author  haftmann 
Thu, 08 Jul 2010 16:19:24 +0200  
changeset 37744  3daaf23b9ab4 
parent 37388  793618618f78 
child 37884  314a88278715 
permissions  rwrr 
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(* Title: HOL/Tools/lin_arith.ML 
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Author: Tjark Weber and Tobias Nipkow, TU Muenchen 
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HOL setup for linear arithmetic (see Provers/Arith/fast_lin_arith.ML). 
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*) 
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signature LIN_ARITH = 
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sig 
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val pre_tac: simpset > int > tactic 
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val simple_tac: Proof.context > int > tactic 
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val tac: Proof.context > int > tactic 
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val simproc: simpset > term > thm option 
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val add_inj_thms: thm list > Context.generic > Context.generic 
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val add_lessD: thm > Context.generic > Context.generic 

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val add_simps: thm list > Context.generic > Context.generic 

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val add_simprocs: simproc list > Context.generic > Context.generic 

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val add_inj_const: string * typ > Context.generic > Context.generic 
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val add_discrete_type: string > Context.generic > Context.generic 
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val set_number_of: (theory > typ > int > cterm) > Context.generic > 
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Context.generic 
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val setup: Context.generic > Context.generic 
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val global_setup: theory > theory 
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val split_limit: int Config.T 
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val neq_limit: int Config.T 

32740  25 
val trace: bool Unsynchronized.ref 
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end; 
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structure Lin_Arith: LIN_ARITH = 
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struct 
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(* Parameters data for general linear arithmetic functor *) 
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structure LA_Logic: LIN_ARITH_LOGIC = 
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struct 
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val ccontr = ccontr; 
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val conjI = conjI; 
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val notI = notI; 
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val sym = sym; 
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val trueI = TrueI; 
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val not_lessD = @{thm linorder_not_less} RS iffD1; 
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val not_leD = @{thm linorder_not_le} RS iffD1; 
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fun mk_Eq thm = thm RS @{thm Eq_FalseI} handle THM _ => thm RS @{thm Eq_TrueI}; 
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val mk_Trueprop = HOLogic.mk_Trueprop; 
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fun atomize thm = case Thm.prop_of thm of 
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Const ("Trueprop", _) $ (Const (@{const_name "op &"}, _) $ _ $ _) => 
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atomize (thm RS conjunct1) @ atomize (thm RS conjunct2) 

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 _ => [thm]; 
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fun neg_prop ((TP as Const("Trueprop", _)) $ (Const (@{const_name Not}, _) $ t)) = TP $ t 
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 neg_prop ((TP as Const("Trueprop", _)) $ t) = TP $ (HOLogic.Not $t) 
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 neg_prop t = raise TERM ("neg_prop", [t]); 
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fun is_False thm = 
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let val _ $ t = Thm.prop_of thm 
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in t = HOLogic.false_const end; 
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fun is_nat t = (fastype_of1 t = HOLogic.natT); 
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fun mk_nat_thm thy t = 
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let 

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val cn = cterm_of thy (Var (("n", 0), HOLogic.natT)) 

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and ct = cterm_of thy t 

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in instantiate ([], [(cn, ct)]) @{thm le0} end; 

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32369  69 
end; (* LA_Logic *) 
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(* arith context data *) 
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structure Lin_Arith_Data = Generic_Data 
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( 
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type T = {splits: thm list, 
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inj_consts: (string * typ) list, 
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discrete: string list}; 
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val empty = {splits = [], inj_consts = [], discrete = []}; 
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val extend = I; 
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fun merge 
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({splits= splits1, inj_consts= inj_consts1, discrete= discrete1}, 
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{splits= splits2, inj_consts= inj_consts2, discrete= discrete2}) : T = 
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{splits = Thm.merge_thms (splits1, splits2), 
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inj_consts = Library.merge (op =) (inj_consts1, inj_consts2), 
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discrete = Library.merge (op =) (discrete1, discrete2)}; 
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); 
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31100  89 
val get_arith_data = Lin_Arith_Data.get o Context.Proof; 
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fun add_split thm = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} => 
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{splits = update Thm.eq_thm_prop thm splits, 

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inj_consts = inj_consts, discrete = discrete}); 

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fun add_discrete_type d = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} => 
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{splits = splits, inj_consts = inj_consts, 
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discrete = update (op =) d discrete}); 
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fun add_inj_const c = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} => 
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{splits = splits, inj_consts = update (op =) c inj_consts, 
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discrete = discrete}); 
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36001  103 
val (split_limit, setup_split_limit) = Attrib.config_int "linarith_split_limit" (K 9); 
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val (neq_limit, setup_neq_limit) = Attrib.config_int "linarith_neq_limit" (K 9); 

