author | haftmann |
Sat, 22 Jun 2019 07:18:55 +0000 | |
changeset 70356 | 4a327c061870 |
parent 69593 | 3dda49e08b9d |
child 74282 | c2ee8d993d6a |
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: Proof.context -> cterm -> thm option |
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val add_inj_thms: thm list -> Context.generic -> Context.generic |
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val add_lessD: thm -> Context.generic -> Context.generic |
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val add_simps: thm list -> Context.generic -> Context.generic |
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val add_simprocs: simproc list -> Context.generic -> Context.generic |
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val add_inj_const: string * typ -> Context.generic -> Context.generic |
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val add_discrete_type: string -> Context.generic -> Context.generic |
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val set_number_of: (Proof.context -> typ -> int -> cterm) -> Context.generic -> Context.generic |
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val global_setup: theory -> theory |
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val init_arith_data: Context.generic -> Context.generic |
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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 trace: bool Config.T |
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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 = @{thm ccontr}; |
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val conjI = conjI; |
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val notI = notI; |
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val sym = sym; |
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val trueI = TrueI; |
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val not_lessD = @{thm linorder_not_less} RS iffD1; |
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val not_leD = @{thm linorder_not_le} RS iffD1; |
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fun mk_Eq thm = thm RS @{thm Eq_FalseI} handle THM _ => thm RS @{thm Eq_TrueI}; |
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val mk_Trueprop = HOLogic.mk_Trueprop; |
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fun atomize thm = case Thm.prop_of thm of |
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Const (\<^const_name>\<open>Trueprop\<close>, _) $ (Const (\<^const_name>\<open>HOL.conj\<close>, _) $ _ $ _) => |
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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(\<^const_name>\<open>Trueprop\<close>, _)) $ (Const (\<^const_name>\<open>Not\<close>, _) $ t)) = TP $ t |
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| neg_prop ((TP as Const(\<^const_name>\<open>Trueprop\<close>, _)) $ 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 = \<^term>\<open>False\<close> 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 val ct = Thm.global_cterm_of thy t |
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in Drule.instantiate_normalize ([], [((("n", 0), HOLogic.natT), ct)]) @{thm le0} end; |
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end; |
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(* arith context data *) |
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structure Lin_Arith_Data = Generic_Data |
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( |
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type T = {splits: thm list, |
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inj_consts: (string * typ) list, |
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discrete: string list}; |
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val empty = {splits = [], inj_consts = [], discrete = []}; |
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val extend = I; |
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fun merge |
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({splits = splits1, inj_consts = inj_consts1, discrete = discrete1}, |
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{splits = splits2, inj_consts = inj_consts2, discrete = discrete2}) : T = |
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{splits = Thm.merge_thms (splits1, splits2), |
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inj_consts = Library.merge (op =) (inj_consts1, inj_consts2), |
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discrete = Library.merge (op =) (discrete1, discrete2)}; |
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); |
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val get_arith_data = Lin_Arith_Data.get o Context.Proof; |
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fun get_splits ctxt = |
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#splits (get_arith_data ctxt) |
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|> map (Thm.transfer' ctxt); |
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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.trim_context 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 = Attrib.setup_config_int \<^binding>\<open>linarith_split_limit\<close> (K 9); |
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val neq_limit = Attrib.setup_config_int \<^binding>\<open>linarith_neq_limit\<close> (K 9); |
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val trace = Attrib.setup_config_bool \<^binding>\<open>linarith_trace\<close> (K false); |
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structure LA_Data: LIN_ARITH_DATA = |
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struct |
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val neq_limit = neq_limit; |
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val trace = trace; |
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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 Envir.aeconv p t of |
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NONE => ((t, m) :: p, i) |
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| SOME n => (AList.update Envir.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 of_field_sort thy U = Sign.of_sort thy (U, \<^sort>\<open>inverse\<close>); |
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fun demult thy (inj_consts : (string * typ) list) : term * Rat.rat -> term option * Rat.rat = |
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144 |
let |
67149 | 145 |
fun demult ((mC as Const (\<^const_name>\<open>Groups.times\<close>, _)) $ s $ t, m) = |
146 |
(case s of Const (\<^const_name>\<open>Groups.times\<close>, _) $ s1 $ s2 => |
|
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|
147 |
(* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *) |
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148 |
demult (mC $ s1 $ (mC $ s2 $ t), m) |
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|
149 |
| _ => |
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|
150 |
(* product 's * t', where either factor can be 'NONE' *) |
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151 |
(case demult (s, m) of |
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152 |
(SOME s', m') => |
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153 |
(case demult (t, m') of |
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|
154 |
(SOME t', m'') => (SOME (mC $ s' $ t'), m'') |
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155 |
| (NONE, m'') => (SOME s', m'')) |
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|
156 |
| (NONE, m') => demult (t, m'))) |
67149 | 157 |
| demult (atom as (mC as Const (\<^const_name>\<open>Rings.divide\<close>, T)) $ s $ t, m) = |
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|
158 |
(* FIXME: Shouldn't we simplify nested quotients, e.g. '(s/t)/u' could |
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|
159 |
become 's/(t*u)', and '(s*t)/u' could become 's*(t/u)' ? Note that |
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|
160 |
if we choose to do so here, the simpset used by arith must be able to |
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|
161 |
perform the same simplifications. *) |
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|
162 |
(* quotient 's / t', where the denominator t can be NONE *) |
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|
163 |
(* Note: will raise Div iff m' is @0 *) |
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|
164 |
if of_field_sort thy (domain_type T) then |
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|
165 |
let |
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|
166 |
val (os',m') = demult (s, m); |
63205 | 167 |
val (ot',p) = demult (t, @1) |
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|
168 |
in (case (os',ot') of |
55375 | 169 |
(SOME s', SOME t') => SOME (mC $ s' $ t') |
170 |
| (SOME s', NONE) => SOME s' |
|
171 |
| (NONE, SOME t') => |
|
67149 | 172 |
SOME (mC $ Const (\<^const_name>\<open>Groups.one\<close>, domain_type (snd (dest_Const mC))) $ t') |
55375 | 173 |
| (NONE, NONE) => NONE, |
174 |
Rat.mult m' (Rat.inv p)) |
|
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|
175 |
end |
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|
176 |
else (SOME atom, m) |
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|
177 |
(* terms that evaluate to numeric constants *) |
67149 | 178 |
| demult (Const (\<^const_name>\<open>Groups.uminus\<close>, _) $ t, m) = demult (t, ~ m) |
179 |
| demult (Const (\<^const_name>\<open>Groups.zero\<close>, _), _) = (NONE, @0) |
|
180 |
| demult (Const (\<^const_name>\<open>Groups.one\<close>, _), m) = (NONE, m) |
|
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parents:
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|
181 |
(*Warning: in rare cases (neg_)numeral encloses a non-numeral, |
62342 | 182 |
