author  lcp 
Tue, 21 Jun 1994 17:20:34 +0200  
changeset 435  ca5356bd315a 
parent 400  3c2c40c87112 
child 561  95225e63ef02 
permissions  rwrr 
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(* Title: Pure/drule.ML 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
0  4 
Copyright 1993 University of Cambridge 
5 

6 
Derived rules and other operations on theorems and theories 

7 
*) 

8 

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infix 0 RS RSN RL RLN MRS MRL COMP; 
0  10 

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signature DRULE = 

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sig 

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structure Thm : THM 

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local open Thm in 

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val asm_rl: thm 

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val assume_ax: theory > string > thm 

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val COMP: thm * thm > thm 

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val compose: thm * int * thm > thm list 

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val cterm_instantiate: (cterm*cterm)list > thm > thm 
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val cut_rl: thm 
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val equal_abs_elim: cterm > thm > thm 
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val equal_abs_elim_list: cterm list > thm > thm 
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val eq_thm: thm * thm > bool 
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val eq_thm_sg: thm * thm > bool 

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val flexpair_abs_elim_list: cterm list > thm > thm 
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val forall_intr_list: cterm list > thm > thm 
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val forall_intr_frees: thm > thm 
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val forall_elim_list: cterm list > thm > thm 
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val forall_elim_var: int > thm > thm 
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val forall_elim_vars: int > thm > thm 

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val implies_elim_list: thm > thm list > thm 

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val implies_intr_list: cterm list > thm > thm 
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val MRL: thm list list * thm list > thm list 
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val MRS: thm list * thm > thm 
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val pprint_cterm: cterm > pprint_args > unit 
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val pprint_ctyp: ctyp > pprint_args > unit 
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val pprint_theory: theory > pprint_args > unit 
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val pprint_thm: thm > pprint_args > unit 
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val pretty_thm: thm > Sign.Syntax.Pretty.T 
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val print_cterm: cterm > unit 
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val print_ctyp: ctyp > unit 
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val print_goals: int > thm > unit 
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val print_goals_ref: (int > thm > unit) ref 
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val print_sign: theory > unit 
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val print_axioms: theory > unit 

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val print_theory: theory > unit 
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val print_thm: thm > unit 

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val prth: thm > thm 

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val prthq: thm Sequence.seq > thm Sequence.seq 

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val prths: thm list > thm list 

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val read_instantiate: (string*string)list > thm > thm 

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val read_instantiate_sg: Sign.sg > (string*string)list > thm > thm 

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val read_insts: 
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Sign.sg > (indexname > typ option) * (indexname > sort option) 
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> (indexname > typ option) * (indexname > sort option) 
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> (string*string)list 
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> (indexname*ctyp)list * (cterm*cterm)list 
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val reflexive_thm: thm 
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val revcut_rl: thm 

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val rewrite_goal_rule: bool*bool > (meta_simpset > thm > thm option) 
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> meta_simpset > int > thm > thm 
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val rewrite_goals_rule: thm list > thm > thm 
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val rewrite_rule: thm list > thm > thm 

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val RS: thm * thm > thm 

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val RSN: thm * (int * thm) > thm 

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val RL: thm list * thm list > thm list 

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val RLN: thm list * (int * thm list) > thm list 

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val show_hyps: bool ref 

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val size_of_thm: thm > int 

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val standard: thm > thm 

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val string_of_cterm: cterm > string 
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val string_of_ctyp: ctyp > string 
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val string_of_thm: thm > string 
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val symmetric_thm: thm 

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val transitive_thm: thm 

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val triv_forall_equality: thm 

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val types_sorts: thm > (indexname> typ option) * (indexname> sort option) 

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val zero_var_indexes: thm > thm 

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end 

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end; 

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functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE = 
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struct 
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structure Thm = Thm; 

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structure Sign = Thm.Sign; 

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structure Type = Sign.Type; 

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structure Pretty = Sign.Syntax.Pretty 

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structure Symtab = Sign.Symtab; 
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local open Thm 
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in 

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(**** More derived rules and operations on theorems ****) 