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31100  107 
structure LA_Data = 
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struct 
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31082  110 
val fast_arith_neq_limit = neq_limit; 
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(* Decomposition of terms *) 
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(*internal representation of linear (in)equations*) 
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type decomp = 
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((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat * bool); 
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fun nT (Type ("fun", [N, _])) = (N = HOLogic.natT) 
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 nT _ = false; 
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fun add_atom (t : term) (m : Rat.rat) (p : (term * Rat.rat) list, i : Rat.rat) : 
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(term * Rat.rat) list * Rat.rat = 
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case AList.lookup Pattern.aeconv p t of 
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NONE => ((t, m) :: p, i) 
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 SOME n => (AList.update Pattern.aeconv (t, Rat.add n m) p, i); 
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(* decompose nested multiplications, bracketing them to the right and combining 
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all their coefficients 
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inj_consts: list of constants to be ignored when encountered 
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(e.g. arithmetic type conversions that preserve value) 
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m: multiplicity associated with the entire product 
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returns either (SOME term, associated multiplicity) or (NONE, constant) 
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*) 
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fun demult (inj_consts : (string * typ) list) : term * Rat.rat > term option * Rat.rat = 
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let 
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fun demult ((mC as Const (@{const_name Groups.times}, _)) $ s $ t, m) = 
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(case s of Const (@{const_name Groups.times}, _) $ s1 $ s2 => 
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(* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *) 
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demult (mC $ s1 $ (mC $ s2 $ t), m) 
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 _ => 
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(* product 's * t', where either factor can be 'NONE' *) 
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(case demult (s, m) of 
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(SOME s', m') => 
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(case demult (t, m') of 
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(SOME t', m'') => (SOME (mC $ s' $ t'), m'') 
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 (NONE, m'') => (SOME s', m'')) 
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 (NONE, m') => demult (t, m'))) 
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 demult ((mC as Const (@{const_name Rings.divide}, _)) $ s $ t, m) = 
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(* FIXME: Shouldn't we simplify nested quotients, e.g. '(s/t)/u' could 
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154 
become 's/(t*u)', and '(s*t)/u' could become 's*(t/u)' ? Note that 
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155 
if we choose to do so here, the simpset used by arith must be able to 
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156 
perform the same simplifications. *) 
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157 
(* FIXME: Currently we treat the numerator as atomic unless the 
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158 
denominator can be reduced to a numeric constant. It might be better 
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159 
to demult the numerator in any case, and invent a new term of the form 
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160 
'1 / t' if the numerator can be reduced, but the denominator cannot. *) 
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161 
(* FIXME: Currently we even treat the whole fraction as atomic unless the 
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162 
denominator can be reduced to a numeric constant. It might be better 
25015  163 
to use the partially reduced denominator (i.e. 's / (2*t)' could be 
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164 
demult'ed to 's / t' with multiplicity .5). This would require a 
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165 
very simple change only below, but it breaks existing proofs. *) 
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166 
(* quotient 's / t', where the denominator t can be NONE *) 
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167 
(* Note: will raise Rat.DIVZERO iff m' is Rat.zero *) 
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168 
(case demult (t, Rat.one) of 
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(SOME _, _) => (SOME (mC $ s $ t), m) 
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170 
 (NONE, m') => apsnd (Rat.mult (Rat.inv m')) (demult (s, m))) 
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(* terms that evaluate to numeric constants *) 
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 demult (Const (@{const_name Groups.uminus}, _) $ t, m) = demult (t, Rat.neg m) 
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 demult (Const (@{const_name Groups.zero}, _), m) = (NONE, Rat.zero) 
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 demult (Const (@{const_name Groups.one}, _), m) = (NONE, m) 
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(*Warning: in rare cases number_of encloses a nonnumeral, 
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176 
in which case dest_numeral raises TERM; hence all the handles below. 
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177 
Same for Sucterms that turn out not to be numerals  
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178 
although the simplifier should eliminate those anyway ...*) 
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 demult (t as Const ("Int.number_class.number_of", _) $ n, m) = 
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((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_numeral n))) 
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181 
handle TERM _ => (SOME t, m)) 
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 demult (t as Const (@{const_name Suc}, _) $ _, m) = 
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((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_nat t))) 
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handle TERM _ => (SOME t, m)) 
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(* injection constants are ignored *) 
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 demult (t as Const f $ x, m) = 
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if member (op =) inj_consts f then demult (x, m) else (SOME t, m) 
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(* everything else is considered atomic *) 
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 demult (atom, m) = (SOME atom, m) 
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in demult end; 
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191 

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fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) : 
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((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option = 
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let 
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(* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of 
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summands and associated multiplicities, plus a constant 'i' (with implicit 
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multiplicity 1) *) 
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fun poly (Const (@{const_name Groups.plus}, _) $ s $ t, 
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m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi)) 
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 poly (all as Const (@{const_name Groups.minus}, T) $ s $ t, m, pi) = 
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if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi)) 
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 poly (all as Const (@{const_name Groups.uminus}, T) $ t, m, pi) = 
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if nT T then add_atom all m pi else poly (t, Rat.neg m, pi) 
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 poly (Const (@{const_name Groups.zero}, _), _, pi) = 
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pi 
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 poly (Const (@{const_name Groups.one}, _), m, (p, i)) = 
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(p, Rat.add i m) 
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 poly (Const (@{const_name Suc}, _) $ t, m, (p, i)) = 
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poly (t, m, (p, Rat.add i m)) 
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 poly (all as Const (@{const_name Groups.times}, _) $ _ $ _, m, pi as (p, i)) = 
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(case demult inj_consts (all, m) of 
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(NONE, m') => (p, Rat.add i m') 
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 (SOME u, m') => add_atom u m' pi) 
35084  214 
 poly (all as Const (@{const_name Rings.divide}, _) $ _ $ _, m, pi as (p, i)) = 
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(case demult inj_consts (all, m) of 
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(NONE, m') => (p, Rat.add i m') 
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 (SOME u, m') => add_atom u m' pi) 
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 poly (all as Const ("Int.number_class.number_of", Type(_,[_,T])) $ t, m, pi as (p, i)) = 
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219 
(let val k = HOLogic.dest_numeral t 
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val k2 = if k < 0 andalso T = HOLogic.natT then 0 else k 
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in (p, Rat.add i (Rat.mult m (Rat.rat_of_int k2))) end 
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222 
handle TERM _ => add_atom all m pi) 
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 poly (all as Const f $ x, m, pi) = 
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224 
if member (op =) inj_consts f then poly (x, m, pi) else add_atom all m pi 
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 poly (all, m, pi) = 
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226 
add_atom all m pi 
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val (p, i) = poly (lhs, Rat.one, ([], Rat.zero)) 
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228 
val (q, j) = poly (rhs, Rat.one, ([], Rat.zero)) 
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229 
in 
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230 
case rel of 
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231 
@{const_name Orderings.less} => SOME (p, i, "<", q, j) 
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232 
 @{const_name Orderings.less_eq} => SOME (p, i, "<=", q, j) 
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 "op =" => SOME (p, i, "=", q, j) 
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234 
 _ => NONE 
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235 
end handle Rat.DIVZERO => NONE; 
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236 

24271  237 
fun of_lin_arith_sort thy U = 
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238 
Sign.of_sort thy (U, @{sort Rings.linordered_idom}); 
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239 

31101
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240 
fun allows_lin_arith thy (discrete : string list) (U as Type (D, [])) : bool * bool = 
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if of_lin_arith_sort thy U then (true, member (op =) discrete D) 
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else if member (op =) discrete D then (true, true) else (false, false) 
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243 
 allows_lin_arith sg discrete U = (of_lin_arith_sort sg U, false); 
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244 