in which case dest_numeral raises TERM; hence all the handles below. |
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|
183 |
Same for Suc-terms that turn out not to be numerals - |
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|
184 |
although the simplifier should eliminate those anyway ...*) |
63948 | 185 |
| demult (t as Const ("Num.numeral_class.numeral", _) (*DYNAMIC BINDING!*) $ n, m) = |
63201 | 186 |
((NONE, Rat.mult m (Rat.of_int (HOLogic.dest_numeral n))) |
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parents:
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|
187 |
handle TERM _ => (SOME t, m)) |
67149 | 188 |
| demult (t as Const (\<^const_name>\<open>Suc\<close>, _) $ _, m) = |
63201 | 189 |
((NONE, Rat.mult m (Rat.of_int (HOLogic.dest_nat t))) |
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parents:
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changeset
|
190 |
handle TERM _ => (SOME t, m)) |
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parents:
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|
191 |
(* injection constants are ignored *) |
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|
192 |
| demult (t as Const f $ x, m) = |
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parents:
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|
193 |
if member (op =) inj_consts f then demult (x, m) else (SOME t, m) |
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|
194 |
(* everything else is considered atomic *) |
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|
195 |
| demult (atom, m) = (SOME atom, m) |
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|
196 |
in demult end; |
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|
197 |
|
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|
198 |
fun decomp0 thy (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) : |
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|
199 |
((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option = |
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parents:
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changeset
|
200 |
let |
24328
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parents:
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changeset
|
201 |
(* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of |
83afe527504d
fixed a bug in demult: -a in (-a * b) is no longer treated as atomic
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parents:
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changeset
|
202 |
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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parents:
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changeset
|
203 |
multiplicity 1) *) |
67149 | 204 |
fun poly (Const (\<^const_name>\<open>Groups.plus\<close>, _) $ s $ t, |
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parents:
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changeset
|
205 |
m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi)) |
67149 | 206 |
| poly (all as Const (\<^const_name>\<open>Groups.minus\<close>, T) $ s $ t, m, pi) = |
63211 | 207 |
if nT T then add_atom all m pi else poly (s, m, poly (t, ~ m, pi)) |
67149 | 208 |
| poly (all as Const (\<^const_name>\<open>Groups.uminus\<close>, T) $ t, m, pi) = |
63211 | 209 |
if nT T then add_atom all m pi else poly (t, ~ m, pi) |
67149 | 210 |
| poly (Const (\<^const_name>\<open>Groups.zero\<close>, _), _, pi) = |
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changeset
|
211 |
pi |
67149 | 212 |
| poly (Const (\<^const_name>\<open>Groups.one\<close>, _), m, (p, i)) = |
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parents:
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changeset
|
213 |
(p, Rat.add i m) |
63949 | 214 |
| poly (all as Const ("Num.numeral_class.numeral", _) (*DYNAMIC BINDING!*) $ t, m, pi as (p, i)) = |
62342 | 215 |
(let val k = HOLogic.dest_numeral t |
63201 | 216 |
in (p, Rat.add i (Rat.mult m (Rat.of_int k))) end |
54489
03ff4d1e6784
eliminiated neg_numeral in favour of - (numeral _)
haftmann
parents:
54249
diff
changeset
|
217 |
handle TERM _ => add_atom all m pi) |
67149 | 218 |
| poly (Const (\<^const_name>\<open>Suc\<close>, _) $ t, m, (p, i)) = |
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parents:
diff
changeset
|
219 |
poly (t, m, (p, Rat.add i m)) |
67149 | 220 |
| poly (all as Const (\<^const_name>\<open>Groups.times\<close>, _) $ _ $ _, m, pi as (p, i)) = |
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haftmann
parents:
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diff
changeset
|
221 |
(case demult thy inj_consts (all, m) of |
24092
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parents:
diff
changeset
|
222 |
(NONE, m') => (p, Rat.add i m') |
71c27b320610
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wenzelm
parents:
diff
changeset
|
223 |
| (SOME u, m') => add_atom u m' pi) |
67149 | 224 |
| poly (all as Const (\<^const_name>\<open>Rings.divide\<close>, T) $ _ $ _, m, pi as (p, i)) = |
60351
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haftmann
parents:
60350
diff
changeset
|
225 |
if of_field_sort thy (domain_type T) then |
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
226 |
(case demult thy inj_consts (all, m) of |
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
227 |
(NONE, m') => (p, Rat.add i m') |
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
228 |
| (SOME u, m') => add_atom u m' pi) |
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
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diff
changeset
|
229 |
else add_atom all m pi |
24092
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parents:
diff
changeset
|
230 |
| poly (all as Const f $ x, m, pi) = |
36692
54b64d4ad524
farewell to old-style mem infixes -- type inference in situations with mem_int and mem_string should provide enough information to resolve the type of (op =)
haftmann
parents:
36001
diff
changeset
|
231 |
if member (op =) inj_consts f then poly (x, m, pi) else add_atom all m pi |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
232 |
| poly (all, m, pi) = |
71c27b320610
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wenzelm
parents:
diff
changeset
|
233 |
add_atom all m pi |
63205 | 234 |
val (p, i) = poly (lhs, @1, ([], @0)) |
235 |
val (q, j) = poly (rhs, @1, ([], @0)) |
|
24092
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wenzelm
parents:
diff
changeset
|
236 |
in |
71c27b320610
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wenzelm
parents:
diff
changeset
|
237 |
case rel of |
67149 | 238 |
\<^const_name>\<open>Orderings.less\<close> => SOME (p, i, "<", q, j) |
239 |
| \<^const_name>\<open>Orderings.less_eq\<close> => SOME (p, i, "<=", q, j) |
|
240 |
| \<^const_name>\<open>HOL.eq\<close> => SOME (p, i, "=", q, j) |
|
24092
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wenzelm
parents:
diff
changeset
|
241 |
| _ => NONE |
63210
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clarified exception -- actually reject denominator = 0;
wenzelm
parents:
63205
diff
changeset
|
242 |
end handle General.Div => NONE; |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
243 |
|
24271 | 244 |
fun of_lin_arith_sort thy U = |
67149 | 245 |
Sign.of_sort thy (U, \<^sort>\<open>Rings.linordered_idom\<close>); |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
246 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
247 |
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
|
248 |
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
|
249 |
else if member (op =) discrete D then (true, true) else (false, false) |
66035
de6cd60b1226
replace non-arithmetic terms by fresh variables before replaying linear-arithmetic proofs: avoid failed proof replays due to an overambitious simpset which may cause proof replay to diverge from the pre-computed proof trace
boehmes
parents:
63950
diff
changeset
|
250 |
| allows_lin_arith sg _ U = (of_lin_arith_sort sg U, false); |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
251 |
|
60351
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explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
252 |
fun decomp_typecheck thy (discrete, inj_consts) (T : typ, xxx) : decomp option = |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
253 |
case T of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
254 |
Type ("fun", [U, _]) => |
71c27b320610
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wenzelm
parents:
diff
changeset
|
255 |
(case allows_lin_arith thy discrete U of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
256 |
(true, d) => |
60351
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
257 |
(case decomp0 thy inj_consts xxx of |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
258 |
NONE => NONE |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
259 |
| 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
|
260 |
| (false, _) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
261 |
NONE) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
262 |
| _ => NONE; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
263 |
|
71c27b320610
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wenzelm
parents:
diff
changeset
|
264 |
fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
265 |
| negate NONE = NONE; |
71c27b320610
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wenzelm
parents:
diff
changeset
|
266 |
|
60351
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
267 |
fun decomp_negation thy data |
67149 | 268 |
((Const (\<^const_name>\<open>Trueprop\<close>, _)) $ (Const (rel, T) $ lhs $ rhs)) : decomp option = |
60351
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
269 |
decomp_typecheck thy data (T, (rel, lhs, rhs)) |
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
270 |
| decomp_negation thy data |
67149 | 271 |
