author | haftmann |
Mon, 11 May 2009 15:57:29 +0200 | |
changeset 31101 | 26c7bb764a38 |
parent 31100 | 6a2e67fe4488 |
child 31510 | e0f2bb4b0021 |
permissions | -rw-r--r-- |
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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: Proof.context -> 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 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 |
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val warning_count: int ref |
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val trace: bool 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 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 Eq_FalseI handle THM _ => thm RS 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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end; |
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(* arith context data *) |
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structure Lin_Arith_Data = GenericDataFun |
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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 = Library.merge Thm.eq_thm_prop (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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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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val (split_limit, setup_split_limit) = Attrib.config_int "linarith_split_limit" 9; |
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val (neq_limit, setup_neq_limit) = Attrib.config_int "linarith_neq_limit" 9; |
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structure LA_Data = |
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struct |
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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 HOL.times}, _)) $ s $ t, m) = |
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(case s of Const (@{const_name HOL.times}, _) $ s1 $ s2 => |
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(* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *) |
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141 |
demult (mC $ s1 $ (mC $ s2 $ t), m) |
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142 |
| _ => |
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143 |
(* product 's * t', where either factor can be 'NONE' *) |
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144 |
(case demult (s, m) of |
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145 |
(SOME s', m') => |
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146 |
(case demult (t, m') of |
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147 |
(SOME t', m'') => (SOME (mC $ s' $ t'), m'') |
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148 |
| (NONE, m'') => (SOME s', m'')) |
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149 |
| (NONE, m') => demult (t, m'))) |
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150 |
| demult ((mC as Const (@{const_name HOL.divide}, _)) $ s $ t, m) = |
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151 |
(* FIXME: Shouldn't we simplify nested quotients, e.g. '(s/t)/u' could |
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152 |
become 's/(t*u)', and '(s*t)/u' could become 's*(t/u)' ? Note that |
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153 |
if we choose to do so here, the simpset used by arith must be able to |
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154 |
perform the same simplifications. *) |
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155 |
(* FIXME: Currently we treat the numerator as atomic unless the |
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156 |
denominator can be reduced to a numeric constant. It might be better |
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157 |
to demult the numerator in any case, and invent a new term of the form |
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158 |
'1 / t' if the numerator can be reduced, but the denominator cannot. *) |
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|
159 |
(* FIXME: Currently we even treat the whole fraction as atomic unless the |
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|
160 |
denominator can be reduced to a numeric constant. It might be better |
25015 | 161 |
to use the partially reduced denominator (i.e. 's / (2*t)' could be |
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|
162 |
demult'ed to 's / t' with multiplicity .5). This would require a |
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163 |
very simple change only below, but it breaks existing proofs. *) |
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|
164 |
(* quotient 's / t', where the denominator t can be NONE *) |
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165 |
(* Note: will raise Rat.DIVZERO iff m' is Rat.zero *) |
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166 |
(case demult (t, Rat.one) of |
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167 |
(SOME _, _) => (SOME (mC $ s $ t), m) |
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168 |
| (NONE, m') => apsnd (Rat.mult (Rat.inv m')) (demult (s, m))) |
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|
169 |
(* terms that evaluate to numeric constants *) |
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170 |
| demult (Const (@{const_name HOL.uminus}, _) $ t, m) = demult (t, Rat.neg m) |
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171 |
| demult (Const (@{const_name HOL.zero}, _), m) = (NONE, Rat.zero) |
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172 |
| demult (Const (@{const_name HOL.one}, _), m) = (NONE, m) |
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|
173 |
(*Warning: in rare cases number_of encloses a non-numeral, |
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|
174 |
in which case dest_numeral raises TERM; hence all the handles below. |
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|
175 |
Same for Suc-terms that turn out not to be numerals - |
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176 |
although the simplifier should eliminate those anyway ...*) |
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|
177 |
| demult (t as Const ("Int.number_class.number_of", _) $ n, m) = |
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|
178 |
((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_numeral n))) |
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|
179 |
handle TERM _ => (SOME t, m)) |
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|
180 |
| demult (t as Const (@{const_name Suc}, _) $ _, m) = |
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|
181 |
((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_nat t))) |
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|
182 |
handle TERM _ => (SOME t, m)) |
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|
183 |
(* injection constants are ignored *) |
24092
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diff
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|
184 |
| demult (t as Const f $ x, m) = |
24328
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|
185 |
if member (op =) inj_consts f then demult (x, m) else (SOME t, m) |
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|
186 |
(* everything else is considered atomic *) |
24092
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|
187 |
| demult (atom, m) = (SOME atom, m) |
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|
188 |
in demult end; |
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|
189 |
|
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|
190 |
fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) : |
71c27b320610
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diff
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|
191 |
((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option = |
71c27b320610
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|
192 |
let |
24328
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|
193 |
(* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of |
83afe527504d
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|
194 |
summands and associated multiplicities, plus a constant 'i' (with implicit |
83afe527504d
fixed a bug in demult: -a in (-a * b) is no longer treated as atomic
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|
195 |
multiplicity 1) *) |
24092
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|
196 |
fun poly (Const (@{const_name HOL.plus}, _) $ s $ t, |
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changeset
|
197 |
m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi)) |
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diff
changeset
|
198 |
| poly (all as Const (@{const_name HOL.minus}, T) $ s $ t, m, pi) = |