26942  245 
fun decomp_typecheck (thy, discrete, inj_consts) (T : typ, xxx) : decomp option = 
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case T of 
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Type ("fun", [U, _]) => 
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248 
(case allows_lin_arith thy discrete U of 
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249 
(true, d) => 
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250 
(case decomp0 inj_consts xxx of 
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251 
NONE => NONE 
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 SOME (p, i, rel, q, j) => SOME (p, i, rel, q, j, d)) 
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253 
 (false, _) => 
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254 
NONE) 
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 _ => NONE; 
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256 

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fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d) 
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 negate NONE = NONE; 
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259 

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260 
fun decomp_negation data 
26942  261 
((Const ("Trueprop", _)) $ (Const (rel, T) $ lhs $ rhs)) : decomp option = 
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262 
decomp_typecheck data (T, (rel, lhs, rhs)) 
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 decomp_negation data ((Const ("Trueprop", _)) $ 
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(Const ("Not", _) $ (Const (rel, T) $ lhs $ rhs))) = 
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negate (decomp_typecheck data (T, (rel, lhs, rhs))) 
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266 
 decomp_negation data _ = 
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267 
NONE; 
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268 

26942  269 
fun decomp ctxt : term > decomp option = 
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270 
let 
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271 
val thy = ProofContext.theory_of ctxt 
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val {discrete, inj_consts, ...} = get_arith_data ctxt 
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273 
in decomp_negation (thy, discrete, inj_consts) end; 
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274 

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fun domain_is_nat (_ $ (Const (_, T) $ _ $ _)) = nT T 
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 domain_is_nat (_ $ (Const ("Not", _) $ (Const (_, T) $ _ $ _))) = nT T 
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 domain_is_nat _ = false; 
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(**) 
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(* the following code performs splitting of certain constants (e.g., min, *) 
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(* max) in a linear arithmetic problem; similar to what split_tac later does *) 
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(* to the proof state *) 
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(**) 
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285 

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(* checks if splitting with 'thm' is implemented *) 
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fun is_split_thm thm = 
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case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => ( 
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(* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *) 
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case head_of lhs of 
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Const (a, _) => member (op =) [@{const_name Orderings.max}, 
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@{const_name Orderings.min}, 
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@{const_name Groups.abs}, 
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@{const_name Groups.minus}, 
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"Int.nat" (*DYNAMIC BINDING!*), 
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"Divides.div_class.mod" (*DYNAMIC BINDING!*), 
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"Divides.div_class.div" (*DYNAMIC BINDING!*)] a 
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 _ => (warning ("Lin. Arith.: wrong format for split rule " ^ 
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Display.string_of_thm_without_context thm); 
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false)) 
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 _ => (warning ("Lin. Arith.: wrong format for split rule " ^ 
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Display.string_of_thm_without_context thm); 
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false); 
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(* substitute new for occurrences of old in a term, incrementing bound *) 
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(* variables as needed when substituting inside an abstraction *) 
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308 

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fun subst_term ([] : (term * term) list) (t : term) = t 
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 subst_term pairs t = 
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(case AList.lookup Pattern.aeconv pairs t of 
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SOME new => 
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new 
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 NONE => 
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(case t of Abs (a, T, body) => 
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let val pairs' = map (pairself (incr_boundvars 1)) pairs 
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in Abs (a, T, subst_term pairs' body) end 
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 t1 $ t2 => 
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subst_term pairs t1 $ subst_term pairs t2 
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 _ => t)); 
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(* approximates the effect of one application of split_tac (followed by NNF *) 
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(* normalization) on the subgoal represented by '(Ts, terms)'; returns a *) 
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(* list of new subgoals (each again represented by a typ list for bound *) 
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(* variables and a term list for premises), or NONE if split_tac would fail *) 
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(* on the subgoal *) 
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327 

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(* FIXME: currently only the effect of certain split theorems is reproduced *) 
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(* (which is why we need 'is_split_thm'). A more canonical *) 
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(* implementation should analyze the righthand side of the split *) 
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331 
(* theorem that can be applied, and modify the subgoal accordingly. *) 
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(* Or even better, the splitter should be extended to provide *) 
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(* splitting on terms as well as splitting on theorems (where the *) 
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(* former can have a faster implementation as it does not need to be *) 
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335 
(* proofproducing). *) 
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336 

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fun split_once_items ctxt (Ts : typ list, terms : term list) : 
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(typ list * term list) list option = 
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339 
let 
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val thy = ProofContext.theory_of ctxt 
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341 
(* takes a list [t1, ..., tn] to the term *) 
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(* tn' > ... > t1' > False , *) 
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(* where ti' = HOLogic.dest_Trueprop ti *) 
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fun REPEAT_DETERM_etac_rev_mp tms = 
345 
fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop tms) 

346 
HOLogic.false_const 

347 
val split_thms = filter is_split_thm (#splits (get_arith_data ctxt)) 

348 
val cmap = Splitter.cmap_of_split_thms split_thms 

349 
val goal_tm = REPEAT_DETERM_etac_rev_mp terms 

350 
val splits = Splitter.split_posns cmap thy Ts goal_tm 

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val split_limit = Config.get ctxt split_limit 
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352 
in 
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if length splits > split_limit then ( 
354 
tracing ("linarith_split_limit exceeded (current value is " ^ 

355 
string_of_int split_limit ^ ")"); 

356 
NONE 

357 
) else case splits of 

358 
[] => 

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359 
(* split_tac would fail: no possible split *) 
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360 
NONE 
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 (_, _::_, _, _, _) :: _ => 
362 
(* disallow a split that involves nonlocally bound variables (except *) 

363 
(* when bound by outermost metaquantifiers) *) 

364 
NONE 

365 
 (_, [], _, split_type, split_term) :: _ => 

366 
(* ignore all but the first possible split *) 