((Const (\<^const_name>\<open>Trueprop\<close>, _)) $ (Const (\<^const_name>\<open>Not\<close>, _) $ (Const (rel, T) $ lhs $ rhs))) = |
60351
5cdf3903a302
explicit check for field sort, to anticipate situation where syntactic checking alone will not be sufficient any longer
haftmann
parents:
60350
diff
changeset
|
272 |
negate (decomp_typecheck thy data (T, (rel, lhs, rhs))) |
66035
de6cd60b1226
replace non-arithmetic terms by fresh variables before replaying linear-arithmetic proofs: avoid failed proof replays due to an overambitious simpset which may cause proof replay to diverge from the pre-computed proof trace
boehmes
parents:
63950
diff
changeset
|
273 |
| decomp_negation _ _ _ = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
274 |
NONE; |
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|
26942 | 276 |
fun decomp ctxt : term -> decomp option = |
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let |
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val thy = Proof_Context.theory_of ctxt |
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val {discrete, inj_consts, ...} = get_arith_data ctxt |
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in decomp_negation thy (discrete, inj_consts) end; |
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281 |
|
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fun domain_is_nat (_ $ (Const (_, T) $ _ $ _)) = nT T |
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| domain_is_nat (_ $ (Const (\<^const_name>\<open>Not\<close>, _) $ (Const (_, T) $ _ $ _))) = nT T |
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| domain_is_nat _ = false; |
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285 |
|
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286 |
|
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(* Abstraction of terms *) |
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|
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289 |
(* |
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290 |
Abstract terms contain only arithmetic operators and relations. |
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291 |
|
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When constructing an abstract term for an arbitrary term, non-arithmetic sub-terms |
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are replaced by fresh variables which are declared in the context. Constructing |
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an abstract term from an arbitrary term follows the strategy of decomp. |
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*) |
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|
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fun apply t u = t $ u |
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|
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fun with2 f c t u cx = f t cx ||>> f u |>> (fn (t, u) => c $ t $ u) |
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|
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fun abstract_atom (t as Free _) cx = (t, cx) |
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| abstract_atom (t as Const _) cx = (t, cx) |
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| abstract_atom t (cx as (terms, ctxt)) = |
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(case AList.lookup Envir.aeconv terms t of |
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SOME u => (u, cx) |
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| NONE => |
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let |
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val (n, ctxt') = yield_singleton Variable.variant_fixes "" ctxt |
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val u = Free (n, fastype_of t) |
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in (u, ((t, u) :: terms, ctxt')) end) |
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|
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fun abstract_num t cx = if can HOLogic.dest_number t then (t, cx) else abstract_atom t cx |
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|
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fun is_field_sort (_, ctxt) T = of_field_sort (Proof_Context.theory_of ctxt) (domain_type T) |
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|
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fun is_inj_const (_, ctxt) f = |
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let val {inj_consts, ...} = get_arith_data ctxt |
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in member (op =) inj_consts f end |
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|
67149 | 320 |
fun abstract_arith ((c as Const (\<^const_name>\<open>Groups.plus\<close>, _)) $ u1 $ u2) cx = |
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321 |
with2 abstract_arith c u1 u2 cx |
67149 | 322 |
| abstract_arith (t as (c as Const (\<^const_name>\<open>Groups.minus\<close>, T)) $ u1 $ u2) cx = |
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323 |
if nT T then abstract_atom t cx else with2 abstract_arith c u1 u2 cx |
67149 | 324 |
| abstract_arith (t as (c as Const (\<^const_name>\<open>Groups.uminus\<close>, T)) $ u) cx = |
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325 |
if nT T then abstract_atom t cx else abstract_arith u cx |>> apply c |
67149 | 326 |
| abstract_arith ((c as Const (\<^const_name>\<open>Suc\<close>, _)) $ u) cx = abstract_arith u cx |>> apply c |
327 |
| abstract_arith ((c as Const (\<^const_name>\<open>Groups.times\<close>, _)) $ u1 $ u2) cx = |
|
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328 |
with2 abstract_arith c u1 u2 cx |
67149 | 329 |
| abstract_arith (t as (c as Const (\<^const_name>\<open>Rings.divide\<close>, T)) $ u1 $ u2) cx = |
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if is_field_sort cx T then with2 abstract_arith c u1 u2 cx else abstract_atom t cx |
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| abstract_arith (t as (c as Const f) $ u) cx = |
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332 |
if is_inj_const cx f then abstract_arith u cx |>> apply c else abstract_num t cx |
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333 |
| abstract_arith t cx = abstract_num t cx |
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334 |
|
67149 | 335 |
fun is_lin_arith_rel \<^const_name>\<open>Orderings.less\<close> = true |
336 |
| is_lin_arith_rel \<^const_name>\<open>Orderings.less_eq\<close> = true |
|
337 |
| is_lin_arith_rel \<^const_name>\<open>HOL.eq\<close> = true |
|
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338 |
| is_lin_arith_rel _ = false |
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339 |
|
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340 |
fun is_lin_arith_type (_, ctxt) T = |
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341 |
let val {discrete, ...} = get_arith_data ctxt |
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342 |
in fst (allows_lin_arith (Proof_Context.theory_of ctxt) discrete T) end |
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343 |
|
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344 |
fun abstract_rel (t as (r as Const (rel, Type ("fun", [U, _]))) $ lhs $ rhs) cx = |
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345 |
if is_lin_arith_rel rel andalso is_lin_arith_type cx U then with2 abstract_arith r lhs rhs cx |
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346 |
else abstract_atom t cx |
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347 |
| abstract_rel t cx = abstract_atom t cx |
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348 |
|
67149 | 349 |
fun abstract_neg ((c as Const (\<^const_name>\<open>Not\<close>, _)) $ t) cx = abstract_rel t cx |>> apply c |
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350 |
| abstract_neg t cx = abstract_rel t cx |
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351 |
|
67149 | 352 |
fun abstract ((c as Const (\<^const_name>\<open>Trueprop\<close>, _)) $ t) cx = abstract_neg t cx |>> apply c |
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|
353 |
| abstract t cx = abstract_atom t cx |
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354 |
|
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|
355 |
|
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|
356 |
(*---------------------------------------------------------------------------*) |
32369 | 357 |
(* the following code performs splitting of certain constants (e.g., min, *) |
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358 |
(* max) in a linear arithmetic problem; similar to what split_tac later does *) |
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|
359 |
(* to the proof state *) |
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|
360 |
(*---------------------------------------------------------------------------*) |
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|
361 |
|
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|
362 |
(* checks if splitting with 'thm' is implemented *) |
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|
363 |
|
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|
364 |
fun is_split_thm ctxt thm = |
59582 | 365 |
(case Thm.concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => |
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|
366 |
(* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *) |
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|
367 |
(case head_of lhs of |
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|
368 |
Const (a, _) => |
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|
369 |
member (op =) |
67149 | 370 |
[\<^const_name>\<open>Orderings.max\<close>, |
371 |
\<^const_name>\<open>Orderings.min\<close>, |
|
372 |
\<^const_name>\<open>Groups.abs\<close>, |
|
373 |
\<^const_name>\<open>Groups.minus\<close>, |
|
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|
374 |
"Int.nat" (*DYNAMIC BINDING!*), |