71c27b320610
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parents:
diff
changeset
|
199 |
if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi)) |
71c27b320610
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parents:
diff
changeset
|
200 |
| poly (all as Const (@{const_name HOL.uminus}, T) $ t, m, pi) = |
71c27b320610
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wenzelm
parents:
diff
changeset
|
201 |
if nT T then add_atom all m pi else poly (t, Rat.neg m, pi) |
71c27b320610
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parents:
diff
changeset
|
202 |
| poly (Const (@{const_name HOL.zero}, _), _, pi) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
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parents:
diff
changeset
|
203 |
pi |
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wenzelm
parents:
diff
changeset
|
204 |
| poly (Const (@{const_name HOL.one}, _), m, (p, i)) = |
71c27b320610
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wenzelm
parents:
diff
changeset
|
205 |
(p, Rat.add i m) |
71c27b320610
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parents:
diff
changeset
|
206 |
| poly (Const (@{const_name Suc}, _) $ t, m, (p, i)) = |
71c27b320610
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parents:
diff
changeset
|
207 |
poly (t, m, (p, Rat.add i m)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
208 |
| poly (all as Const (@{const_name HOL.times}, _) $ _ $ _, m, pi as (p, i)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
209 |
(case demult inj_consts (all, m) of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
210 |
(NONE, m') => (p, Rat.add i m') |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
211 |
| (SOME u, m') => add_atom u m' pi) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
212 |
| poly (all as Const (@{const_name HOL.divide}, _) $ _ $ _, m, pi as (p, i)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
213 |
(case demult inj_consts (all, m) of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
214 |
(NONE, m') => (p, Rat.add i m') |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
215 |
| (SOME u, m') => add_atom u m' pi) |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
216 |
| poly (all as Const ("Int.number_class.number_of", Type(_,[_,T])) $ t, m, pi as (p, i)) = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
217 |
(let val k = HOLogic.dest_numeral t |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
218 |
val k2 = if k < 0 andalso T = HOLogic.natT then 0 else k |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
219 |
in (p, Rat.add i (Rat.mult m (Rat.rat_of_int k2))) end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
220 |
handle TERM _ => add_atom all m pi) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
221 |
| poly (all as Const f $ x, m, pi) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
222 |
if f mem inj_consts then poly (x, m, pi) else add_atom all m pi |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
223 |
| poly (all, m, pi) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
224 |
add_atom all m pi |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
225 |
val (p, i) = poly (lhs, Rat.one, ([], Rat.zero)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
226 |
val (q, j) = poly (rhs, Rat.one, ([], Rat.zero)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
227 |
in |
71c27b320610
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wenzelm
parents:
diff
changeset
|
228 |
case rel of |
71c27b320610
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wenzelm
parents:
diff
changeset
|
229 |
@{const_name HOL.less} => SOME (p, i, "<", q, j) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
230 |
| @{const_name HOL.less_eq} => SOME (p, i, "<=", q, j) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
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parents:
diff
changeset
|
231 |
| "op =" => SOME (p, i, "=", q, j) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
232 |
| _ => NONE |
24328
83afe527504d
fixed a bug in demult: -a in (-a * b) is no longer treated as atomic
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|
233 |
end handle Rat.DIVZERO => NONE; |
24092
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parents:
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|
234 |
|
24271 | 235 |
fun of_lin_arith_sort thy U = |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
236 |
Sign.of_sort thy (U, @{sort Ring_and_Field.ordered_idom}); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
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parents:
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changeset
|
237 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
238 |
fun allows_lin_arith thy (discrete : string list) (U as Type (D, [])) : bool * bool = |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
239 |
if of_lin_arith_sort thy U then (true, member (op =) discrete D) |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
240 |
else if member (op =) discrete D then (true, true) else (false, false) |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
241 |
| allows_lin_arith sg discrete U = (of_lin_arith_sort sg U, false); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
242 |
|
26942 | 243 |
fun decomp_typecheck (thy, discrete, inj_consts) (T : typ, xxx) : decomp option = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
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|
244 |
case T of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
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|
245 |
Type ("fun", [U, _]) => |
71c27b320610
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wenzelm
parents:
diff
changeset
|
246 |
(case allows_lin_arith thy discrete U of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
247 |
(true, d) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
248 |
(case decomp0 inj_consts xxx of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
249 |
NONE => NONE |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
250 |
| SOME (p, i, rel, q, j) => SOME (p, i, rel, q, j, d)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
251 |
| (false, _) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
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|
252 |
NONE) |
71c27b320610
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253 |
| _ => NONE; |
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|
254 |
|
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|
255 |
fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d) |
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|
256 |
| negate NONE = NONE; |
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|
257 |
|
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|
258 |
fun decomp_negation data |
26942 | 259 |
((Const ("Trueprop", _)) $ (Const (rel, T) $ lhs $ rhs)) : decomp option = |
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|
260 |
decomp_typecheck data (T, (rel, lhs, rhs)) |
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|
261 |
| decomp_negation data ((Const ("Trueprop", _)) $ |
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|
262 |
(Const ("Not", _) $ (Const (rel, T) $ lhs $ rhs))) = |
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|
263 |
negate (decomp_typecheck data (T, (rel, lhs, rhs))) |
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|
264 |
| decomp_negation data _ = |
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|
265 |
NONE; |
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|
266 |
|
26942 | 267 |
fun decomp ctxt : term -> decomp option = |
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|
268 |
let |
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|
269 |
val thy = ProofContext.theory_of ctxt |
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|
270 |
val {discrete, inj_consts, ...} = get_arith_data ctxt |
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|
271 |
in decomp_negation (thy, discrete, inj_consts) end; |
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|
272 |
|
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|
273 |
fun domain_is_nat (_ $ (Const (_, T) $ _ $ _)) = nT T |
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|
274 |
| domain_is_nat (_ $ (Const ("Not", _) $ (Const (_, T) $ _ $ _))) = nT T |
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|
275 |
| domain_is_nat _ = false; |
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|
276 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
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|
277 |
val mk_number = HOLogic.mk_number; |
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|
278 |
|
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|
279 |
(*---------------------------------------------------------------------------*) |
