author  paulson 
Fri, 22 Dec 1995 11:09:28 +0100  
changeset 1418  f5f97ee67cbb 
parent 742  faa3efc1d130 
child 1461  6bcb44e4d6e5 
permissions  rwrr 
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(* Title: ZF/indsyntax.ML 
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ID: $Id$ 

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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

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Copyright 1993 University of Cambridge 

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Abstract Syntax functions for Inductive Definitions 

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*) 

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(*The structure protects these items from redeclaration (somewhat!). The 
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datatype definitions in theory files refer to these items by name! 

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*) 

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structure Ind_Syntax = 

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struct 

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(** Abstract syntax definitions for FOL and ZF **) 

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val iT = Type("i",[]) 

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and oT = Type("o",[]); 

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(*Given u expecting arguments of types [T1,...,Tn], create term of 

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type T1*...*Tn => i using split*) 

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fun ap_split split u [ ] = Abs("null", iT, u) 

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 ap_split split u [_] = u 

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 ap_split split u [_,_] = split $ u 

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 ap_split split u (T::Ts) = 

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split $ (Abs("v", T, ap_split split (u $ Bound(length Ts  2)) Ts)); 

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val conj = Const("op &", [oT,oT]>oT) 

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and disj = Const("op ", [oT,oT]>oT) 

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and imp = Const("op >", [oT,oT]>oT); 

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val eq_const = Const("op =", [iT,iT]>oT); 

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val mem_const = Const("op :", [iT,iT]>oT); 

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val exists_const = Const("Ex", [iT>oT]>oT); 

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fun mk_exists (Free(x,T),P) = exists_const $ (absfree (x,T,P)); 

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val all_const = Const("All", [iT>oT]>oT); 

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fun mk_all (Free(x,T),P) = all_const $ (absfree (x,T,P)); 

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(*Creates All(%v.v:A > P(v)) rather than Ball(A,P) *) 

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fun mk_all_imp (A,P) = 

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all_const $ Abs("v", iT, imp $ (mem_const $ Bound 0 $ A) $ (P $ Bound 0)); 

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val Part_const = Const("Part", [iT,iT>iT]>iT); 

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val Collect_const = Const("Collect", [iT,iT>oT]>iT); 

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fun mk_Collect (a,D,t) = Collect_const $ D $ absfree(a, iT, t); 

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val Trueprop = Const("Trueprop",oT>propT); 

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fun mk_tprop P = Trueprop $ P; 

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(*simple errorchecking in the premises of an inductive definition*) 
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fun chk_prem rec_hd (Const("op &",_) $ _ $ _) = 

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error"Premises may not be conjuctive" 

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 chk_prem rec_hd (Const("op :",_) $ t $ X) = 

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deny (Logic.occs(rec_hd,t)) "Recursion term on left of member symbol" 

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 chk_prem rec_hd t = 

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deny (Logic.occs(rec_hd,t)) "Recursion term in side formula"; 

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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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(*Return the conclusion of a rule, of the form t:X*) 
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fun rule_concl rl = 
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let val Const("Trueprop",_) $ (Const("op :",_) $ t $ X) = 
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Logic.strip_imp_concl rl 

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in (t,X) end; 

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(*As above, but return error message if bad*) 

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fun rule_concl_msg sign rl = rule_concl rl 

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handle Bind => error ("Illformed conclusion of introduction rule: " ^ 

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Sign.string_of_term sign rl); 

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(*For deriving cases rules. CollectD2 discards the domain, which is redundant; 

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read_instantiate replaces a propositional variable by a formula variable*) 

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val equals_CollectD = 

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read_instantiate [("W","?Q")] 

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(make_elim (equalityD1 RS subsetD RS CollectD2)); 

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(** For datatype definitions **) 
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fun dest_mem (Const("op :",_) $ x $ A) = (x,A) 

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 dest_mem _ = error "Constructor specifications must have the form x:A"; 

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(*read a constructor specification*) 

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fun read_construct sign (id, sprems, syn) = 

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let val prems = map (readtm sign oT) sprems 

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val args = map (#1 o dest_mem) prems 

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val T = (map (#2 o dest_Free) args) > iT 

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handle TERM _ => error 

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"Bad variable in constructor specification" 

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val name = Syntax.const_name id syn (*handle infix constructors*) 
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in ((id,T,syn), name, args, prems) end; 
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val read_constructs = map o map o read_construct; 

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(*convert constructor specifications into introduction rules*) 
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fun mk_intr_tms (rec_tm, constructs) = 

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let fun mk_intr ((id,T,syn), name, args, prems) = 

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Logic.list_implies 

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(map mk_tprop prems, 

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mk_tprop (mem_const $ list_comb(Const(name,T), args) $ rec_tm)) 

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in map mk_intr constructs end; 

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val mk_all_intr_tms = flat o map mk_intr_tms o op ~~; 

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val Un = Const("op Un", [iT,iT]>iT) 
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and empty = Const("0", iT) 

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and univ = Const("univ", iT>iT) 

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and quniv = Const("quniv", iT>iT); 

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(*Make a datatype's domain: form the union of its set parameters*) 
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fun union_params rec_tm = 

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let val (_,args) = strip_comb rec_tm 

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in case (filter (fn arg => type_of arg = iT) args) of 

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[] => empty 

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 iargs => fold_bal (app Un) iargs 

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end; 

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(*Previously these both did replicate (length rec_tms); however now 
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[q]univ itself constitutes the sum domain for mutual recursion!*) 
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fun data_domain rec_tms = univ $ union_params (hd rec_tms); 
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fun Codata_domain rec_tms = quniv $ union_params (hd rec_tms); 
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(*Could go to FOL, but it's hardly general*) 

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val def_swap_iff = prove_goal IFOL.thy "a==b ==> a=c <> c=b" 
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(fn [def] => [(rewtac def), (rtac iffI 1), (REPEAT (etac sym 1))]); 

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val def_trans = prove_goal IFOL.thy "[ f==g; g(a)=b ] ==> f(a)=b" 

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(fn [rew,prem] => [ rewtac rew, rtac prem 1 ]); 

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(*Delete needless equality assumptions*) 
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val refl_thin = prove_goal IFOL.thy "!!P. [ a=a; P ] ==> P" 

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(fn _ => [assume_tac 1]); 

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(*Includes rules for succ and Pair since they are common constructions*) 
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val elim_rls = [asm_rl, FalseE, succ_neq_0, sym RS succ_neq_0, 
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Pair_neq_0, sym RS Pair_neq_0, Pair_inject, 
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make_elim succ_inject, 
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refl_thin, conjE, exE, disjE]; 
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(*Turns iff rules into safe elimination rules*) 
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fun mk_free_SEs iffs = map (gen_make_elim [conjE,FalseE]) (iffs RL [iffD1]); 
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end; 
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