367 
(case strip_comb split_term of 

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368 
(* ?P (max ?i ?j) = ((?i <= ?j > ?P ?j) & (~ ?i <= ?j > ?P ?i)) *) 
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(Const (@{const_name Orderings.max}, _), [t1, t2]) => 
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370 
let 
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371 
val rev_terms = rev terms 
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val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
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val terms2 = map (subst_term [(split_term, t2)]) rev_terms 
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val t1_leq_t2 = Const (@{const_name Orderings.less_eq}, 
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split_type > split_type > HOLogic.boolT) $ t1 $ t2 
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val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 
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val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
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val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms2 @ [not_false] 
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379 
val subgoal2 = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms1 @ [not_false] 
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380 
in 
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381 
SOME [(Ts, subgoal1), (Ts, subgoal2)] 
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382 
end 
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383 
(* ?P (min ?i ?j) = ((?i <= ?j > ?P ?i) & (~ ?i <= ?j > ?P ?j)) *) 
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384 
 (Const (@{const_name Orderings.min}, _), [t1, t2]) => 
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385 
let 
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386 
val rev_terms = rev terms 
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387 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
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388 
val terms2 = map (subst_term [(split_term, t2)]) rev_terms 
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val t1_leq_t2 = Const (@{const_name Orderings.less_eq}, 
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390 
split_type > split_type > HOLogic.boolT) $ t1 $ t2 
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391 
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 
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392 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
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393 
val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms1 @ [not_false] 
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394 
val subgoal2 = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms2 @ [not_false] 
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395 
in 
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396 
SOME [(Ts, subgoal1), (Ts, subgoal2)] 
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397 
end 
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398 
(* ?P (abs ?a) = ((0 <= ?a > ?P ?a) & (?a < 0 > ?P ( ?a))) *) 
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399 
 (Const (@{const_name Groups.abs}, _), [t1]) => 
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400 
let 
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401 
val rev_terms = rev terms 
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402 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
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403 
val terms2 = map (subst_term [(split_term, Const (@{const_name Groups.uminus}, 
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404 
split_type > split_type) $ t1)]) rev_terms 
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405 
val zero = Const (@{const_name Groups.zero}, split_type) 
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406 
val zero_leq_t1 = Const (@{const_name Orderings.less_eq}, 
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407 
split_type > split_type > HOLogic.boolT) $ zero $ t1 
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408 
val t1_lt_zero = Const (@{const_name Orderings.less}, 
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409 
split_type > split_type > HOLogic.boolT) $ t1 $ zero 
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410 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
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411 
val subgoal1 = (HOLogic.mk_Trueprop zero_leq_t1) :: terms1 @ [not_false] 
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412 
val subgoal2 = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false] 
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413 
in 
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parents:
diff
changeset

414 
SOME [(Ts, subgoal1), (Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

415 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

416 
(* ?P (?a  ?b) = ((?a < ?b > ?P 0) & (ALL d. ?a = ?b + d > ?P d)) *) 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

417 
 (Const (@{const_name Groups.minus}, _), [t1, t2]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

418 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

419 
(* "d" in the above theorem becomes a new bound variable after NNF *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

420 
(* transformation, therefore some adjustment of indices is necessary *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

421 
val rev_terms = rev terms 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

422 
val zero = Const (@{const_name Groups.zero}, split_type) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

423 
val d = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

424 
val terms1 = map (subst_term [(split_term, zero)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

425 
val terms2 = map (subst_term [(incr_boundvars 1 split_term, d)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

426 
(map (incr_boundvars 1) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

427 
val t1' = incr_boundvars 1 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

428 
val t2' = incr_boundvars 1 t2 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

429 
val t1_lt_t2 = Const (@{const_name Orderings.less}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

430 
split_type > split_type > HOLogic.boolT) $ t1 $ t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

431 
val t1_eq_t2_plus_d = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

432 
(Const (@{const_name Groups.plus}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

433 
split_type > split_type > split_type) $ t2' $ d) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

434 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

435 
val subgoal1 = (HOLogic.mk_Trueprop t1_lt_t2) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

436 
val subgoal2 = (HOLogic.mk_Trueprop t1_eq_t2_plus_d) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

437 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

438 
SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

439 
end 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

440 
(* ?P (nat ?i) = ((ALL n. ?i = of_nat n > ?P n) & (?i < 0 > ?P 0)) *) 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

441 
 (Const ("Int.nat", _), [t1]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

442 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

443 
val rev_terms = rev terms 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

444 
val zero_int = Const (@{const_name Groups.zero}, HOLogic.intT) 
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

445 
val zero_nat = Const (@{const_name Groups.zero}, HOLogic.natT) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

446 
val n = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

447 
val terms1 = map (subst_term [(incr_boundvars 1 split_term, n)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

448 
(map (incr_boundvars 1) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

449 
val terms2 = map (subst_term [(split_term, zero_nat)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

450 
val t1' = incr_boundvars 1 t1 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

451 
val t1_eq_nat_n = Const ("op =", HOLogic.intT > HOLogic.intT > HOLogic.boolT) $ t1' $ 
24196  452 
(Const (@{const_name of_nat}, HOLogic.natT > HOLogic.intT) $ n) 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

453 
val t1_lt_zero = Const (@{const_name Orderings.less}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

454 
HOLogic.intT > HOLogic.intT > HOLogic.boolT) $ t1 $ zero_int 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

455 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

456 
val subgoal1 = (HOLogic.mk_Trueprop t1_eq_nat_n) :: terms1 @ [not_false] 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

457 
val subgoal2 = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

458 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

459 
SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

460 
end 
33719  461 
(* ?P ((?n::nat) mod (number_of ?k)) = 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

462 
((number_of ?k = 0 > ?P ?n) & (~ (number_of ?k = 0) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

463 
(ALL i j. j < number_of ?k > ?n = number_of ?k * i + j > ?P j))) *) 
37388  464 
 (Const ("Divides.div_class.mod", Type ("fun", [@{typ nat}, _])), [t1, t2]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

465 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

466 
val rev_terms = rev terms 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

467 
val zero = Const (@{const_name Groups.zero}, split_type) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

468 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

469 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

470 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

471 
val terms2 = map (subst_term [(incr_boundvars 2 split_term, j)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

472 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

473 
val t1' = incr_boundvars 2 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

474 
val t2' = incr_boundvars 2 t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

475 
val t2_eq_zero = Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

476 
split_type > split_type > HOLogic.boolT) $ t2 $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

477 
val t2_neq_zero = HOLogic.mk_not (Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

478 
split_type > split_type > HOLogic.boolT) $ t2' $ zero) 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

479 
val j_lt_t2 = Const (@{const_name Orderings.less}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

480 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

481 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

482 
(Const (@{const_name Groups.plus}, split_type > split_type > split_type) $ 
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

