun chk_prem rec_hd (Const("op &",_) $ _ $ _) =
error"Premises may not be conjuctive"
| chk_prem rec_hd (Const("op :",_) $ t $ X) =
deny (Logic.occs(rec_hd,t)) "Recursion term on left of member symbol"
| chk_prem rec_hd t =
deny (Logic.occs(rec_hd,t)) "Recursion term in side formula";
(*Return the conclusion of a rule, of the form t:X*)
fun rule_concl rl =
let val Const("Trueprop",_) $ (Const("op :",_) $ t $ X) =
Logic.strip_imp_concl rl
in (t,X) end;
(*As above, but return error message if bad*)
fun rule_concl_msg sign rl = rule_concl rl
handle Bind => error ("Ill-formed conclusion of introduction rule: " ^
Sign.string_of_term sign rl);
(*For deriving cases rules. CollectD2 discards the domain, which is redundant;
read_instantiate replaces a propositional variable by a formula variable*)
val equals_CollectD =
read_instantiate [("W","?Q")]
(make_elim (equalityD1 RS subsetD RS CollectD2));
(** For datatype definitions **)
fun dest_mem (Const("op :",_) $ x $ A) = (x,A)
| dest_mem _ = error "Constructor specifications must have the form x:A";
(*read a constructor specification*)
fun read_construct sign (id, sprems, syn) =
let val prems = map (readtm sign oT) sprems
val args = map (#1 o dest_mem) prems
val T = (map (#2 o dest_Free) args) ---> iT
handle TERM _ => error
"Bad variable in constructor specification"
val name = Syntax.const_name id syn (*handle infix constructors*)
in ((id,T,syn), name, args, prems) end;
val read_constructs = map o map o read_construct;
(*convert constructor specifications into introduction rules*)
fun mk_intr_tms (rec_tm, constructs) =
let fun mk_intr ((id,T,syn), name, args, prems) =
Logic.list_implies
(map mk_tprop prems,
mk_tprop (mem_const $ list_comb(Const(name,T), args) $ rec_tm))
in map mk_intr constructs end;
val mk_all_intr_tms = flat o map mk_intr_tms o op ~~;
val Un = Const("op Un", [iT,iT]--->iT)
and empty = Const("0", iT)
and univ = Const("univ", iT-->iT)
and quniv = Const("quniv", iT-->iT);
(*Make a datatype's domain: form the union of its set parameters*)
fun union_params rec_tm =
let val (_,args) = strip_comb rec_tm
in case (filter (fn arg => type_of arg = iT) args) of
[] => empty
| iargs => fold_bal (app Un) iargs
end;
fun data_domain rec_tms =
replicate (length rec_tms) (univ $ union_params (hd rec_tms));
fun Codata_domain rec_tms =
replicate (length rec_tms) (quniv $ union_params (hd rec_tms));
(*Could go to FOL, but it's hardly general*)
val def_swap_iff = prove_goal IFOL.thy "a==b ==> a=c <-> c=b"
(fn [def] => [(rewtac def), (rtac iffI 1), (REPEAT (etac sym 1))]);
val def_trans = prove_goal IFOL.thy "[| f==g; g(a)=b |] ==> f(a)=b"
(fn [rew,prem] => [ rewtac rew, rtac prem 1 ]);
(*Delete needless equality assumptions*)
val refl_thin = prove_goal IFOL.thy "!!P. [| a=a; P |] ==> P"
(fn _ => [assume_tac 1]);
end;