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|
280 |
(* the following code performs splitting of certain constants (e.g. min, *) |
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|
281 |
(* max) in a linear arithmetic problem; similar to what split_tac later does *) |
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|
282 |
(* to the proof state *) |
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|
283 |
(*---------------------------------------------------------------------------*) |
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|
284 |
|
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|
285 |
(* checks if splitting with 'thm' is implemented *) |
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|
286 |
|
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|
287 |
fun is_split_thm (thm : thm) : bool = |
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|
288 |
case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => ( |
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|
289 |
(* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *) |
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290 |
case head_of lhs of |
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291 |
Const (a, _) => member (op =) [@{const_name Orderings.max}, |
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292 |
@{const_name Orderings.min}, |
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|
293 |
@{const_name HOL.abs}, |
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|
294 |
@{const_name HOL.minus}, |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
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|
295 |
"Int.nat", |
24092
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|
296 |
"Divides.div_class.mod", |
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|
297 |
"Divides.div_class.div"] a |
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|
298 |
| _ => (warning ("Lin. Arith.: wrong format for split rule " ^ |
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|
299 |
Display.string_of_thm thm); |
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|
300 |
false)) |
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|
301 |
| _ => (warning ("Lin. Arith.: wrong format for split rule " ^ |
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|
302 |
Display.string_of_thm thm); |
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|
303 |
false); |
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|
304 |
|
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|
305 |
(* substitute new for occurrences of old in a term, incrementing bound *) |
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|
306 |
(* variables as needed when substituting inside an abstraction *) |
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|
307 |
|
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|
308 |
fun subst_term ([] : (term * term) list) (t : term) = t |
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|
309 |
| subst_term pairs t = |
29528 | 310 |
(case AList.lookup Pattern.aeconv pairs t of |
24092
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|
311 |
SOME new => |
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|
312 |
new |
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|
313 |
| NONE => |
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|
314 |
(case t of Abs (a, T, body) => |
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|
315 |
let val pairs' = map (pairself (incr_boundvars 1)) pairs |
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|
316 |
in Abs (a, T, subst_term pairs' body) end |
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|
317 |
| t1 $ t2 => |
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|
318 |
subst_term pairs t1 $ subst_term pairs t2 |
71c27b320610
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changeset
|
319 |
| _ => t)); |
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|
320 |
|
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|
321 |
(* approximates the effect of one application of split_tac (followed by NNF *) |
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|
322 |
(* normalization) on the subgoal represented by '(Ts, terms)'; returns a *) |
71c27b320610
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|
323 |
(* list of new subgoals (each again represented by a typ list for bound *) |
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|
324 |
(* variables and a term list for premises), or NONE if split_tac would fail *) |
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|
325 |
(* on the subgoal *) |
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|
326 |
|
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|
327 |
(* FIXME: currently only the effect of certain split theorems is reproduced *) |
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|
328 |
(* (which is why we need 'is_split_thm'). A more canonical *) |
71c27b320610
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parents:
diff
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|
329 |
(* implementation should analyze the right-hand side of the split *) |
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diff
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|
330 |
(* theorem that can be applied, and modify the subgoal accordingly. *) |
71c27b320610
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parents:
diff
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|
331 |
(* Or even better, the splitter should be extended to provide *) |
71c27b320610
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parents:
diff
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|
332 |
(* splitting on terms as well as splitting on theorems (where the *) |
71c27b320610
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parents:
diff
changeset
|
333 |
(* former can have a faster implementation as it does not need to be *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
334 |
(* proof-producing). *) |
71c27b320610
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wenzelm
parents:
diff
changeset
|
335 |
|
71c27b320610
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wenzelm
parents:
diff
changeset
|
336 |
fun split_once_items ctxt (Ts : typ list, terms : term list) : |
71c27b320610
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parents:
diff
changeset
|
337 |
(typ list * term list) list option = |
71c27b320610
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wenzelm
parents:
diff
changeset
|
338 |
let |
71c27b320610
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wenzelm
parents:
diff
changeset
|
339 |
val thy = ProofContext.theory_of ctxt |
71c27b320610
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wenzelm
parents:
diff
changeset
|
340 |
(* takes a list [t1, ..., tn] to the term *) |
71c27b320610
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parents:
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changeset
|
341 |
(* tn' --> ... --> t1' --> False , *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
342 |
(* where ti' = HOLogic.dest_Trueprop ti *) |
71c27b320610
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parents:
diff
changeset
|
343 |
fun REPEAT_DETERM_etac_rev_mp terms' = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
344 |
fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop terms') HOLogic.false_const |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
345 |
val split_thms = filter is_split_thm (#splits (get_arith_data ctxt)) |
71c27b320610
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parents:
diff
changeset
|
346 |
val cmap = Splitter.cmap_of_split_thms split_thms |
71c27b320610
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wenzelm
parents:
diff
changeset
|
347 |
val splits = Splitter.split_posns cmap thy Ts (REPEAT_DETERM_etac_rev_mp terms) |
31082 | 348 |
val split_limit = Config.get ctxt split_limit |
24092
71c27b320610
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parents:
diff
changeset
|
349 |
in |
71c27b320610
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wenzelm
parents:
diff
changeset
|
350 |
if length splits > split_limit then |
31082 | 351 |
(tracing ("linarith_split_limit exceeded (current value is " ^ |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
352 |
string_of_int split_limit ^ ")"); NONE) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
353 |
else ( |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
354 |
case splits of [] => |
71c27b320610
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wenzelm
parents:
diff
changeset
|
355 |
(* split_tac would fail: no possible split *) |
71c27b320610
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wenzelm
parents:
diff
changeset
