author | lcp |
Thu, 18 Aug 1994 17:41:40 +0200 | |
changeset 543 | e961b2092869 |
parent 516 | 1957113f0d7d |
child 568 | 756b0e2a6cac |
permissions | -rw-r--r-- |
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(* Title: ZF/ind-syntax.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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(*Make a definition lhs==rhs, checking that vars on lhs contain those of rhs*) |
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fun mk_defpair (lhs, rhs) = |
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0d19ab250cc9
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let val Const(name, _) = head_of lhs |
0d19ab250cc9
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in (name ^ "_def", Logic.mk_equals (lhs, rhs)) end; |
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fun get_def thy s = get_axiom thy (s^"_def"); |
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fun lookup_const sign a = Symtab.lookup(#const_tab (Sign.rep_sg sign), a); |
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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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fun ap t u = t$u; |
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fun app t (u1,u2) = t $ u1 $ u2; |
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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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(*Read an assumption in the given theory*) |
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fun assume_read thy a = assume (read_cterm (sign_of thy) (a,propT)); |
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fun readtm sign T a = |
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read_cterm sign (a,T) |> term_of |
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handle ERROR => error ("The error above occurred for " ^ a); |
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(*Skipping initial blanks, find the first identifier*) |
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fun scan_to_id s = |
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s |> explode |> take_prefix is_blank |> #2 |> Lexicon.scan_id |> #1 |
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handle LEXICAL_ERROR => error ("Expected to find an identifier in " ^ s); |
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fun is_backslash c = c = "\\"; |
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(*Apply string escapes to a quoted string; see Def of Standard ML, page 3 |
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Does not handle the \ddd form; no error checking*) |
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fun escape [] = [] |
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| escape cs = (case take_prefix (not o is_backslash) cs of |
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(front, []) => front |
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| (front, _::"n"::rest) => front @ ("\n" :: escape rest) |
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| (front, _::"t"::rest) => front @ ("\t" :: escape rest) |
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| (front, _::"^"::c::rest) => front @ (chr(ord(c)-64) :: escape rest) |
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| (front, _::"\""::rest) => front @ ("\"" :: escape rest) |
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| (front, _::"\\"::rest) => front @ ("\\" :: escape rest) |
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| (front, b::c::rest) => |
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if is_blank c (*remove any further blanks and the following \ *) |
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then front @ escape (tl (snd (take_prefix is_blank rest))) |
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else error ("Unrecognized string escape: " ^ implode(b::c::rest))); |
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(*Remove the first and last charaters -- presumed to be quotes*) |
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val trim = implode o escape o rev o tl o rev o tl o explode; |
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(*simple error-checking 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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(*Make distinct individual variables a1, a2, a3, ..., an. *) |
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fun mk_frees a [] = [] |
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| mk_frees a (T::Ts) = Free(a,T) :: mk_frees (bump_string a) Ts; |
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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 ("Ill-formed 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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(*From HOL/ex/meson.ML: raises exception if no rules apply -- unlike RL*) |
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fun tryres (th, rl::rls) = (th RS rl handle THM _ => tryres(th,rls)) |
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| tryres (th, []) = raise THM("tryres", 0, [th]); |
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fun gen_make_elim elim_rls rl = |
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standard (tryres (rl, elim_rls @ [revcut_rl])); |
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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 = 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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fun data_domain rec_tms = |
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replicate (length rec_tms) (univ $ union_params (hd rec_tms)); |
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fun Codata_domain rec_tms = |
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replicate (length 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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end; |
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