483 
(Const (@{const_name Groups.times}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

484 
split_type > split_type > split_type) $ t2' $ i) $ j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

485 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

486 
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

487 
val subgoal2 = (map HOLogic.mk_Trueprop 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

488 
[t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

489 
@ terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

490 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

491 
SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

492 
end 
33719  493 
(* ?P ((?n::nat) div (number_of ?k)) = 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

494 
((number_of ?k = 0 > ?P 0) & (~ (number_of ?k = 0) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

495 
(ALL i j. j < number_of ?k > ?n = number_of ?k * i + j > ?P i))) *) 
37388  496 
 (Const ("Divides.div_class.div", Type ("fun", [@{typ nat}, _])), [t1, t2]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

497 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

498 
val rev_terms = rev terms 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

499 
val zero = Const (@{const_name Groups.zero}, split_type) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

500 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

501 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

502 
val terms1 = map (subst_term [(split_term, zero)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

503 
val terms2 = map (subst_term [(incr_boundvars 2 split_term, i)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

504 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

505 
val t1' = incr_boundvars 2 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

506 
val t2' = incr_boundvars 2 t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

507 
val t2_eq_zero = Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

508 
split_type > split_type > HOLogic.boolT) $ t2 $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

509 
val t2_neq_zero = HOLogic.mk_not (Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

510 
split_type > split_type > HOLogic.boolT) $ t2' $ zero) 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

511 
val j_lt_t2 = Const (@{const_name Orderings.less}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

512 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

513 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

514 
(Const (@{const_name Groups.plus}, split_type > split_type > split_type) $ 
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

515 
(Const (@{const_name Groups.times}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

516 
split_type > split_type > split_type) $ t2' $ i) $ j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

517 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

518 
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

519 
val subgoal2 = (map HOLogic.mk_Trueprop 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

520 
[t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

521 
@ terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

522 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

523 
SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

524 
end 
33719  525 
(* ?P ((?n::int) mod (number_of ?k)) = 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

526 
((number_of ?k = 0 > ?P ?n) & 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

527 
(0 < number_of ?k > 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

528 
(ALL i j. 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

529 
0 <= j & j < number_of ?k & ?n = number_of ?k * i + j > ?P j)) & 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

530 
(number_of ?k < 0 > 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

531 
(ALL i j. 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

532 
number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j > ?P j))) *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

533 
 (Const ("Divides.div_class.mod", 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

534 
Type ("fun", [Type ("Int.int", []), _])), [t1, t2]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

535 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

536 
val rev_terms = rev terms 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

537 
val zero = Const (@{const_name Groups.zero}, split_type) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

538 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

539 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

540 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

541 
val terms2_3 = map (subst_term [(incr_boundvars 2 split_term, j)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

542 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

543 
val t1' = incr_boundvars 2 t1 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

544 
val t2' = incr_boundvars 2 t2 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

545 
val t2_eq_zero = Const ("op =", 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

546 
split_type > split_type > HOLogic.boolT) $ t2 $ zero 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

547 
val zero_lt_t2 = Const (@{const_name Orderings.less}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

548 
split_type > split_type > HOLogic.boolT) $ zero $ t2' 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

549 
val t2_lt_zero = Const (@{const_name Orderings.less}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

550 
split_type > split_type > HOLogic.boolT) $ t2' $ zero 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

551 
val zero_leq_j = Const (@{const_name Orderings.less_eq}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

552 
split_type > split_type > HOLogic.boolT) $ zero $ j 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

553 
val j_leq_zero = Const (@{const_name Orderings.less_eq}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

554 
split_type > split_type > HOLogic.boolT) $ j $ zero 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

555 
val j_lt_t2 = Const (@{const_name Orderings.less}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

556 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

557 
val t2_lt_j = Const (@{const_name Orderings.less}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

558 
split_type > split_type> HOLogic.boolT) $ t2' $ j 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

559 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

560 
(Const (@{const_name Groups.plus}, split_type > split_type > split_type) $ 
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

561 
(Const (@{const_name Groups.times}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

562 
split_type > split_type > split_type) $ t2' $ i) $ j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

563 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

564 
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

565 
val subgoal2 = (map HOLogic.mk_Trueprop [zero_lt_t2, zero_leq_j]) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

566 
@ hd terms2_3 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

567 
:: (if tl terms2_3 = [] then [not_false] else []) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

568 
@ (map HOLogic.mk_Trueprop [j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

569 
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

570 
val subgoal3 = (map HOLogic.mk_Trueprop [t2_lt_zero, t2_lt_j]) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

571 
@ hd terms2_3 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

572 
:: (if tl terms2_3 = [] then [not_false] else []) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

573 
@ (map HOLogic.mk_Trueprop [j_leq_zero, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

574 
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

575 
val Ts' = split_type :: split_type :: Ts 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

576 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

577 
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

578 
end 
33719  579 
(* ?P ((?n::int) div (number_of ?k)) = 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

580 
((number_of ?k = 0 > ?P 0) & 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

581 
(0 < number_of ?k > 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

582 
(ALL i j. 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

583 
0 <= j & j < number_of ?k & ?n = number_of ?k * i + j > ?P i)) & 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

584 
(number_of ?k < 0 > 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

585 
(ALL i j. 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

586 
number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j > ?P i))) *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

587 
 (Const ("Divides.div_class.div", 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

588 
Type ("fun", [Type ("Int.int", []), _])), [t1, t2]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

589 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

590 
val rev_terms = rev terms 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

591 
val zero = Const (@{const_name Groups.zero}, split_type) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

592 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

593 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

594 
val terms1 = map (subst_term [(split_term, zero)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

595 
val terms2_3 = map (subst_term [(incr_boundvars 2 split_term, i)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

596 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

597 
val t1' = incr_boundvars 2 t1 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

598 
val t2' = incr_boundvars 2 t2 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

599 
val t2_eq_zero = Const ("op =", 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

600 
split_type > split_type > HOLogic.boolT) $ t2 $ zero 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

601 
val zero_lt_t2 = Const (@{const_name Orderings.less}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

602 
split_type > split_type > HOLogic.boolT) $ zero $ t2' 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

603 
val t2_lt_zero = Const (@{const_name Orderings.less}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

604 
split_type > split_type > HOLogic.boolT) $ t2' $ zero 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