|
356 |
NONE |
71c27b320610
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wenzelm
parents:
diff
changeset
|
357 |
| ((_, _, _, split_type, split_term) :: _) => ( |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
358 |
(* ignore all but the first possible split *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
359 |
case strip_comb split_term of |
71c27b320610
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wenzelm
parents:
diff
changeset
|
360 |
(* ?P (max ?i ?j) = ((?i <= ?j --> ?P ?j) & (~ ?i <= ?j --> ?P ?i)) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
361 |
(Const (@{const_name Orderings.max}, _), [t1, t2]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
362 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
363 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
364 |
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
|
365 |
val terms2 = map (subst_term [(split_term, t2)]) rev_terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
366 |
val t1_leq_t2 = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
367 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
368 |
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
369 |
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
|
370 |
val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms2 @ [not_false] |
71c27b320610
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wenzelm
parents:
diff
changeset
|
371 |
val subgoal2 = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms1 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
372 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
373 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
374 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
375 |
(* ?P (min ?i ?j) = ((?i <= ?j --> ?P ?i) & (~ ?i <= ?j --> ?P ?j)) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
376 |
| (Const (@{const_name Orderings.min}, _), [t1, t2]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
377 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
378 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
379 |
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
|
380 |
val terms2 = map (subst_term [(split_term, t2)]) rev_terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
381 |
val t1_leq_t2 = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
382 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
383 |
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
384 |
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
|
385 |
val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms1 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
386 |
val subgoal2 = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
387 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
388 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
389 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
390 |
(* ?P (abs ?a) = ((0 <= ?a --> ?P ?a) & (?a < 0 --> ?P (- ?a))) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
391 |
| (Const (@{const_name HOL.abs}, _), [t1]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
392 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
393 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
394 |
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
|
395 |
val terms2 = map (subst_term [(split_term, Const (@{const_name HOL.uminus}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
396 |
split_type --> split_type) $ t1)]) rev_terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
397 |
val zero = Const (@{const_name HOL.zero}, split_type) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
398 |
val zero_leq_t1 = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
399 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
400 |
val t1_lt_zero = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
401 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ zero |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
402 |
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
|
403 |
val subgoal1 = (HOLogic.mk_Trueprop zero_leq_t1) :: terms1 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
404 |
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
|
405 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
406 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
407 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
408 |
(* ?P (?a - ?b) = ((?a < ?b --> ?P 0) & (ALL d. ?a = ?b + d --> ?P d)) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
409 |
| (Const (@{const_name HOL.minus}, _), [t1, t2]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
410 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
411 |
(* "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
|
412 |
(* transformation, therefore some adjustment of indices is necessary *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
413 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
414 |
val zero = Const (@{const_name HOL.zero}, split_type) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
415 |
val d = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
416 |
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
|
417 |
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
|
418 |
(map (incr_boundvars 1) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
419 |
val t1' = incr_boundvars 1 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
420 |
val t2' = incr_boundvars 1 t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
421 |
val t1_lt_t2 = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
422 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
423 |
val t1_eq_t2_plus_d = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
424 |
(Const (@{const_name HOL.plus}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
425 |
split_type --> split_type --> split_type) $ t2' $ d) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
426 |
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
|
427 |
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
|
428 |
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
|
429 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
430 |
SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
431 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
432 |
(* ?P (nat ?i) = ((ALL n. ?i = int n --> ?P n) & (?i < 0 --> ?P 0)) *) |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
433 |
| (Const ("Int.nat", _), [t1]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
434 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
435 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
436 |
val zero_int = Const (@{const_name HOL.zero}, HOLogic.intT) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
437 |
val zero_nat = Const (@{const_name HOL.zero}, HOLogic.natT) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
438 |
val n = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
439 |
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
|
440 |
(map (incr_boundvars 1) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
441 |
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
|
442 |
val t1' = incr_boundvars 1 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
443 |
val t1_eq_int_n = Const ("op =", HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1' $ |
24196 | 444 |
(Const (@{const_name of_nat}, HOLogic.natT --> HOLogic.intT) $ n) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
445 |
val t1_lt_zero = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
446 |
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
|
447 |
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
|
448 |
val subgoal1 = (HOLogic.mk_Trueprop t1_eq_int_n) :: terms1 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
449 |
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
|
450 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
451 |
SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
452 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
453 |
(* "?P ((?n::nat) mod (number_of ?k)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
454 |
((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
|
455 |
(ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P j))) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
456 |
| (Const ("Divides.div_class.mod", Type ("fun", [Type ("nat", []), _])), [t1, t2]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
457 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
458 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
459 |
val zero = Const (@{const_name HOL.zero}, split_type) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
460 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
461 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
462 |
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
|
463 |