67149 | 375 |
\<^const_name>\<open>Rings.modulo\<close>, |
376 |
\<^const_name>\<open>Rings.divide\<close>] a |
|
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|
377 |
| _ => |
59352
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
378 |
(if Context_Position.is_visible ctxt then |
61268 | 379 |
warning ("Lin. Arith.: wrong format for split rule " ^ Thm.string_of_thm ctxt thm) |
59352
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
380 |
else (); false)) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
381 |
| _ => |
59352
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
382 |
(if Context_Position.is_visible ctxt then |
61268 | 383 |
warning ("Lin. Arith.: wrong format for split rule " ^ Thm.string_of_thm ctxt thm) |
59352
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
384 |
else (); false)); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
385 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
386 |
(* substitute new for occurrences of old in a term, incrementing bound *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
387 |
(* variables as needed when substituting inside an abstraction *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
388 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
389 |
fun subst_term ([] : (term * term) list) (t : term) = t |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
390 |
| subst_term pairs t = |
52131 | 391 |
(case AList.lookup Envir.aeconv pairs t of |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
392 |
SOME new => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
393 |
new |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
394 |
| NONE => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
395 |
(case t of Abs (a, T, body) => |
59058
a78612c67ec0
renamed "pairself" to "apply2", in accordance to @{apply 2};
wenzelm
parents:
58956
diff
changeset
|
396 |
let val pairs' = map (apply2 (incr_boundvars 1)) pairs |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
397 |
in Abs (a, T, subst_term pairs' body) end |
59058
a78612c67ec0
renamed "pairself" to "apply2", in accordance to @{apply 2};
wenzelm
parents:
58956
diff
changeset
|
398 |
| t1 $ t2 => subst_term pairs t1 $ subst_term pairs t2 |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
399 |
| _ => t)); |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
400 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
401 |
(* approximates the effect of one application of split_tac (followed by NNF *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
402 |
(* normalization) on the subgoal represented by '(Ts, terms)'; returns a *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
403 |
(* list of new subgoals (each again represented by a typ list for bound *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
404 |
(* variables and a term list for premises), or NONE if split_tac would fail *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
405 |
(* on the subgoal *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
406 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
407 |
(* FIXME: currently only the effect of certain split theorems is reproduced *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
408 |
(* (which is why we need 'is_split_thm'). A more canonical *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
409 |
(* implementation should analyze the right-hand side of the split *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
410 |
(* theorem that can be applied, and modify the subgoal accordingly. *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
411 |
(* Or even better, the splitter should be extended to provide *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
412 |
(* splitting on terms as well as splitting on theorems (where the *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
413 |
(* 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
|
414 |
(* proof-producing). *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
415 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
416 |
fun split_once_items ctxt (Ts : typ list, terms : term list) : |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
417 |
(typ list * term list) list option = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
418 |
let |
42361 | 419 |
val thy = Proof_Context.theory_of ctxt |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
420 |
(* takes a list [t1, ..., tn] to the term *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
421 |
(* tn' --> ... --> t1' --> False , *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
422 |
(* where ti' = HOLogic.dest_Trueprop ti *) |
32369 | 423 |
fun REPEAT_DETERM_etac_rev_mp tms = |
67149 | 424 |
fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop tms) \<^term>\<open>False\<close> |
67631 | 425 |
val split_thms = filter (is_split_thm ctxt) (get_splits ctxt) |
32369 | 426 |
val cmap = Splitter.cmap_of_split_thms split_thms |
427 |
val goal_tm = REPEAT_DETERM_etac_rev_mp terms |
|
428 |
val splits = Splitter.split_posns cmap thy Ts goal_tm |
|
31082 | 429 |
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
|
430 |
in |
32369 | 431 |
if length splits > split_limit then ( |
432 |
tracing ("linarith_split_limit exceeded (current value is " ^ |
|
433 |
string_of_int split_limit ^ ")"); |
|
434 |
NONE |
|
435 |
) else case splits of |
|
436 |
[] => |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
437 |
(* split_tac would fail: no possible split *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
438 |
NONE |
32369 | 439 |
| (_, _::_, _, _, _) :: _ => |
440 |
(* disallow a split that involves non-locally bound variables (except *) |
|
441 |
(* when bound by outermost meta-quantifiers) *) |
|
442 |
NONE |
|
443 |
| (_, [], _, split_type, split_term) :: _ => |
|
444 |
(* ignore all but the first possible split *) |
|
445 |
(case strip_comb split_term of |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
446 |
(* ?P (max ?i ?j) = ((?i <= ?j --> ?P ?j) & (~ ?i <= ?j --> ?P ?i)) *) |
67149 | 447 |
(Const (\<^const_name>\<open>Orderings.max\<close>, _), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
448 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
449 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
450 |
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
|
451 |
val terms2 = map (subst_term [(split_term, t2)]) rev_terms |
67149 | 452 |
val t1_leq_t2 = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
453 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
454 |
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 |
67149 | 455 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
456 |
val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
457 |
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
|
458 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
459 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
460 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
461 |
(* ?P (min ?i ?j) = ((?i <= ?j --> ?P ?i) & (~ ?i <= ?j --> ?P ?j)) *) |
67149 | 462 |
| (Const (\<^const_name>\<open>Orderings.min\<close>, _), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
463 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
464 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
465 |
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
|
466 |
val terms2 = map (subst_term [(split_term, t2)]) rev_terms |
67149 | 467 |
val t1_leq_t2 = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
468 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
469 |
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 |
67149 | 470 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
471 |
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
|
472 |
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
|
473 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
474 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
475 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
476 |
(* ?P (abs ?a) = ((0 <= ?a --> ?P ?a) & (?a < 0 --> ?P (- ?a))) *) |
67149 | 477 |
| (Const (\<^const_name>\<open>Groups.abs\<close>, _), [t1]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
478 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
479 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
480 |
val terms1 = map (subst_term [(split_term, t1)]) rev_terms |
67149 | 481 |
val terms2 = map (subst_term [(split_term, Const (\<^const_name>\<open>Groups.uminus\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
482 |
split_type --> split_type) $ t1)]) rev_terms |
67149 | 483 |
val zero = Const (\<^const_name>\<open>Groups.zero\<close>, split_type) |
484 |
val zero_leq_t1 = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
485 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t1 |
67149 | 486 |
val t1_lt_zero = Const (\<^const_name>\<open>Orderings.less\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
487 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ zero |
67149 | 488 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
489 |
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
|
490 |
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
|
491 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
492 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
493 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
494 |
(* ?P (?a - ?b) = ((?a < ?b --> ?P 0) & (ALL d. ?a = ?b + d --> ?P d)) *) |
67149 | 495 |
| (Const (\<^const_name>\<open>Groups.minus\<close>, _), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
496 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
497 |
(* "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
|
498 |
(* transformation, therefore some adjustment of indices is necessary *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
499 |
val rev_terms = rev terms |
67149 | 500 |
val zero = Const (\<^const_name>\<open>Groups.zero\<close>, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