605 
val zero_leq_j = Const (@{const_name Orderings.less_eq}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

606 
split_type > split_type > HOLogic.boolT) $ zero $ j 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

607 
val j_leq_zero = Const (@{const_name Orderings.less_eq}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

608 
split_type > split_type > HOLogic.boolT) $ j $ zero 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

609 
val j_lt_t2 = Const (@{const_name Orderings.less}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

610 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset

611 
val t2_lt_j = Const (@{const_name Orderings.less}, 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

612 
split_type > split_type> HOLogic.boolT) $ t2' $ j 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

613 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

614 
(Const (@{const_name Groups.plus}, split_type > split_type > split_type) $ 
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset

615 
(Const (@{const_name Groups.times}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

616 
split_type > split_type > split_type) $ t2' $ i) $ j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

617 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

618 
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

619 
val subgoal2 = (map HOLogic.mk_Trueprop [zero_lt_t2, zero_leq_j]) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

620 
@ hd terms2_3 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

621 
:: (if tl terms2_3 = [] then [not_false] else []) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

622 
@ (map HOLogic.mk_Trueprop [j_lt_t2, t1_eq_t2_times_i_plus_j]) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

623 
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

624 
val subgoal3 = (map HOLogic.mk_Trueprop [t2_lt_zero, t2_lt_j]) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

625 
@ hd terms2_3 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

626 
:: (if tl terms2_3 = [] then [not_false] else []) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

627 
@ (map HOLogic.mk_Trueprop [j_leq_zero, t1_eq_t2_times_i_plus_j]) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

628 
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

629 
val Ts' = split_type :: split_type :: Ts 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

630 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

631 
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

632 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

633 
(* this will only happen if a split theorem can be applied for which no *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

634 
(* code exists above  in which case either the split theorem should be *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

635 
(* implemented above, or 'is_split_thm' should be modified to filter it *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

636 
(* out *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

637 
 (t, ts) => ( 
24920  638 
warning ("Lin. Arith.: split rule for " ^ Syntax.string_of_term ctxt t ^ 
32369  639 
" (with " ^ string_of_int (length ts) ^ 
640 
" argument(s)) not implemented; proof reconstruction is likely to fail"); 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

641 
NONE 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

642 
)) 
32369  643 
end; (* split_once_items *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

644 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

645 
(* remove terms that do not satisfy 'p'; change the order of the remaining *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

646 
(* terms in the same way as filter_prems_tac does *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

647 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

648 
fun filter_prems_tac_items (p : term > bool) (terms : term list) : term list = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

649 
let 
33339  650 
fun filter_prems t (left, right) = 
651 
if p t then (left, right @ [t]) else (left @ right, []) 

652 
val (left, right) = fold filter_prems terms ([], []) 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

653 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

654 
right @ left 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

655 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

656 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

657 
(* return true iff TRY (etac notE) THEN eq_assume_tac would succeed on a *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

658 
(* subgoal that has 'terms' as premises *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

659 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

660 
fun negated_term_occurs_positively (terms : term list) : bool = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

661 
List.exists 
32369  662 
(fn (Trueprop $ (Const ("Not", _) $ t)) => 
663 
member Pattern.aeconv terms (Trueprop $ t) 

664 
 _ => false) 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

665 
terms; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

666 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

667 
fun pre_decomp ctxt (Ts : typ list, terms : term list) : (typ list * term list) list = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

668 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

669 
(* repeatedly split (including newly emerging subgoals) until no further *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

670 
(* splitting is possible *) 
32369  671 
fun split_loop ([] : (typ list * term list) list) = 
672 
([] : (typ list * term list) list) 

673 
 split_loop (subgoal::subgoals) = 

674 
(case split_once_items ctxt subgoal of 

675 
SOME new_subgoals => split_loop (new_subgoals @ subgoals) 

676 
 NONE => subgoal :: split_loop subgoals) 

33035  677 
fun is_relevant t = is_some (decomp ctxt t) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

678 
(* filter_prems_tac is_relevant: *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

679 
val relevant_terms = filter_prems_tac_items is_relevant terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

680 
(* split_tac, NNF normalization: *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

681 
val split_goals = split_loop [(Ts, relevant_terms)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

682 
(* necessary because split_once_tac may normalize terms: *) 
32369  683 
val beta_eta_norm = map (apsnd (map (Envir.eta_contract o Envir.beta_norm))) 
684 
split_goals 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

685 
(* TRY (etac notE) THEN eq_assume_tac: *) 
33317  686 
val result = filter_out (negated_term_occurs_positively o snd) 
32369  687 
beta_eta_norm 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

688 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

689 
result 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

690 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

691 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

692 
(* takes the ith subgoal [ A1; ...; An ] ==> B to *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

693 
(* An > ... > A1 > B, performs splitting with the given 'split_thms' *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

694 
(* (resulting in a different subgoal P), takes P to ~P ==> False, *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

695 
(* performs NNFnormalization of ~P, and eliminates conjunctions, *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

696 
(* disjunctions and existential quantifiers from the premises, possibly (in *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

697 
(* the case of disjunctions) resulting in several new subgoals, each of the *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

698 
(* general form [ Q1; ...; Qm ] ==> False. Fails if more than *) 
31082  699 
(* !split_limit splits are possible. *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

700 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

701 
local 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

702 
val nnf_simpset = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

703 
empty_ss setmkeqTrue mk_eq_True 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

704 
setmksimps (mksimps mksimps_pairs) 
35410  705 
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, 
706 
@{thm de_Morgan_conj}, not_all, not_ex, not_not] 

35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

707 
fun prem_nnf_tac ss = full_simp_tac (Simplifier.inherit_context ss nnf_simpset) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

708 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

709 

35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

710 
fun split_once_tac ss split_thms = 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

711 
let 
35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

712 
val ctxt = Simplifier.the_context ss 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

713 
val thy = ProofContext.theory_of ctxt 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

714 
val cond_split_tac = SUBGOAL (fn (subgoal, i) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

715 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

716 
val Ts = rev (map snd (Logic.strip_params subgoal)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

717 
val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl subgoal) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

718 
val cmap = Splitter.cmap_of_split_thms split_thms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

719 
val splits = Splitter.split_posns cmap thy Ts concl 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