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
|
464 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
465 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
466 |
val t2' = incr_boundvars 2 t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
467 |
val t2_eq_zero = Const ("op =", |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
468 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
469 |
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
|
470 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
471 |
val j_lt_t2 = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
472 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
473 |
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
474 |
(Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
475 |
(Const (@{const_name HOL.times}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
476 |
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
|
477 |
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
|
478 |
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
|
479 |
val subgoal2 = (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
480 |
[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
|
481 |
@ terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
482 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
483 |
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
|
484 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
485 |
(* "?P ((?n::nat) div (number_of ?k)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
486 |
((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
|
487 |
(ALL i j. j < number_of ?k --> ?n = number_of ?k * i + j --> ?P i))) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
488 |
| (Const ("Divides.div_class.div", Type ("fun", [Type ("nat", []), _])), [t1, t2]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
489 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
490 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
491 |
val zero = Const (@{const_name HOL.zero}, split_type) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
492 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
493 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
494 |
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
|
495 |
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
|
496 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
497 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
498 |
val t2' = incr_boundvars 2 t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
499 |
val t2_eq_zero = Const ("op =", |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
500 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
501 |
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
|
502 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
503 |
val j_lt_t2 = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
504 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
505 |
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
506 |
(Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
507 |
(Const (@{const_name HOL.times}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
508 |
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
|
509 |
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
|
510 |
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
|
511 |
val subgoal2 = (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
512 |
[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
|
513 |
@ terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
514 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
515 |
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
|
516 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
517 |
(* "?P ((?n::int) mod (number_of ?k)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
518 |
((iszero (number_of ?k) --> ?P ?n) & |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
519 |
(neg (number_of (uminus ?k)) --> |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
520 |
(ALL i j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j --> ?P j)) & |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
521 |
(neg (number_of ?k) --> |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
522 |
(ALL i j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j --> ?P j))) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
523 |
| (Const ("Divides.div_class.mod", |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
524 |
Type ("fun", [Type ("Int.int", []), _])), [t1, t2 as (number_of $ k)]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
525 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
526 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
527 |
val zero = Const (@{const_name HOL.zero}, split_type) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
528 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
529 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
530 |
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
|
531 |
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
|
532 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
533 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
534 |
val (t2' as (_ $ k')) = incr_boundvars 2 t2 |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
535 |
val iszero_t2 = Const ("Int.iszero", split_type --> HOLogic.boolT) $ t2 |
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
536 |
val neg_minus_k = Const ("Int.neg", split_type --> HOLogic.boolT) $ |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
537 |
(number_of $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
538 |
(Const (@{const_name HOL.uminus}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
539 |
HOLogic.intT --> HOLogic.intT) $ k')) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
540 |
val zero_leq_j = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
541 |
split_type --> split_type --> HOLogic.boolT) $ zero $ j |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
542 |
val j_lt_t2 = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
543 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
544 |
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
545 |
(Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
546 |
(Const (@{const_name HOL.times}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
547 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
548 |
val neg_t2 = Const ("Int.neg", split_type --> HOLogic.boolT) $ t2' |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
549 |
val t2_lt_j = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
550 |
split_type --> split_type--> HOLogic.boolT) $ t2' $ j |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
551 |
val j_leq_zero = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
552 |
split_type --> split_type --> HOLogic.boolT) $ j $ zero |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
553 |
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
|
554 |
val subgoal1 = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
555 |
val subgoal2 = (map HOLogic.mk_Trueprop [neg_minus_k, zero_leq_j]) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
556 |
@ hd terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
557 |
:: (if tl terms2_3 = [] then [not_false] else []) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
558 |
@ (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
|
559 |
@ (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
|
560 |
val subgoal3 = (map HOLogic.mk_Trueprop [neg_t2, t2_lt_j]) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
561 |
@ hd terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
562 |
:: (if tl terms2_3 = [] then [not_false] else []) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
563 |
@ (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
|
564 |
@ (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
|
565 |
val Ts' = split_type :: split_type :: Ts |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
566 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
567 |
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
568 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
569 |
(* "?P ((?n::int) div (number_of ?k)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
570 |
((iszero (number_of ?k) --> ?P 0) & |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
571 |
(neg (number_of (uminus ?k)) --> |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
572 |
(ALL i. (EX j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j) --> ?P i)) & |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
573 |
(neg (number_of ?k) --> |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
574 |
(ALL i. (EX j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j) --> ?P i))) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
575 |