501 |
val d = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
502 |
val terms1 = map (subst_term [(split_term, zero)]) rev_terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
503 |
val terms2 = map (subst_term [(incr_boundvars 1 split_term, d)]) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
504 |
(map (incr_boundvars 1) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
505 |
val t1' = incr_boundvars 1 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
506 |
val t2' = incr_boundvars 1 t2 |
67149 | 507 |
val t1_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
508 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
67149 | 509 |
val t1_eq_t2_plus_d = Const (\<^const_name>\<open>HOL.eq\<close>, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
510 |
(Const (\<^const_name>\<open>Groups.plus\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
511 |
split_type --> split_type --> split_type) $ t2' $ d) |
67149 | 512 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
513 |
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
|
514 |
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
|
515 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
516 |
SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
517 |
end |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
518 |
(* ?P (nat ?i) = ((ALL n. ?i = of_nat n --> ?P n) & (?i < 0 --> ?P 0)) *) |
63948 | 519 |
| (Const ("Int.nat", _), (*DYNAMIC BINDING!*) [t1]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
520 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
521 |
val rev_terms = rev terms |
67149 | 522 |
val zero_int = Const (\<^const_name>\<open>Groups.zero\<close>, HOLogic.intT) |
523 |
val zero_nat = Const (\<^const_name>\<open>Groups.zero\<close>, HOLogic.natT) |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
524 |
val n = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
525 |
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
|
526 |
(map (incr_boundvars 1) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
527 |
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
|
528 |
val t1' = incr_boundvars 1 t1 |
67149 | 529 |
val t1_eq_nat_n = Const (\<^const_name>\<open>HOL.eq\<close>, HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1' $ |
530 |
(Const (\<^const_name>\<open>of_nat\<close>, HOLogic.natT --> HOLogic.intT) $ n) |
|
531 |
val t1_lt_zero = Const (\<^const_name>\<open>Orderings.less\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
532 |
HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1 $ zero_int |
67149 | 533 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
534 |
val subgoal1 = (HOLogic.mk_Trueprop t1_eq_nat_n) :: terms1 @ [not_false] |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
535 |
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
|
536 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
537 |
SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
538 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
539 |
(* ?P ((?n::nat) mod (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
540 |
((numeral ?k = 0 --> ?P ?n) & (~ (numeral ?k = 0) --> |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
541 |
(ALL i j. j < numeral ?k --> ?n = numeral ?k * i + j --> ?P j))) *) |
67149 | 542 |
| (Const (\<^const_name>\<open>Rings.modulo\<close>, Type ("fun", [\<^typ>\<open>nat\<close>, _])), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
543 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
544 |
val rev_terms = rev terms |
67149 | 545 |
val zero = Const (\<^const_name>\<open>Groups.zero\<close>, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
546 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
547 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
548 |
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
|
549 |
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
|
550 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
551 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
552 |
val t2' = incr_boundvars 2 t2 |
67149 | 553 |
val t2_eq_zero = Const (\<^const_name>\<open>HOL.eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
554 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
67149 | 555 |
val t2_neq_zero = HOLogic.mk_not (Const (\<^const_name>\<open>HOL.eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
556 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero) |
67149 | 557 |
val j_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
558 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
67149 | 559 |
val t1_eq_t2_times_i_plus_j = Const (\<^const_name>\<open>HOL.eq\<close>, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
560 |
(Const (\<^const_name>\<open>Groups.plus\<close>, split_type --> split_type --> split_type) $ |
|
561 |
(Const (\<^const_name>\<open>Groups.times\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
562 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
67149 | 563 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
564 |
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
|
565 |
val subgoal2 = (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
566 |
[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
|
567 |
@ terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
568 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
569 |
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
|
570 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
571 |
(* ?P ((?n::nat) div (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
572 |
((numeral ?k = 0 --> ?P 0) & (~ (numeral ?k = 0) --> |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
573 |
(ALL i j. j < numeral ?k --> ?n = numeral ?k * i + j --> ?P i))) *) |
67149 | 574 |
| (Const (\<^const_name>\<open>Rings.divide\<close>, Type ("fun", [\<^typ>\<open>nat\<close>, _])), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
575 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
576 |
val rev_terms = rev terms |
67149 | 577 |
val zero = Const (\<^const_name>\<open>Groups.zero\<close>, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
578 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
579 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
580 |
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
|
581 |
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
|
582 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
583 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
584 |
val t2' = incr_boundvars 2 t2 |
67149 | 585 |
val t2_eq_zero = Const (\<^const_name>\<open>HOL.eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
586 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
67149 | 587 |
val t2_neq_zero = HOLogic.mk_not (Const (\<^const_name>\<open>HOL.eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
588 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero) |
67149 | 589 |
val j_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
590 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
67149 | 591 |
val t1_eq_t2_times_i_plus_j = Const (\<^const_name>\<open>HOL.eq\<close>, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
592 |
(Const (\<^const_name>\<open>Groups.plus\<close>, split_type --> split_type --> split_type) $ |
|
593 |
(Const (\<^const_name>\<open>Groups.times\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
594 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
67149 | 595 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
596 |
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
|
597 |
val subgoal2 = (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
598 |
[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
|
599 |
@ terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
600 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
601 |
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
|
602 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
603 |
(* ?P ((?n::int) mod (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
604 |
((numeral ?k = 0 --> ?P ?n) & |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
605 |
(0 < numeral ?k --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
606 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
607 |
0 <= j & j < numeral ?k & ?n = numeral ?k * i + j --> ?P j)) & |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
608 |
(numeral ?k < 0 --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
609 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
610 |
numeral ?k < j & j <= 0 & ?n = numeral ?k * i + j --> ?P j))) *) |
67149 | 611 |
| (Const (\<^const_name>\<open>Rings.modulo\<close>, |
63948 | 612 |
Type ("fun", [Type ("Int.int", []), _])), (*DYNAMIC BINDING!*) [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
613 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
614 |
val rev_terms = rev terms |
67149 | 615 |
val zero = Const (\<^const_name>\<open>Groups.zero\<close>, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
616 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
617 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
618 |
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
|
619 |
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
|
620 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
621 |
val t1' = incr_boundvars 2 t1 |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
622 |
val t2' = incr_boundvars 2 t2 |
67149 | 623 |
val t2_eq_zero = Const (\<^const_name>\<open>HOL.eq\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
624 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
67149 | 625 |
val zero_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
626 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t2' |
67149 | 627 |
val t2_lt_zero = Const (\<^const_name>\<open>Orderings.less\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
628 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero |
67149 | 629 |
val zero_leq_j = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
630 |
split_type --> split_type --> HOLogic.boolT) $ zero $ j |
67149 | 631 |
val j_leq_zero = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
632 |
split_type --> split_type --> HOLogic.boolT) $ j $ zero |
67149 | 633 |
val j_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
634 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
67149 | 635 |
val t2_lt_j = Const (\<^const_name>\<open>Orderings.less\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
636 |
split_type --> split_type--> HOLogic.boolT) $ t2' $ j |
67149 | 637 |
val t1_eq_t2_times_i_plus_j = Const (\<^const_name>\<open>HOL.eq\<close>, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
638 |
(Const (\<^const_name>\<open>Groups.plus\<close>, split_type --> split_type --> split_type) $ |
|
639 |
(Const (\<^const_name>\<open>Groups.times\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
640 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
67149 | 641 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
642 |
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
643 |
val subgoal2 = (map HOLogic.mk_Trueprop [zero_lt_t2, zero_leq_j]) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
644 |
@ hd terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
645 |
:: (if tl terms2_3 = [] then [not_false] else []) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
646 |
@ (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
|
647 |
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
648 |
val subgoal3 = (map HOLogic.mk_Trueprop [t2_lt_zero, t2_lt_j]) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
649 |
@ hd terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
650 |
:: (if tl terms2_3 = [] then [not_false] else []) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
651 |
@ (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
|
652 |
@ (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
|
653 |
val Ts' = split_type :: split_type :: Ts |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
654 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
655 |
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
656 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
657 |
(* ?P ((?n::int) div (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
658 |
((numeral ?k = 0 --> ?P 0) & |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
659 |
(0 < numeral ?k --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
660 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
661 |
0 <= j & j < numeral ?k & ?n = numeral ?k * i + j --> ?P i)) & |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
662 |
(numeral ?k < 0 --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
663 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
664 |
numeral ?k < j & j <= 0 & ?n = numeral ?k * i + j --> ?P i))) *) |
67149 | 665 |
| (Const (\<^const_name>\<open>Rings.divide\<close>, |
63948 | 666 |
Type ("fun", [Type ("Int.int", []), _])), (*DYNAMIC BINDING!*) [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
667 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
668 |
val rev_terms = rev terms |
67149 | 669 |
val zero = Const (\<^const_name>\<open>Groups.zero\<close>, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
670 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
671 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
672 |
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
|
673 |
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
|
674 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
675 |
val t1' = incr_boundvars 2 t1 |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
676 |
val t2' = incr_boundvars 2 t2 |
67149 | 677 |
val t2_eq_zero = Const (\<^const_name>\<open>HOL.eq\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
678 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
67149 | 679 |
val zero_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
680 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t2' |
67149 | 681 |
val t2_lt_zero = Const (\<^const_name>\<open>Orderings.less\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
682 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero |
67149 | 683 |
val zero_leq_j = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
684 |
split_type --> split_type --> HOLogic.boolT) $ zero $ j |
67149 | 685 |
val j_leq_zero = Const (\<^const_name>\<open>Orderings.less_eq\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
686 |
split_type --> split_type --> HOLogic.boolT) $ j $ zero |
67149 | 687 |
val j_lt_t2 = Const (\<^const_name>\<open>Orderings.less\<close>, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
688 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
67149 | 689 |
val t2_lt_j = Const (\<^const_name>\<open>Orderings.less\<close>, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
690 |
split_type --> split_type--> HOLogic.boolT) $ t2' $ j |
67149 | 691 |
val t1_eq_t2_times_i_plus_j = Const (\<^const_name>\<open>HOL.eq\<close>, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
692 |
(Const (\<^const_name>\<open>Groups.plus\<close>, split_type --> split_type --> split_type) $ |
|
693 |
(Const (\<^const_name>\<open>Groups.times\<close>, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
694 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
67149 | 695 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ \<^term>\<open>False\<close>) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
696 |
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
697 |
val subgoal2 = (map HOLogic.mk_Trueprop [zero_lt_t2, zero_leq_j]) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
698 |
@ hd terms2_3 |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
699 |
:: (if tl terms2_3 = [] then [not_false] else []) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
700 |
@ (map HOLogic.mk_Trueprop [j_lt_t2, t1_eq_t2_times_i_plus_j]) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
701 |
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
702 |
val subgoal3 = (map HOLogic.mk_Trueprop [t2_lt_zero, t2_lt_j]) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
703 |
@ hd terms2_3 |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
704 |
:: (if tl terms2_3 = [] then [not_false] else []) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
705 |
@ (map HOLogic.mk_Trueprop [j_leq_zero, t1_eq_t2_times_i_plus_j]) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
706 |
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
707 |
val Ts' = split_type :: split_type :: Ts |
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 |
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
710 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
711 |
(* 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
|
712 |
(* 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
|
713 |
(* 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
|
714 |
(* out *) |
59352
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
715 |
| (t, ts) => |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
716 |
(if Context_Position.is_visible ctxt then |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
717 |
warning ("Lin. Arith.: split rule for " ^ Syntax.string_of_term ctxt t ^ |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
718 |
" (with " ^ string_of_int (length ts) ^ |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
719 |
" argument(s)) not implemented; proof reconstruction is likely to fail") |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
720 |
else (); NONE)) |
32369 | 721 |
end; (* split_once_items *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
722 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
723 |
(* 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
|
724 |
(* 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
|
725 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
726 |
fun filter_prems_tac_items (p : term -> bool) (terms : term list) : term list = |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
727 |
let |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
728 |
fun filter_prems t (left, right) = |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
729 |
if p t then (left, right @ [t]) else (left @ right, []) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
730 |
val (left, right) = fold filter_prems terms ([], []) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
731 |
in |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
732 |
right @ left |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
733 |
end; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
734 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
735 |
(* 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
|
736 |
(* subgoal that has 'terms' as premises *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
737 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
738 |
fun negated_term_occurs_positively (terms : term list) : bool = |
58412 | 739 |
exists |
67149 | 740 |
(fn (Trueprop $ (Const (\<^const_name>\<open>Not\<close>, _) $ t)) => |
52131 | 741 |
member Envir.aeconv terms (Trueprop $ t) |
32369 | 742 |
| _ => false) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
743 |
terms; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
744 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
745 |
fun pre_decomp ctxt (Ts : typ list, terms : term list) : (typ list * term list) list = |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
746 |
let |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
747 |
(* repeatedly split (including newly emerging subgoals) until no further *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
748 |
(* splitting is possible *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
749 |