720 
in 
32369  721 
if null splits orelse length splits > Config.get ctxt split_limit then 
722 
no_tac 

723 
else if null (#2 (hd splits)) then 

724 
split_tac split_thms i 

725 
else 

726 
(* disallow a split that involves nonlocally bound variables *) 

727 
(* (except when bound by outermost metaquantifiers) *) 

728 
no_tac 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

729 
end) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

730 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

731 
EVERY' [ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

732 
REPEAT_DETERM o etac rev_mp, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

733 
cond_split_tac, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

734 
rtac ccontr, 
35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

735 
prem_nnf_tac ss, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

736 
TRY o REPEAT_ALL_NEW (DETERM o (eresolve_tac [conjE, exE] ORELSE' etac disjE)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

737 
] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

738 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

739 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

740 
end; (* local *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

741 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

742 
(* remove irrelevant premises, then split the ith subgoal (and all new *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

743 
(* subgoals) by using 'split_once_tac' repeatedly. Betaetanormalize new *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

744 
(* subgoals and finally attempt to solve them by finding an immediate *) 
32369  745 
(* contradiction (i.e., a term and its negation) in their premises. *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

746 

35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

747 
fun pre_tac ss i = 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

748 
let 
35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

749 
val ctxt = Simplifier.the_context ss; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

750 
val split_thms = filter is_split_thm (#splits (get_arith_data ctxt)) 
33035  751 
fun is_relevant t = is_some (decomp ctxt t) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

752 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

753 
DETERM ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

754 
TRY (filter_prems_tac is_relevant i) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

755 
THEN ( 
35230
be006fbcfb96
Lin_Arith.pre_tac: inherit proper simplifier context, and get rid of posthoc renaming of bound variables;
wenzelm
parents:
35092
diff
changeset

756 
(TRY o REPEAT_ALL_NEW (split_once_tac ss split_thms)) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

757 
THEN_ALL_NEW 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

758 
(CONVERSION Drule.beta_eta_conversion 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

759 
THEN' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

760 
(TRY o (etac notE THEN' eq_assume_tac))) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

761 
) i 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

762 
) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

763 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

764 

31100  765 
end; (* LA_Data *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

766 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

767 

31100  768 
val pre_tac = LA_Data.pre_tac; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

769 

31100  770 
structure Fast_Arith = Fast_Lin_Arith(structure LA_Logic = LA_Logic and LA_Data = LA_Data); 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

771 

31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

772 
fun map_inj_thms f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} = 
31100  773 
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = f inj_thms, 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

774 
lessD = lessD, neqE = neqE, simpset = simpset, number_of = number_of}; 
31100  775 

31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

776 
fun map_lessD f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} = 
31100  777 
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

778 
lessD = f lessD, neqE = neqE, simpset = simpset, number_of = number_of}; 
31100  779 

31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

780 
fun map_simpset f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} = 
31100  781 
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

782 
lessD = lessD, neqE = neqE, simpset = f simpset, number_of = number_of}; 
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

783 

e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

784 
fun map_number_of f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} = 
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

785 
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, 
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

786 
lessD = lessD, neqE = neqE, simpset = simpset, number_of = f number_of}; 
31100  787 

788 
fun add_inj_thms thms = Fast_Arith.map_data (map_inj_thms (append thms)); 

789 
fun add_lessD thm = Fast_Arith.map_data (map_lessD (fn thms => thms @ [thm])); 

790 
fun add_simps thms = Fast_Arith.map_data (map_simpset (fn simpset => simpset addsimps thms)); 

791 
fun add_simprocs procs = Fast_Arith.map_data (map_simpset (fn simpset => simpset addsimprocs procs)); 

792 

31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

793 
fun set_number_of f = Fast_Arith.map_data (map_number_of (K (serial (), f))) 
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

794 

e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

795 

31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

796 
fun simple_tac ctxt = Fast_Arith.lin_arith_tac ctxt false; 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

797 
val lin_arith_tac = Fast_Arith.lin_arith_tac; 
31082  798 
val trace = Fast_Arith.trace; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

799 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

800 
(* reduce contradictory <= to False. 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

801 
Most of the work is done by the cancel tactics. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

802 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

803 
val init_arith_data = 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

804 
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, number_of, ...} => 
35028
108662d50512
more consistent naming of type classes involving orderings (and lattices)  c.f. NEWS
haftmann
parents:
34974
diff
changeset

805 
{add_mono_thms = @{thms add_mono_thms_linordered_semiring} @ @{thms add_mono_thms_linordered_field} @ add_mono_thms, 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

806 
mult_mono_thms = @{thm mult_strict_left_mono} :: @{thm mult_left_mono} :: 
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

807 
@{lemma "a = b ==> c*a = c*b" by (rule arg_cong)} :: mult_mono_thms, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

808 
inj_thms = inj_thms, 
31082  809 
lessD = lessD @ [@{thm "Suc_leI"}], 
35028
108662d50512
more consistent naming of type classes involving orderings (and lattices)  c.f. NEWS
haftmann
parents:
34974
diff
changeset

810 
neqE = [@{thm linorder_neqE_nat}, @{thm linorder_neqE_linordered_idom}], 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

811 
simpset = HOL_basic_ss 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

812 
addsimps @{thms ring_distribs} 
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

813 
addsimps [@{thm if_True}, @{thm if_False}] 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

814 
addsimps 
35050
9f841f20dca6
renamed OrderedGroup to Groups; split theory Ring_and_Field into Rings Fields
haftmann
parents:
35028
diff
changeset

815 
[@{thm add_0_left}, 
9f841f20dca6
renamed OrderedGroup to Groups; split theory Ring_and_Field into Rings Fields
haftmann
parents:
35028
diff
changeset

816 
@{thm add_0_right}, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

817 
@{thm "Zero_not_Suc"}, @{thm "Suc_not_Zero"}, @{thm "le_0_eq"}, @{thm "One_nat_def"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

818 
@{thm "order_less_irrefl"}, @{thm "zero_neq_one"}, @{thm "zero_less_one"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

819 
@{thm "zero_le_one"}, @{thm "zero_neq_one"} RS not_sym, @{thm "not_one_le_zero"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

820 
@{thm "not_one_less_zero"}] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

821 
addsimprocs [ab_group_add_cancel.sum_conv, ab_group_add_cancel.rel_conv] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