| (Const ("Divides.div_class.div", |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
576 |
Type ("fun", [Type ("Int.int", []), _])), [t1, t2 as (number_of $ k)]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
577 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
578 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
579 |
val zero = Const (@{const_name HOL.zero}, split_type) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
580 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
581 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
582 |
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
|
583 |
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
|
584 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
585 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
586 |
val (t2' as (_ $ k')) = incr_boundvars 2 t2 |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
587 |
val iszero_t2 = Const ("Int.iszero", split_type --> HOLogic.boolT) $ t2 |
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
588 |
val neg_minus_k = Const ("Int.neg", split_type --> HOLogic.boolT) $ |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
589 |
(number_of $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
590 |
(Const (@{const_name HOL.uminus}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
591 |
HOLogic.intT --> HOLogic.intT) $ k')) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
592 |
val zero_leq_j = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
593 |
split_type --> split_type --> HOLogic.boolT) $ zero $ j |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
594 |
val j_lt_t2 = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
595 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
596 |
val t1_eq_t2_times_i_plus_j = Const ("op =", |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
597 |
split_type --> split_type --> HOLogic.boolT) $ t1' $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
598 |
(Const (@{const_name HOL.plus}, split_type --> split_type --> split_type) $ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
599 |
(Const (@{const_name HOL.times}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
600 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
601 |
val neg_t2 = Const ("Int.neg", split_type --> HOLogic.boolT) $ t2' |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
602 |
val t2_lt_j = Const (@{const_name HOL.less}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
603 |
split_type --> split_type--> HOLogic.boolT) $ t2' $ j |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
604 |
val j_leq_zero = Const (@{const_name HOL.less_eq}, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
605 |
split_type --> split_type --> HOLogic.boolT) $ j $ zero |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
606 |
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
|
607 |
val subgoal1 = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
608 |
val subgoal2 = (HOLogic.mk_Trueprop neg_minus_k) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
609 |
:: terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
610 |
@ not_false |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
611 |
:: (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
612 |
[zero_leq_j, 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
|
613 |
val subgoal3 = (HOLogic.mk_Trueprop neg_t2) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
614 |
:: terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
615 |
@ not_false |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
616 |
:: (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
617 |
[t2_lt_j, 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
|
618 |
val Ts' = split_type :: split_type :: Ts |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
619 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
620 |
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
621 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
622 |
(* 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
|
623 |
(* 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
|
624 |
(* 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
|
625 |
(* out *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
626 |
| (t, ts) => ( |
24920 | 627 |
warning ("Lin. Arith.: split rule for " ^ Syntax.string_of_term ctxt t ^ |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
628 |
" (with " ^ string_of_int (length ts) ^ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
629 |
" argument(s)) not implemented; proof reconstruction is likely to fail"); |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
630 |
NONE |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
631 |
)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
632 |
) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
633 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
634 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
635 |
(* 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
|
636 |
(* 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
|
637 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
638 |
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
|
639 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
640 |
fun filter_prems (t, (left, right)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
641 |
if p t then (left, right @ [t]) else (left @ right, []) |
30190 | 642 |
val (left, right) = List.foldl filter_prems ([], []) terms |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
643 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
644 |
right @ left |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
645 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
646 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
647 |
(* 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
|
648 |
(* subgoal that has 'terms' as premises *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
649 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
650 |
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
|
651 |
List.exists |
29528 | 652 |
(fn (Trueprop $ (Const ("Not", _) $ t)) => member Pattern.aeconv terms (Trueprop $ t) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
653 |
| _ => false) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
654 |
terms; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
655 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
656 |
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
|
657 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
658 |
(* 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
|
659 |
(* splitting is possible *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
660 |
fun split_loop ([] : (typ list * term list) list) = ([] : (typ list * term list) list) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
661 |
| split_loop (subgoal::subgoals) = ( |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
662 |
case split_once_items ctxt subgoal of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
663 |
SOME new_subgoals => split_loop (new_subgoals @ subgoals) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
664 |
| NONE => subgoal :: split_loop subgoals |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
665 |
) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
666 |
fun is_relevant t = isSome (decomp ctxt t) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
667 |
(* filter_prems_tac is_relevant: *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
668 |
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
|
669 |
(* split_tac, NNF normalization: *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
670 |
val split_goals = split_loop [(Ts, relevant_terms)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
671 |
(* necessary because split_once_tac may normalize terms: *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
672 |
val beta_eta_norm = map (apsnd (map (Envir.eta_contract o Envir.beta_norm))) split_goals |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
673 |
(* TRY (etac notE) THEN eq_assume_tac: *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
674 |
val result = List.filter (not o negated_term_occurs_positively o snd) beta_eta_norm |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
675 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
676 |
result |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
677 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
678 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
679 |
(* takes the i-th subgoal [| A1; ...; An |] ==> B to *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
680 |
(* 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
|
681 |
(* (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
|
682 |
