(* Title: ZF/Datatype.ML ID: $Id: Datatype.ML,v 1.27 2005/09/15 15:17:00 wenzelm Exp $ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1993 University of Cambridge (Co)Datatype Definitions for Zermelo-Fraenkel Set Theory *) (*Typechecking rules for most datatypes involving univ*) structure Data_Arg = struct val intrs = [SigmaI, InlI, InrI, Pair_in_univ, Inl_in_univ, Inr_in_univ, zero_in_univ, A_into_univ, nat_into_univ, UnCI]; val elims = [make_elim InlD, make_elim InrD, (*for mutual recursion*) SigmaE, sumE]; (*allows * and + in spec*) end; structure Data_Package = Add_datatype_def_Fun (structure Fp=Lfp and Pr=Standard_Prod and CP=Standard_CP and Su=Standard_Sum and Ind_Package = Ind_Package and Datatype_Arg = Data_Arg val coind = false); (*Typechecking rules for most codatatypes involving quniv*) structure CoData_Arg = struct val intrs = [QSigmaI, QInlI, QInrI, QPair_in_quniv, QInl_in_quniv, QInr_in_quniv, zero_in_quniv, A_into_quniv, nat_into_quniv, UnCI]; val elims = [make_elim QInlD, make_elim QInrD, (*for mutual recursion*) QSigmaE, qsumE]; (*allows * and + in spec*) end; structure CoData_Package = Add_datatype_def_Fun (structure Fp=Gfp and Pr=Quine_Prod and CP=Quine_CP and Su=Quine_Sum and Ind_Package = CoInd_Package and Datatype_Arg = CoData_Arg val coind = true); (*Simproc for freeness reasoning: compare datatype constructors for equality*) structure DataFree = struct val trace = ref false; fun mk_new ([],[]) = Const("True",FOLogic.oT) | mk_new (largs,rargs) = fold_bal FOLogic.mk_conj (map FOLogic.mk_eq (ListPair.zip (largs,rargs))); val datatype_ss = simpset (); fun proc sg ss old = let val _ = if !trace then writeln ("data_free: OLD = " ^ string_of_cterm (cterm_of sg old)) else () val (lhs,rhs) = FOLogic.dest_eq old val (lhead, largs) = strip_comb lhs and (rhead, rargs) = strip_comb rhs val lname = #1 (dest_Const lhead) handle TERM _ => raise Match; val rname = #1 (dest_Const rhead) handle TERM _ => raise Match; val lcon_info = the (Symtab.lookup (ConstructorsData.get sg) lname) handle Option => raise Match; val rcon_info = the (Symtab.lookup (ConstructorsData.get sg) rname) handle Option => raise Match; val new = if #big_rec_name lcon_info = #big_rec_name rcon_info andalso not (null (#free_iffs lcon_info)) then if lname = rname then mk_new (largs, rargs) else Const("False",FOLogic.oT) else raise Match val _ = if !trace then writeln ("NEW = " ^ string_of_cterm (Thm.cterm_of sg new)) else (); val goal = Logic.mk_equals (old, new) val thm = Tactic.prove sg [] [] goal (fn _ => rtac iff_reflection 1 THEN simp_tac (Simplifier.inherit_bounds ss datatype_ss addsimps #free_iffs lcon_info) 1) handle ERROR_MESSAGE msg => (warning (msg ^ "\ndata_free simproc:\nfailed to prove " ^ Sign.string_of_term sg goal); raise Match) in SOME thm end handle Match => NONE; val conv = Simplifier.simproc (theory "ZF") "data_free" ["(x::i) = y"] proc; end; Addsimprocs [DataFree.conv];