822 
(*abel_cancel helps it work in abstract algebraic domains*) 
31082  823 
addsimprocs Nat_Arith.nat_cancel_sums_add 
35410  824 
addcongs [@{thm if_weak_cong}], 
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset

825 
number_of = number_of}) #> 
31082  826 
add_discrete_type @{type_name nat}; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

827 

29849
a2baf1b221be
new attribute "arith" for facts supplied to arith.
nipkow
parents:
29548
diff
changeset

828 
fun add_arith_facts ss = 
30686
47a32dd1b86e
moved generic arith_tac (formerly silent_arith_tac), verbose_arith_tac (formerly arith_tac) to Arith_Data; simple_arithtac now named linear_arith_tac
haftmann
parents:
30528
diff
changeset

829 
add_prems (Arith_Data.get_arith_facts (MetaSimplifier.the_context ss)) ss; 
29849
a2baf1b221be
new attribute "arith" for facts supplied to arith.
nipkow
parents:
29548
diff
changeset

830 

31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

831 
val simproc = add_arith_facts #> Fast_Arith.lin_arith_simproc; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

832 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

833 

26110  834 
(* generic refutation procedure *) 
835 

836 
(* parameters: 

837 

838 
test: term > bool 

839 
tests if a term is at all relevant to the refutation proof; 

840 
if not, then it can be discarded. Can improve performance, 

841 
esp. if disjunctions can be discarded (no case distinction needed!). 

842 

843 
prep_tac: int > tactic 

844 
A preparation tactic to be applied to the goal once all relevant premises 

845 
have been moved to the conclusion. 

846 

847 
ref_tac: int > tactic 

848 
the actual refutation tactic. Should be able to deal with goals 

849 
[ A1; ...; An ] ==> False 

850 
where the Ai are atomic, i.e. no toplevel &,  or EX 

851 
*) 

852 

853 
local 

854 
val nnf_simpset = 

855 
empty_ss setmkeqTrue mk_eq_True 

856 
setmksimps (mksimps mksimps_pairs) 

857 
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, 

858 
@{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}]; 

859 
fun prem_nnf_tac i st = 

35232
f588e1169c8b
renamed Simplifier.theory_context to Simplifier.global_context to emphasize that this is not the real thing;
wenzelm
parents:
35230
diff
changeset

860 
full_simp_tac (Simplifier.global_context (Thm.theory_of_thm st) nnf_simpset) i st; 
26110  861 
in 
862 
fun refute_tac test prep_tac ref_tac = 

863 
let val refute_prems_tac = 

864 
REPEAT_DETERM 

865 
(eresolve_tac [@{thm conjE}, @{thm exE}] 1 ORELSE 

866 
filter_prems_tac test 1 ORELSE 

867 
etac @{thm disjE} 1) THEN 

868 
(DETERM (etac @{thm notE} 1 THEN eq_assume_tac 1) ORELSE 

869 
ref_tac 1); 

870 
in EVERY'[TRY o filter_prems_tac test, 

871 
REPEAT_DETERM o etac @{thm rev_mp}, prep_tac, rtac @{thm ccontr}, prem_nnf_tac, 

872 
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] 

873 
end; 

874 
end; 

875 

876 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

877 
(* arith proof method *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

878 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

879 
local 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

880 

31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

881 
fun raw_tac ctxt ex = 
33035  882 
(* FIXME: K true should be replaced by a sensible test (perhaps "is_some o 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

883 
decomp sg"?  but note that the test is applied to terms already before 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

884 
they are split/normalized) to speed things up in case there are lots of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

885 
irrelevant terms involved; elimination of min/max can be optimized: 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

886 
(max m n + k <= r) = (m+k <= r & n+k <= r) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

887 
(l <= min m n + k) = (l <= m+k & l <= n+k) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

888 
*) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

889 
refute_tac (K true) 
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

890 
(* Splitting is also done inside simple_tac, but not completely  *) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

891 
(* split_tac may use split theorems that have not been implemented in *) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

892 
(* simple_tac (cf. pre_decomp and split_once_items above), and *) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

893 
(* split_limit may trigger. *) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

894 
(* Therefore splitting outside of simple_tac may allow us to prove *) 
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset

895 
(* some goals that simple_tac alone would fail on. *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

896 
(REPEAT_DETERM o split_tac (#splits (get_arith_data ctxt))) 
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

897 
(lin_arith_tac ctxt ex); 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

898 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

899 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

900 

31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

901 
fun gen_tac ex ctxt = FIRST' [simple_tac ctxt, 
35625  902 
Object_Logic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_tac ctxt ex]; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

903 

31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

904 
val tac = gen_tac true; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

905 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

906 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

907 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

908 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

909 
(* context setup *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

910 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

911 
val setup = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

912 
init_arith_data #> 
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

913 
Simplifier.map_ss (fn ss => ss addsimprocs [Simplifier.simproc (@{theory}) "fast_nat_arith" 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

914 
["(m::nat) < n","(m::nat) <= n", "(m::nat) = n"] (K simproc)] 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

915 
(* Because of fast_nat_arith_simproc, the arithmetic solver is really only 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

916 
useful to detect inconsistencies among the premises for subgoals which are 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

917 
*not* themselves (in)equalities, because the latter activate 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

918 
fast_nat_arith_simproc anyway. However, it seems cheaper to activate the 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

919 
solver all the time rather than add the additional check. *) 
29850  920 
addSolver (mk_solver' "lin_arith" 
31100  921 
(add_arith_facts #> Fast_Arith.cut_lin_arith_tac))) 
922 

923 
val global_setup = 

924 
setup_split_limit #> setup_neq_limit #> 

925 
Attrib.setup @{binding arith_split} (Scan.succeed (Thm.declaration_attribute add_split)) 

926 
"declaration of split rules for arithmetic procedure" #> 

927 
Method.setup @{binding linarith} 

33554  928 
(Scan.succeed (fn ctxt => 
31100  929 
METHOD (fn facts => 
33554  930 
HEADGOAL (Method.insert_tac (Arith_Data.get_arith_facts ctxt @ facts) 
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

931 
THEN' tac ctxt)))) "linear arithmetic" #> 
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset

932 
Arith_Data.add_tactic "linear arithmetic" gen_tac; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

933 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

934 
end; 