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(** reading of instantiations **) 
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fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v 
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 _ => error("Lexical error in variable name " ^ quote (implode cs)); 
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fun absent ixn = 
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error("No such variable in term: " ^ Syntax.string_of_vname ixn); 
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fun inst_failure ixn = 
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error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails"); 
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fun read_insts sign (rtypes,rsorts) (types,sorts) insts = 
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let val {tsig,...} = Sign.rep_sg sign 
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fun split([],tvs,vs) = (tvs,vs) 
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 split((sv,st)::l,tvs,vs) = (case explode sv of 
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"'"::cs => split(l,(indexname cs,st)::tvs,vs) 
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 cs => split(l,tvs,(indexname cs,st)::vs)); 
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val (tvs,vs) = split(insts,[],[]); 
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fun readT((a,i),st) = 
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let val ixn = ("'" ^ a,i); 
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val S = case rsorts ixn of Some S => S  None => absent ixn; 
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val T = Sign.read_typ (sign,sorts) st; 
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in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T) 
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else inst_failure ixn 
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end 
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val tye = map readT tvs; 
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fun add_cterm ((cts,tye), (ixn,st)) = 
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let val T = case rtypes ixn of 
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Some T => typ_subst_TVars tye T 
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 None => absent ixn; 
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val (ct,tye2) = read_def_cterm (sign,types,sorts) (st,T); 
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val cv = cterm_of sign (Var(ixn,typ_subst_TVars tye2 T)) 
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in ((cv,ct)::cts,tye2 @ tye) end 
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val (cterms,tye') = foldl add_cterm (([],tye), vs); 
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in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', cterms) end; 
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(*** Printing of theories, theorems, etc. ***) 
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(*If false, hypotheses are printed as dots*) 
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val show_hyps = ref true; 
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fun pretty_thm th = 
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let val {sign, hyps, prop,...} = rep_thm th 
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val hsymbs = if null hyps then [] 
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else if !show_hyps then 
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[Pretty.brk 2, 
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Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)] 
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else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @ 
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[Pretty.str"]"]; 
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in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end; 
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val string_of_thm = Pretty.string_of o pretty_thm; 
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val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm; 
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(** Toplevel commands for printing theorems **) 
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val print_thm = writeln o string_of_thm; 
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fun prth th = (print_thm th; th); 
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(*Print and return a sequence of theorems, separated by blank lines. *) 
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fun prthq thseq = 
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(Sequence.prints (fn _ => print_thm) 100000 thseq; thseq); 
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(*Print and return a list of theorems, separated by blank lines. *) 
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fun prths ths = (print_list_ln print_thm ths; ths); 
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(* other printing commands *) 
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fun pprint_ctyp cT = 
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let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end; 
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171 
fun string_of_ctyp cT = 
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let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end; 
229
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173 

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val print_ctyp = writeln o string_of_ctyp; 
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175 

252
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176 
fun pprint_cterm ct = 
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177 
let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end; 
229
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178 

252
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fun string_of_cterm ct = 
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let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end; 
229
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181 

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182 
val print_cterm = writeln o string_of_cterm; 
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183 

252
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184 

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185 
(* print theory *) 
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186 

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187 
val pprint_theory = Sign.pprint_sg o sign_of; 
229
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188 

385  189 
val print_sign = Sign.print_sg o sign_of; 
190 

191 
fun print_axioms thy = 

252
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192 
let 
400  193 
val {sign, new_axioms, ...} = rep_theory thy; 
194 
val axioms = Symtab.dest new_axioms; 

229
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195 

385  196 
fun prt_axm (a, t) = Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1, 
197 
Pretty.quote (Sign.pretty_term sign t)]; 

252
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198 
in 
385  199 
Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms)) 
252
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200 
end; 
229
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201 

385  202 
fun print_theory thy = (print_sign thy; print_axioms thy); 
203 

229
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205 

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206 
(** Print thm A1,...,An/B in "goal style"  premises as numbered subgoals **) 
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207 

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208 
fun prettyprints es = writeln(Pretty.string_of(Pretty.blk(0,es))); 
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209 

