src/ZF/ind_syntax.ML
author paulson
Thu Nov 28 10:44:24 1996 +0100 (1996-11-28 ago)
changeset 2266 82aef6857c5b
parent 2226 f3c6a22681b1
child 3925 90f499226ab9
permissions -rw-r--r--
Replaced map...~~ by ListPair.map
     1 (*  Title:      ZF/ind-syntax.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1993  University of Cambridge
     5 
     6 Abstract Syntax functions for Inductive Definitions
     7 *)
     8 
     9 (*The structure protects these items from redeclaration (somewhat!).  The 
    10   datatype definitions in theory files refer to these items by name!
    11 *)
    12 structure Ind_Syntax =
    13 struct
    14 
    15 (** Abstract syntax definitions for FOL and ZF **)
    16 
    17 val iT = Type("i",[])
    18 and oT = Type("o",[]);
    19 
    20 
    21 (** Logical constants **)
    22 
    23 val conj = Const("op &", [oT,oT]--->oT)
    24 and disj = Const("op |", [oT,oT]--->oT)
    25 and imp = Const("op -->", [oT,oT]--->oT);
    26 
    27 val eq_const = Const("op =", [iT,iT]--->oT);
    28 
    29 val mem_const = Const("op :", [iT,iT]--->oT);
    30 
    31 val exists_const = Const("Ex", [iT-->oT]--->oT);
    32 fun mk_exists (Free(x,T),P) = exists_const $ (absfree (x,T,P));
    33 
    34 val all_const = Const("All", [iT-->oT]--->oT);
    35 fun mk_all (Free(x,T),P) = all_const $ (absfree (x,T,P));
    36 
    37 (*Creates All(%v.v:A --> P(v)) rather than Ball(A,P) *)
    38 fun mk_all_imp (A,P) = 
    39     all_const $ Abs("v", iT, imp $ (mem_const $ Bound 0 $ A) $ (P $ Bound 0));
    40 
    41 val Part_const = Const("Part", [iT,iT-->iT]--->iT);
    42 
    43 val Collect_const = Const("Collect", [iT,iT-->oT]--->iT);
    44 fun mk_Collect (a,D,t) = Collect_const $ D $ absfree(a, iT, t);
    45 
    46 val Trueprop = Const("Trueprop",oT-->propT);
    47 fun mk_tprop P = Trueprop $ P;
    48 
    49 (*simple error-checking in the premises of an inductive definition*)
    50 fun chk_prem rec_hd (Const("op &",_) $ _ $ _) =
    51         error"Premises may not be conjuctive"
    52   | chk_prem rec_hd (Const("op :",_) $ t $ X) = 
    53         deny (Logic.occs(rec_hd,t)) "Recursion term on left of member symbol"
    54   | chk_prem rec_hd t = 
    55         deny (Logic.occs(rec_hd,t)) "Recursion term in side formula";
    56 
    57 (*Return the conclusion of a rule, of the form t:X*)
    58 fun rule_concl rl = 
    59     let val Const("Trueprop",_) $ (Const("op :",_) $ t $ X) = 
    60                 Logic.strip_imp_concl rl
    61     in  (t,X)  end;
    62 
    63 (*As above, but return error message if bad*)
    64 fun rule_concl_msg sign rl = rule_concl rl
    65     handle Bind => error ("Ill-formed conclusion of introduction rule: " ^ 
    66                           Sign.string_of_term sign rl);
    67 
    68 (*For deriving cases rules.  CollectD2 discards the domain, which is redundant;
    69   read_instantiate replaces a propositional variable by a formula variable*)
    70 val equals_CollectD = 
    71     read_instantiate [("W","?Q")]
    72         (make_elim (equalityD1 RS subsetD RS CollectD2));
    73 
    74 
    75 (** For datatype definitions **)
    76 
    77 fun dest_mem (Const("op :",_) $ x $ A) = (x,A)
    78   | dest_mem _ = error "Constructor specifications must have the form x:A";
    79 
    80 (*read a constructor specification*)
    81 fun read_construct sign (id, sprems, syn) =
    82     let val prems = map (readtm sign oT) sprems
    83         val args = map (#1 o dest_mem) prems
    84         val T = (map (#2 o dest_Free) args) ---> iT
    85                 handle TERM _ => error 
    86                     "Bad variable in constructor specification"
    87         val name = Syntax.const_name id syn  (*handle infix constructors*)
    88     in ((id,T,syn), name, args, prems) end;
    89 
    90 val read_constructs = map o map o read_construct;
    91 
    92 (*convert constructor specifications into introduction rules*)
    93 fun mk_intr_tms (rec_tm, constructs) =
    94   let fun mk_intr ((id,T,syn), name, args, prems) =
    95           Logic.list_implies
    96               (map mk_tprop prems,
    97                mk_tprop (mem_const $ list_comb(Const(name,T), args) $ rec_tm)) 
    98   in  map mk_intr constructs  end;
    99 
   100 fun mk_all_intr_tms arg = List.concat (ListPair.map mk_intr_tms arg);
   101 
   102 val Un          = Const("op Un", [iT,iT]--->iT)
   103 and empty       = Const("0", iT)
   104 and univ        = Const("univ", iT-->iT)
   105 and quniv       = Const("quniv", iT-->iT);
   106 
   107 (*Make a datatype's domain: form the union of its set parameters*)
   108 fun union_params rec_tm =
   109   let val (_,args) = strip_comb rec_tm
   110   in  case (filter (fn arg => type_of arg = iT) args) of
   111          []    => empty
   112        | iargs => fold_bal (app Un) iargs
   113   end;
   114 
   115 (*Previously these both did    replicate (length rec_tms);  however now
   116   [q]univ itself constitutes the sum domain for mutual recursion!*)
   117 fun data_domain rec_tms = univ $ union_params (hd rec_tms);
   118 fun Codata_domain rec_tms = quniv $ union_params (hd rec_tms);
   119 
   120 (*Could go to FOL, but it's hardly general*)
   121 val def_swap_iff = prove_goal IFOL.thy "a==b ==> a=c <-> c=b"
   122  (fn [def] => [(rewtac def), (rtac iffI 1), (REPEAT (etac sym 1))]);
   123 
   124 val def_trans = prove_goal IFOL.thy "[| f==g;  g(a)=b |] ==> f(a)=b"
   125   (fn [rew,prem] => [ rewtac rew, rtac prem 1 ]);
   126 
   127 (*Delete needless equality assumptions*)
   128 val refl_thin = prove_goal IFOL.thy "!!P. [| a=a;  P |] ==> P"
   129      (fn _ => [assume_tac 1]);
   130 
   131 (*Includes rules for succ and Pair since they are common constructions*)
   132 val elim_rls = [asm_rl, FalseE, succ_neq_0, sym RS succ_neq_0, 
   133                 Pair_neq_0, sym RS Pair_neq_0, Pair_inject,
   134                 make_elim succ_inject, 
   135                 refl_thin, conjE, exE, disjE];
   136 
   137 (*Turns iff rules into safe elimination rules*)
   138 fun mk_free_SEs iffs = map (gen_make_elim [conjE,FalseE]) (iffs RL [iffD1]);
   139 
   140 end;
   141