fun split_loop ([] : (typ list * term list) list) = ([] : (typ list * term list) list) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
750 |
| split_loop (subgoal::subgoals) = |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
751 |
(case split_once_items ctxt subgoal of |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
752 |
SOME new_subgoals => split_loop (new_subgoals @ subgoals) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
753 |
| NONE => subgoal :: split_loop subgoals) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
754 |
fun is_relevant t = is_some (decomp ctxt t) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
755 |
(* filter_prems_tac is_relevant: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
756 |
val relevant_terms = filter_prems_tac_items is_relevant terms |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
757 |
(* split_tac, NNF normalization: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
758 |
val split_goals = split_loop [(Ts, relevant_terms)] |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
759 |
(* necessary because split_once_tac may normalize terms: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
760 |
val beta_eta_norm = map (apsnd (map (Envir.eta_contract o Envir.beta_norm))) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
761 |
split_goals |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
762 |
(* TRY (etac notE) THEN eq_assume_tac: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
763 |
val result = filter_out (negated_term_occurs_positively o snd) beta_eta_norm |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
764 |
in |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
765 |
result |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
766 |
end; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
767 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
768 |
(* 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
|
769 |
(* 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
|
770 |
(* (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
|
771 |
(* performs NNF-normalization of ~P, and eliminates conjunctions, *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
772 |
(* 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
|
773 |
(* 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
|
774 |
(* general form [| Q1; ...; Qm |] ==> False. Fails if more than *) |
31082 | 775 |
(* !split_limit splits are possible. *) |
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 |
local |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
778 |
fun nnf_simpset ctxt = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
779 |
(empty_simpset ctxt |
45625
750c5a47400b
modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents:
45620
diff
changeset
|
780 |
|> Simplifier.set_mkeqTrue mk_eq_True |
750c5a47400b
modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents:
45620
diff
changeset
|
781 |
|> Simplifier.set_mksimps (mksimps mksimps_pairs)) |
35410 | 782 |
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, |
783 |
@{thm de_Morgan_conj}, not_all, not_ex, not_not] |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
784 |
fun prem_nnf_tac ctxt = full_simp_tac (nnf_simpset ctxt) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
785 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
786 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
787 |
fun split_once_tac ctxt split_thms = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
788 |
let |
42361 | 789 |
val thy = Proof_Context.theory_of ctxt |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
790 |
val cond_split_tac = SUBGOAL (fn (subgoal, i) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
791 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
792 |
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
|
793 |
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
|
794 |
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
|
795 |
val splits = Splitter.split_posns cmap thy Ts concl |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
796 |
in |
32369 | 797 |
if null splits orelse length splits > Config.get ctxt split_limit then |
798 |
no_tac |
|
799 |
else if null (#2 (hd splits)) then |
|
58956
a816aa3ff391
proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents:
58839
diff
changeset
|
800 |
split_tac ctxt split_thms i |
32369 | 801 |
else |
802 |
(* disallow a split that involves non-locally bound variables *) |
|
803 |
(* (except when bound by outermost meta-quantifiers) *) |
|
804 |
no_tac |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
805 |
end) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
806 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
807 |
EVERY' [ |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
808 |
REPEAT_DETERM o eresolve_tac ctxt [rev_mp], |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
809 |
cond_split_tac, |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
810 |
resolve_tac ctxt @{thms ccontr}, |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
811 |
prem_nnf_tac ctxt, |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
812 |
TRY o REPEAT_ALL_NEW |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
813 |
(DETERM o (eresolve_tac ctxt [conjE, exE] ORELSE' eresolve_tac ctxt [disjE])) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
814 |
] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
815 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
816 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
817 |
end; (* local *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
818 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
819 |
(* 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
|
820 |
(* 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
|
821 |
(* subgoals and finally attempt to solve them by finding an immediate *) |
32369 | 822 |
(* contradiction (i.e., a term and its negation) in their premises. *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
823 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
824 |
fun pre_tac ctxt i = |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
825 |
let |
67631 | 826 |
val split_thms = filter (is_split_thm ctxt) (get_splits ctxt) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
827 |
fun is_relevant t = is_some (decomp ctxt t) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
828 |
in |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
829 |
DETERM ( |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
830 |
TRY (filter_prems_tac ctxt is_relevant i) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
831 |
THEN ( |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
832 |
(TRY o REPEAT_ALL_NEW (split_once_tac ctxt split_thms)) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
833 |
THEN_ALL_NEW |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
834 |
(CONVERSION Drule.beta_eta_conversion |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
835 |
THEN' |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
836 |
(TRY o (eresolve_tac ctxt [notE] THEN' eq_assume_tac))) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
837 |
) i |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
838 |
) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
839 |
end; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
840 |
|
31100 | 841 |
end; (* LA_Data *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
842 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
843 |
|
31100 | 844 |
val pre_tac = LA_Data.pre_tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
845 |
|
31100 | 846 |
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
|
847 |
|
38762
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
848 |
val add_inj_thms = Fast_Arith.add_inj_thms; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
849 |
val add_lessD = Fast_Arith.add_lessD; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
850 |
val add_simps = Fast_Arith.add_simps; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
851 |
val add_simprocs = Fast_Arith.add_simprocs; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
852 |
val set_number_of = Fast_Arith.set_number_of; |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31101
diff
changeset
|
853 |
|
59656 | 854 |
val simple_tac = Fast_Arith.lin_arith_tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
855 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
856 |
(* reduce contradictory <= to False. |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
857 |
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
|
858 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
859 |
val init_arith_data = |
54249 | 860 |
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, number_of, ...} => |
61097 | 861 |
{add_mono_thms = |
862 |
map Thm.trim_context @{thms add_mono_thms_linordered_semiring add_mono_thms_linordered_field} |
|
863 |
@ add_mono_thms, |
|
864 |
mult_mono_thms = |
|
865 |
map Thm.trim_context |
|
866 |
(@{thms mult_strict_left_mono mult_left_mono} @ |
|
867 |
[@{lemma "a = b ==> c * a = c * b" by (rule arg_cong)}]) @ mult_mono_thms, |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
868 |
inj_thms = inj_thms, |
54249 | 869 |
lessD = lessD, |
61097 | 870 |
neqE = map Thm.trim_context @{thms linorder_neqE_nat linorder_neqE_linordered_idom} @ neqE, |
871 |
simpset = |
|
69593 | 872 |
put_simpset HOL_basic_ss \<^context> |> Simplifier.add_cong @{thm if_weak_cong} |> simpset_of, |
54249 | 873 |
number_of = number_of}); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
874 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
875 |
(* FIXME !?? *) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
876 |
fun add_arith_facts ctxt = |
69593 | 877 |
Simplifier.add_prems (rev (Named_Theorems.get ctxt \<^named_theorems>\<open>arith\<close>)) ctxt; |
29849
a2baf1b221be
new attribute "arith" for facts supplied to arith.