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210 
fun print_goals maxgoals th : unit = 
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211 
let val {sign, hyps, prop,...} = rep_thm th; 
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212 
fun printgoals (_, []) = () 
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 printgoals (n, A::As) = 
252
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214 
let val prettyn = Pretty.str(" " ^ string_of_int n ^ ". "); 
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val prettyA = Sign.pretty_term sign A 
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216 
in prettyprints[prettyn,prettyA]; 
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217 
printgoals (n+1,As) 
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218 
end; 
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219 
fun prettypair(t,u) = 
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220 
Pretty.blk(0, [Sign.pretty_term sign t, Pretty.str" =?=", Pretty.brk 1, 
252
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221 
Sign.pretty_term sign u]); 
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222 
fun printff [] = () 
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223 
 printff tpairs = 
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224 
writeln("\nFlexflex pairs:\n" ^ 
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225 
Pretty.string_of(Pretty.lst("","") (map prettypair tpairs))) 
229
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226 
val (tpairs,As,B) = Logic.strip_horn(prop); 
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227 
val ngoals = length As 
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228 
in 
229
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writeln (Sign.string_of_term sign B); 
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230 
if ngoals=0 then writeln"No subgoals!" 
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231 
else if ngoals>maxgoals 
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232 
then (printgoals (1, take(maxgoals,As)); 
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233 
writeln("A total of " ^ string_of_int ngoals ^ " subgoals...")) 
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234 
else printgoals (1, As); 
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235 
printff tpairs 
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236 
end; 
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237 

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238 
(*"hook" for user interfaces: allows print_goals to be replaced*) 
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239 
val print_goals_ref = ref print_goals; 
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240 

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241 
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term 
0  242 
Used for establishing default types (of variables) and sorts (of 
243 
type variables) when reading another term. 

244 
Index 1 indicates that a (T)Free rather than a (T)Var is wanted. 

245 
***) 

246 

247 
fun types_sorts thm = 

248 
let val {prop,hyps,...} = rep_thm thm; 

252
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249 
val big = list_comb(prop,hyps); (* bogus term! *) 
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250 
val vars = map dest_Var (term_vars big); 
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val frees = map dest_Free (term_frees big); 
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val tvars = term_tvars big; 
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253 
val tfrees = term_tfrees big; 
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254 
fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i)); 
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255 
fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); 
0  256 
in (typ,sort) end; 
257 

258 
(** Standardization of rules **) 

259 

260 
(*Generalization over a list of variables, IGNORING bad ones*) 

261 
fun forall_intr_list [] th = th 

262 
 forall_intr_list (y::ys) th = 

252
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263 
let val gth = forall_intr_list ys th 
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264 
in forall_intr y gth handle THM _ => gth end; 
0  265 

266 
(*Generalization over all suitable Free variables*) 

267 
fun forall_intr_frees th = 

268 
let val {prop,sign,...} = rep_thm th 

269 
in forall_intr_list 

252
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270 
(map (cterm_of sign) (sort atless (term_frees prop))) 
0  271 
th 
272 
end; 

273 

274 
(*Replace outermost quantified variable by Var of given index. 

275 
Could clash with Vars already present.*) 

252
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276 
fun forall_elim_var i th = 
0  277 
let val {prop,sign,...} = rep_thm th 
278 
in case prop of 

252
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279 
Const("all",_) $ Abs(a,T,_) => 
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280 
forall_elim (cterm_of sign (Var((a,i), T))) th 
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281 
 _ => raise THM("forall_elim_var", i, [th]) 
0  282 
end; 
283 

284 
(*Repeat forall_elim_var until all outer quantifiers are removed*) 

252
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285 
fun forall_elim_vars i th = 
0  286 
forall_elim_vars i (forall_elim_var i th) 
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287 
handle THM _ => th; 
0  288 

289 
(*Specialization over a list of cterms*) 

290 
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th); 

291 

292 
(* maps [A1,...,An], B to [ A1;...;An ] ==> B *) 

293 
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th); 

294 

295 
(* maps [ A1;...;An ] ==> B and [A1,...,An] to B *) 

296 
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths); 

297 

298 
(*Reset Var indexes to zero, renaming to preserve distinctness*) 

252
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299 
fun zero_var_indexes th = 
0  300 
let val {prop,sign,...} = rep_thm th; 
301 
val vars = term_vars prop 

302 
val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars) 

252
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303 
val inrs = add_term_tvars(prop,[]); 
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304 
val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); 
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305 
val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms') 
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306 
val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye; 
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307 
fun varpairs([],[]) = [] 
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308 
 varpairs((var as Var(v,T)) :: vars, b::bs) = 
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309 
let val T' = typ_subst_TVars tye T 
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310 
in (cterm_of sign (Var(v,T')), 
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311 
cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs) 
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312 
end 
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313 
 varpairs _ = raise TERM("varpairs", []); 
0  314 
in instantiate (ctye, varpairs(vars,rev bs)) th end; 
315 