(* performs NNF-normalization of ~P, and eliminates conjunctions, *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
683 |
(* 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
|
684 |
(* 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
|
685 |
(* general form [| Q1; ...; Qm |] ==> False. Fails if more than *) |
31082 | 686 |
(* !split_limit splits are possible. *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
687 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
688 |
local |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
689 |
val nnf_simpset = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
690 |
empty_ss setmkeqTrue mk_eq_True |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
691 |
setmksimps (mksimps mksimps_pairs) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
692 |
addsimps [imp_conv_disj, iff_conv_conj_imp, de_Morgan_disj, de_Morgan_conj, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
693 |
not_all, not_ex, not_not] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
694 |
fun prem_nnf_tac i st = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
695 |
full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
696 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
697 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
698 |
fun split_once_tac ctxt split_thms = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
699 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
700 |
val thy = ProofContext.theory_of ctxt |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
701 |
val cond_split_tac = SUBGOAL (fn (subgoal, i) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
702 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
703 |
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
|
704 |
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
|
705 |
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
|
706 |
val splits = Splitter.split_posns cmap thy Ts concl |
31082 | 707 |
val split_limit = Config.get ctxt split_limit |
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 |
if length splits > split_limit then no_tac |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
710 |
else split_tac split_thms i |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
711 |
end) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
712 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
713 |
EVERY' [ |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
714 |
REPEAT_DETERM o etac rev_mp, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
715 |
cond_split_tac, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
716 |
rtac ccontr, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
717 |
prem_nnf_tac, |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
718 |
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
|
719 |
] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
720 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
721 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
722 |
end; (* local *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
723 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
724 |
(* remove irrelevant premises, then split the i-th subgoal (and all new *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
725 |
(* subgoals) by using 'split_once_tac' repeatedly. Beta-eta-normalize new *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
726 |
(* subgoals and finally attempt to solve them by finding an immediate *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
727 |
(* contradiction (i.e. a term and its negation) in their premises. *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
728 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
729 |
fun pre_tac ctxt i = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
730 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
731 |
val split_thms = filter is_split_thm (#splits (get_arith_data ctxt)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
732 |
fun is_relevant t = isSome (decomp ctxt t) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
733 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
734 |
DETERM ( |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
735 |
TRY (filter_prems_tac is_relevant i) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
736 |
THEN ( |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
737 |
(TRY o REPEAT_ALL_NEW (split_once_tac ctxt split_thms)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
738 |
THEN_ALL_NEW |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
739 |
(CONVERSION Drule.beta_eta_conversion |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
740 |
THEN' |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
741 |
(TRY o (etac notE THEN' eq_assume_tac))) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
742 |
) i |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
743 |
) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
744 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
745 |
|
31100 | 746 |
end; (* LA_Data *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
747 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
748 |
|
31100 | 749 |
val pre_tac = LA_Data.pre_tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
750 |
|
31100 | 751 |
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
|
752 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
753 |
val map_data = Fast_Arith.map_data; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
754 |
|
31100 | 755 |
fun map_inj_thms f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} = |
756 |
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = f inj_thms, |
|
757 |
lessD = lessD, neqE = neqE, simpset = simpset}; |
|
758 |
||
759 |
fun map_lessD f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} = |
|
760 |
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, |
|
761 |
lessD = f lessD, neqE = neqE, simpset = simpset}; |
|
762 |
||
763 |
fun map_simpset f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} = |
|
764 |
{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, |
|
765 |
lessD = lessD, neqE = neqE, simpset = f simpset}; |
|
766 |
||
767 |
fun add_inj_thms thms = Fast_Arith.map_data (map_inj_thms (append thms)); |
|
768 |
fun add_lessD thm = Fast_Arith.map_data (map_lessD (fn thms => thms @ [thm])); |
|
769 |
fun add_simps thms = Fast_Arith.map_data (map_simpset (fn simpset => simpset addsimps thms)); |
|
770 |
fun add_simprocs procs = Fast_Arith.map_data (map_simpset (fn simpset => simpset addsimprocs procs)); |
|
771 |
||
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
772 |
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
|
773 |
val lin_arith_tac = Fast_Arith.lin_arith_tac; |
31082 | 774 |
val trace = Fast_Arith.trace; |
27017
1e0e8c1adf8c
added warning_count for issued reconstruction failure messages;
wenzelm
parents:
26942
diff
changeset
|
775 |
val warning_count = Fast_Arith.warning_count; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
776 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
777 |
(* reduce contradictory <= to False. |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
778 |
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
|
779 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
780 |
val init_arith_data = |
31100 | 781 |
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, ...} => |
31082 | 782 |
{add_mono_thms = @{thms add_mono_thms_ordered_semiring} @ @{thms add_mono_thms_ordered_field} @ add_mono_thms, |
783 |
mult_mono_thms = @{thm mult_strict_left_mono} :: @{thm mult_left_mono} :: mult_mono_thms, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
784 |
inj_thms = inj_thms, |
31082 | 785 |
lessD = lessD @ [@{thm "Suc_leI"}], |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
786 |
neqE = [@{thm linorder_neqE_nat}, @{thm linorder_neqE_ordered_idom}], |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
787 |
simpset = HOL_basic_ss |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
788 |
addsimps |
28053 | 789 |
[@{thm "monoid_add_class.add_0_left"}, |
790 |
@{thm "monoid_add_class.add_0_right"}, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
791 |
@{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
|
792 |
@{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
|
793 |
@{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
|
794 |
@{thm "not_one_less_zero"}] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
795 |
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
|
796 |
(*abel_cancel helps it work in abstract algebraic domains*) |
31082 | 797 |
addsimprocs Nat_Arith.nat_cancel_sums_add |
798 |
addcongs [if_weak_cong]}) #> |
|
799 |
add_discrete_type @{type_name nat}; |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
800 |
|
29849
a2baf1b221be
new attribute "arith" for facts supplied to arith.