nipkow
parents:
29548
diff
changeset
|
878 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
879 |
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
|
880 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
881 |
|
26110 | 882 |
(* generic refutation procedure *) |
883 |
||
884 |
(* parameters: |
|
885 |
||
886 |
test: term -> bool |
|
887 |
tests if a term is at all relevant to the refutation proof; |
|
888 |
if not, then it can be discarded. Can improve performance, |
|
889 |
esp. if disjunctions can be discarded (no case distinction needed!). |
|
890 |
||
891 |
prep_tac: int -> tactic |
|
892 |
A preparation tactic to be applied to the goal once all relevant premises |
|
893 |
have been moved to the conclusion. |
|
894 |
||
895 |
ref_tac: int -> tactic |
|
896 |
the actual refutation tactic. Should be able to deal with goals |
|
897 |
[| A1; ...; An |] ==> False |
|
898 |
where the Ai are atomic, i.e. no top-level &, | or EX |
|
899 |
*) |
|
900 |
||
901 |
local |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
902 |
fun nnf_simpset ctxt = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
903 |
(empty_simpset ctxt |
45625
750c5a47400b
modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents:
45620
diff
changeset
|
904 |
|> Simplifier.set_mkeqTrue mk_eq_True |
750c5a47400b
modernized some old-style infix operations, which were left over from the time of ML proof scripts;
wenzelm
parents:
45620
diff
changeset
|
905 |
|> Simplifier.set_mksimps (mksimps mksimps_pairs)) |
26110 | 906 |
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, |
907 |
@{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}]; |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
908 |
fun prem_nnf_tac ctxt = full_simp_tac (nnf_simpset ctxt); |
26110 | 909 |
in |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
910 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
911 |
fun refute_tac ctxt test prep_tac ref_tac = |
26110 | 912 |
let val refute_prems_tac = |
913 |
REPEAT_DETERM |
|
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
914 |
(eresolve_tac ctxt [@{thm conjE}, @{thm exE}] 1 ORELSE |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
915 |
filter_prems_tac ctxt test 1 ORELSE |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
916 |
eresolve_tac ctxt @{thms disjE} 1) THEN |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
917 |
(DETERM (eresolve_tac ctxt @{thms notE} 1 THEN eq_assume_tac 1) ORELSE |
26110 | 918 |
ref_tac 1); |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
919 |
in EVERY'[TRY o filter_prems_tac ctxt test, |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
920 |
REPEAT_DETERM o eresolve_tac ctxt @{thms rev_mp}, prep_tac, |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
921 |
resolve_tac ctxt @{thms ccontr}, prem_nnf_tac ctxt, |
26110 | 922 |
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] |
923 |
end; |
|
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
924 |
|
26110 | 925 |
end; |
926 |
||
927 |
||
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
928 |
(* arith proof method *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
929 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
930 |
local |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
931 |
|
59656 | 932 |
fun raw_tac ctxt = |
33035 | 933 |
(* FIXME: K true should be replaced by a sensible test (perhaps "is_some o |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
934 |
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
|
935 |
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
|
936 |
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
|
937 |
(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
|
938 |
(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
|
939 |
*) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
940 |
refute_tac ctxt (K true) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
941 |
(* Splitting is also done inside simple_tac, but not completely -- *) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
942 |
(* split_tac may use split theorems that have not been implemented in *) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
943 |
(* simple_tac (cf. pre_decomp and split_once_items above), and *) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
944 |
(* split_limit may trigger. *) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
945 |
(* Therefore splitting outside of simple_tac may allow us to prove *) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
946 |
(* some goals that simple_tac alone would fail on. *) |
67631 | 947 |
(REPEAT_DETERM o split_tac ctxt (get_splits ctxt)) |
59656 | 948 |
(Fast_Arith.lin_arith_tac ctxt); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
949 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
950 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
951 |
|
59656 | 952 |
fun tac ctxt = |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
54489
diff
changeset
|
953 |
FIRST' [simple_tac ctxt, |
58839 | 954 |
Object_Logic.full_atomize_tac ctxt THEN' |
59656 | 955 |
(REPEAT_DETERM o resolve_tac ctxt [impI]) THEN' raw_tac ctxt]; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
956 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
957 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
958 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
959 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
960 |
(* context setup *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
961 |
|
31100 | 962 |
val global_setup = |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
963 |
map_theory_simpset (fn ctxt => ctxt |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
964 |
addSolver (mk_solver "lin_arith" (add_arith_facts #> Fast_Arith.prems_lin_arith_tac))) #> |
67149 | 965 |
Attrib.setup \<^binding>\<open>arith_split\<close> (Scan.succeed (Thm.declaration_attribute add_split)) |
31100 | 966 |
"declaration of split rules for arithmetic procedure" #> |
67149 | 967 |
Method.setup \<^binding>\<open>linarith\<close> |
33554 | 968 |
(Scan.succeed (fn ctxt => |
31100 | 969 |
METHOD (fn facts => |
61841
4d3527b94f2a
more general types Proof.method / context_tactic;
wenzelm
parents:
61268
diff
changeset
|
970 |
HEADGOAL |
4d3527b94f2a
more general types Proof.method / context_tactic;
wenzelm
parents:
61268
diff
changeset
|
971 |
(Method.insert_tac ctxt |
69593 | 972 |
(rev (Named_Theorems.get ctxt \<^named_theorems>\<open>arith\<close>) @ facts) |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
973 |
THEN' tac ctxt)))) "linear arithmetic" #> |
59657
2441a80fb6c1
eliminated unused arith "verbose" flag -- tools that need options can use the context;
wenzelm
parents:
59656
diff
changeset
|
974 |
Arith_Data.add_tactic "linear arithmetic" tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
975 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
976 |
end; |