316 

317 
(*Standard form of objectrule: no hypotheses, Frees, or outer quantifiers; 

318 
all generality expressed by Vars having index 0.*) 

319 
fun standard th = 

320 
let val {maxidx,...} = rep_thm th 

252
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321 
in varifyT (zero_var_indexes (forall_elim_vars(maxidx+1) 
0  322 
(forall_intr_frees(implies_intr_hyps th)))) 
323 
end; 

324 

252
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325 
(*Assume a new formula, read following the same conventions as axioms. 
0  326 
Generalizes over Free variables, 
327 
creates the assumption, and then strips quantifiers. 

328 
Example is [ ALL x:?A. ?P(x) ] ==> [ ?P(?a) ] 

252
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329 
[ !(A,P,a)[ ALL x:A. P(x) ] ==> [ P(a) ] ] *) 
0  330 
fun assume_ax thy sP = 
331 
let val sign = sign_of thy 

252
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332 
val prop = Logic.close_form (term_of (read_cterm sign 
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333 
(sP, propT))) 
229
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334 
in forall_elim_vars 0 (assume (cterm_of sign prop)) end; 
0  335 

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336 
(*Resolution: exactly one resolvent must be produced.*) 
0  337 
fun tha RSN (i,thb) = 
338 
case Sequence.chop (2, biresolution false [(false,tha)] i thb) of 

339 
([th],_) => th 

340 
 ([],_) => raise THM("RSN: no unifiers", i, [tha,thb]) 

341 
 _ => raise THM("RSN: multiple unifiers", i, [tha,thb]); 

342 

343 
(*resolution: P==>Q, Q==>R gives P==>R. *) 

344 
fun tha RS thb = tha RSN (1,thb); 

345 

346 
(*For joining lists of rules*) 

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347 
fun thas RLN (i,thbs) = 
0  348 
let val resolve = biresolution false (map (pair false) thas) i 
349 
fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => [] 

350 
in flat (map resb thbs) end; 

351 

352 
fun thas RL thbs = thas RLN (1,thbs); 

353 

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354 
(*Resolve a list of rules against bottom_rl from right to left; 
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355 
makes proof trees*) 
252
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diff
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356 
fun rls MRS bottom_rl = 
11
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parents:
0
diff
changeset

357 
let fun rs_aux i [] = bottom_rl 
252
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diff
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358 
 rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls) 
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

359 
in rs_aux 1 rls end; 
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0
diff
changeset

360 

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Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

361 
(*As above, but for rule lists*) 
252
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diff
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362 
fun rlss MRL bottom_rls = 
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

363 
let fun rs_aux i [] = bottom_rls 
252
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229
diff
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364 
 rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss) 
11
d0e17c42dbb4
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lcp
parents:
0
diff
changeset

365 
in rs_aux 1 rlss end; 
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lcp
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0
diff
changeset

366 

252
7532f95d7f44
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367 
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R 
0  368 
with no lifting or renaming! Q may contain ==> or metaquants 
369 
ALWAYS deletes premise i *) 

252
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diff
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370 
fun compose(tha,i,thb) = 
0  371 
Sequence.list_of_s (bicompose false (false,tha,0) i thb); 
372 

373 
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*) 

374 
fun tha COMP thb = 

375 
case compose(tha,1,thb) of 

252
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diff
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376 
[th] => th 
0  377 
 _ => raise THM("COMP", 1, [tha,thb]); 
378 

379 
(*Instantiate theorem th, reading instantiations under signature sg*) 

380 
fun read_instantiate_sg sg sinsts th = 

381 
let val ts = types_sorts th; 

229
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diff
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382 
in instantiate (read_insts sg ts ts sinsts) th end; 
0  383 

384 
(*Instantiate theorem th, reading instantiations under theory of th*) 

385 
fun read_instantiate sinsts th = 

386 
read_instantiate_sg (#sign (rep_thm th)) sinsts th; 

387 

388 

389 
(*Lefttoright replacements: tpairs = [...,(vi,ti),...]. 