nipkow
parents:
29548
diff
changeset
|
801 |
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_arith-tac now named linear_arith_tac
haftmann
parents:
30528
diff
changeset
|
802 |
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
|
803 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
804 |
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
|
805 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
806 |
|
26110 | 807 |
(* generic refutation procedure *) |
808 |
||
809 |
(* parameters: |
|
810 |
||
811 |
test: term -> bool |
|
812 |
tests if a term is at all relevant to the refutation proof; |
|
813 |
if not, then it can be discarded. Can improve performance, |
|
814 |
esp. if disjunctions can be discarded (no case distinction needed!). |
|
815 |
||
816 |
prep_tac: int -> tactic |
|
817 |
A preparation tactic to be applied to the goal once all relevant premises |
|
818 |
have been moved to the conclusion. |
|
819 |
||
820 |
ref_tac: int -> tactic |
|
821 |
the actual refutation tactic. Should be able to deal with goals |
|
822 |
[| A1; ...; An |] ==> False |
|
823 |
where the Ai are atomic, i.e. no top-level &, | or EX |
|
824 |
*) |
|
825 |
||
826 |
local |
|
827 |
val nnf_simpset = |
|
828 |
empty_ss setmkeqTrue mk_eq_True |
|
829 |
setmksimps (mksimps mksimps_pairs) |
|
830 |
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, |
|
831 |
@{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}]; |
|
832 |
fun prem_nnf_tac i st = |
|
833 |
full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st; |
|
834 |
in |
|
835 |
fun refute_tac test prep_tac ref_tac = |
|
836 |
let val refute_prems_tac = |
|
837 |
REPEAT_DETERM |
|
838 |
(eresolve_tac [@{thm conjE}, @{thm exE}] 1 ORELSE |
|
839 |
filter_prems_tac test 1 ORELSE |
|
840 |
etac @{thm disjE} 1) THEN |
|
841 |
(DETERM (etac @{thm notE} 1 THEN eq_assume_tac 1) ORELSE |
|
842 |
ref_tac 1); |
|
843 |
in EVERY'[TRY o filter_prems_tac test, |
|
844 |
REPEAT_DETERM o etac @{thm rev_mp}, prep_tac, rtac @{thm ccontr}, prem_nnf_tac, |
|
845 |
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] |
|
846 |
end; |
|
847 |
end; |
|
848 |
||
849 |
||
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
850 |
(* arith proof method *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
851 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
852 |
local |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
853 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
854 |
fun raw_tac ctxt ex = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
855 |
(* FIXME: K true should be replaced by a sensible test (perhaps "isSome o |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
856 |
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
|
857 |
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
|
858 |
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
|
859 |
(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
|
860 |
(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
|
861 |
*) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
862 |
refute_tac (K true) |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
863 |
(* Splitting is also done inside simple_tac, but not completely -- *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
864 |
(* split_tac may use split theorems that have not been implemented in *) |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
865 |
(* simple_tac (cf. pre_decomp and split_once_items above), and *) |
31082 | 866 |
(* split_limit may trigger. *) |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
867 |
(* Therefore splitting outside of simple_tac may allow us to prove *) |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
868 |
(* 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
|
869 |
(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
|
870 |
(lin_arith_tac ctxt ex); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
871 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
872 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
873 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
874 |
fun gen_tac ex ctxt = FIRST' [simple_tac ctxt, |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
875 |
ObjectLogic.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
|
876 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
877 |
val tac = gen_tac true; |
24092
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 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
880 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
881 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
882 |
(* context setup *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
883 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
884 |
val setup = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
885 |
init_arith_data #> |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
886 |
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
|
887 |
["(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
|
888 |
(* 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
|
889 |
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
|
890 |
*not* themselves (in)equalities, because the latter activate |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
891 |
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
|
892 |
solver all the time rather than add the additional check. *) |
29850 | 893 |
addSolver (mk_solver' "lin_arith" |
31100 | 894 |
(add_arith_facts #> Fast_Arith.cut_lin_arith_tac))) |
895 |
||
896 |
val global_setup = |
|
897 |
setup_split_limit #> setup_neq_limit #> |
|
898 |
Attrib.setup @{binding arith_split} (Scan.succeed (Thm.declaration_attribute add_split)) |
|
899 |
"declaration of split rules for arithmetic procedure" #> |
|
900 |
Method.setup @{binding linarith} |
|
901 |
(Args.bang_facts >> (fn prems => fn ctxt => |
|
902 |
METHOD (fn facts => |
|
903 |
HEADGOAL (Method.insert_tac (prems @ Arith_Data.get_arith_facts ctxt @ facts) |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
904 |
THEN' tac ctxt)))) "linear arithmetic" #> |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
905 |
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
|
906 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
907 |
end; |