390 
Instantiates distinct Vars by terms, inferring type instantiations. *) 

391 
local 

392 
fun add_types ((ct,cu), (sign,tye)) = 

229
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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diff
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393 
let val {sign=signt, t=t, T= T, ...} = rep_cterm ct 
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diff
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394 
and {sign=signu, t=u, T= U, ...} = rep_cterm cu 
0  395 
val sign' = Sign.merge(sign, Sign.merge(signt, signu)) 
252
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396 
val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye) 
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397 
handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u]) 
0  398 
in (sign', tye') end; 
399 
in 

252
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400 
fun cterm_instantiate ctpairs0 th = 
0  401 
let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[])) 
402 
val tsig = #tsig(Sign.rep_sg sign); 

403 
fun instT(ct,cu) = let val inst = subst_TVars tye 

252
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404 
in (cterm_fun inst ct, cterm_fun inst cu) end 
229
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diff
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405 
fun ctyp2 (ix,T) = (ix, ctyp_of sign T) 
0  406 
in instantiate (map ctyp2 tye, map instT ctpairs0) th end 
252
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407 
handle TERM _ => 
0  408 
raise THM("cterm_instantiate: incompatible signatures",0,[th]) 
409 
 TYPE _ => raise THM("cterm_instantiate: types", 0, [th]) 

410 
end; 

411 

412 

413 
(** theorem equality test is exported and used by BEST_FIRST **) 

414 

252
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415 
(*equality of theorems uses equality of signatures and 
0  416 
the aconvertible test for terms*) 
252
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417 
fun eq_thm (th1,th2) = 
0  418 
let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1 
252
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419 
and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2 
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420 
in Sign.eq_sg (sg1,sg2) andalso 
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wenzelm
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421 
aconvs(hyps1,hyps2) andalso 
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422 
prop1 aconv prop2 
0  423 
end; 
424 

425 
(*Do the two theorems have the same signature?*) 

252
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diff
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426 
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); 
0  427 

428 
(*Useful "distance" function for BEST_FIRST*) 

429 
val size_of_thm = size_of_term o #prop o rep_thm; 

430 

431 

432 
(*** MetaRewriting Rules ***) 

433 

434 

435 
val reflexive_thm = 

385  436 
let val cx = cterm_of Sign.pure (Var(("x",0),TVar(("'a",0),logicS))) 
0  437 
in Thm.reflexive cx end; 
438 

439 
val symmetric_thm = 

229
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214
diff
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440 
let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT) 
0  441 
in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end; 
442 

443 
val transitive_thm = 

229
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diff
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444 
let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT) 
4002c4cd450c
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diff
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445 
val yz = read_cterm Sign.pure ("y::'a::logic == z",propT) 
0  446 
val xythm = Thm.assume xy and yzthm = Thm.assume yz 
447 
in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end; 

448 

229
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diff
changeset

449 
(** Below, a "conversion" has type cterm > thm **) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

450 

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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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parents:
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diff
changeset

451 
val refl_cimplies = reflexive (cterm_of Sign.pure implies); 
0  452 

453 
(*In [A1,...,An]==>B, rewrite the selected A's only  for rewrite_goals_tac*) 

214
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parents:
211
diff
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454 
(*Do not rewrite flexflex pairs*) 
252
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229
diff
changeset

455 
fun goals_conv pred cv = 
229
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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parents:
214
diff
changeset

456 
let fun gconv i ct = 
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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parents:
214
diff
changeset

457 
let val (A,B) = Thm.dest_cimplies ct 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

458 
val (thA,j) = case term_of A of 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

459 
Const("=?=",_)$_$_ => (reflexive A, i) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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parents:
214
diff
changeset

460 
 _ => (if pred i then cv A else reflexive A, i+1) 
252
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wenzelm
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229
diff
changeset

461 
in combination (combination refl_cimplies thA) (gconv j B) end 
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

462 
handle TERM _ => reflexive ct 
0  463 
in gconv 1 end; 
464 

465 
(*Use a conversion to transform a theorem*) 

229
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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parents:
214
diff
changeset

466 
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th; 
0  467 

468 
(*rewriting conversion*) 

229
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

469 
fun rew_conv mode prover mss = rewrite_cterm mode mss prover; 
0  470 

471 
(*Rewrite a theorem*) 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

472 
fun rewrite_rule thms = 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

473 
fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms)); 
0  474 

475 
(*Rewrite the subgoals of a proof state (represented by a theorem) *) 

476 
fun rewrite_goals_rule thms = 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

477 
fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None)) 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

478 
(Thm.mss_of thms))); 
0  479 

480 
(*Rewrite the subgoal of a proof state (represented by a theorem) *) 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

481 
fun rewrite_goal_rule mode prover mss i thm = 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

482 
if 0 < i andalso i <= nprems_of thm 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

483 
then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

484 
else raise THM("rewrite_goal_rule",i,[thm]); 
0  485 

486 

487 
(** Derived rules mainly for METAHYPS **) 

488 

489 
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*) 

490 
fun equal_abs_elim ca eqth = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

491 
let val {sign=signa, t=a, ...} = rep_cterm ca 
0  492 
and combth = combination eqth (reflexive ca) 
493 
val {sign,prop,...} = rep_thm eqth 

494 
val (abst,absu) = Logic.dest_equals prop 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

495 
val cterm = cterm_of (Sign.merge (sign,signa)) 
0  496 
in transitive (symmetric (beta_conversion (cterm (abst$a)))) 
497 
(transitive combth (beta_conversion (cterm (absu$a)))) 

498 
end 

499 
handle THM _ => raise THM("equal_abs_elim", 0, [eqth]); 

500 

501 
(*Calling equal_abs_elim with multiple terms*) 

502 
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th); 

503 

504 
local 

505 
open Logic 

506 
val alpha = TVar(("'a",0), []) (* type ?'a::{} *) 

507 
fun err th = raise THM("flexpair_inst: ", 0, [th]) 

508 
fun flexpair_inst def th = 

509 
let val {prop = Const _ $ t $ u, sign,...} = rep_thm th 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

510 
val cterm = cterm_of sign 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

511 
fun cvar a = cterm(Var((a,0),alpha)) 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

512 
val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)] 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

513 
def 
0  514 
in equal_elim def' th 
515 
end 

516 
handle THM _ => err th  bind => err th 

517 
in 

518 
val flexpair_intr = flexpair_inst (symmetric flexpair_def) 

519 
and flexpair_elim = flexpair_inst flexpair_def 

520 
end; 

521 

522 
(*Version for flexflex pairs  this supports lifting.*) 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

523 
fun flexpair_abs_elim_list cts = 
0  524 
flexpair_intr o equal_abs_elim_list cts o flexpair_elim; 
525 

526 

527 
(*** Some useful metatheorems ***) 

528 

529 
(*The rule V/V, obtains assumption solving for eresolve_tac*) 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

530 
val asm_rl = trivial(read_cterm Sign.pure ("PROP ?psi",propT)); 
0  531 

532 
(*Metalevel cut rule: [ V==>W; V ] ==> W *) 

252
7532f95d7f44
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wenzelm
parents:
229
diff
changeset

533 
val cut_rl = trivial(read_cterm Sign.pure 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

534 
("PROP ?psi ==> PROP ?theta", propT)); 
0  535 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

536 
(*Generalized elim rule for one conclusion; cut_rl with reversed premises: 
0  537 
[ PROP V; PROP V ==> PROP W ] ==> PROP W *) 
538 
val revcut_rl = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

539 
let val V = read_cterm Sign.pure ("PROP V", propT) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

540 
and VW = read_cterm Sign.pure ("PROP V ==> PROP W", propT); 
252
7532f95d7f44
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wenzelm
parents:
229
diff
changeset

541 
in standard (implies_intr V 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

542 
(implies_intr VW 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

543 
(implies_elim (assume VW) (assume V)))) 
0  544 
end; 
545 

546 
(* (!!x. PROP ?V) == PROP ?V Allows removal of redundant parameters*) 

547 
val triv_forall_equality = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

548 
let val V = read_cterm Sign.pure ("PROP V", propT) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

549 
and QV = read_cterm Sign.pure ("!!x::'a. PROP V", propT) 
385  550 
and x = read_cterm Sign.pure ("x", TFree("'a",logicS)); 
0  551 
in standard (equal_intr (implies_intr QV (forall_elim x (assume QV))) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

552 
(implies_intr V (forall_intr x (assume V)))) 
0  553 
end; 
554 

555 
end 

556 
end; 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

557 