author | wenzelm |
Tue, 10 Feb 2015 14:48:26 +0100 | |
changeset 59498 | 50b60f501b05 |
parent 59352 | 63c02d051661 |
child 59582 | 0fbed69ff081 |
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 -> term -> thm option |
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val add_inj_thms: thm list -> Context.generic -> Context.generic |
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val add_lessD: thm -> Context.generic -> Context.generic |
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val add_simps: thm list -> Context.generic -> Context.generic |
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val add_simprocs: simproc list -> Context.generic -> Context.generic |
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val add_inj_const: string * typ -> Context.generic -> Context.generic |
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val add_discrete_type: string -> Context.generic -> Context.generic |
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val set_number_of: (theory -> typ -> int -> cterm) -> Context.generic -> Context.generic |
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val setup: Context.generic -> Context.generic |
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val global_setup: theory -> theory |
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val split_limit: int Config.T |
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val neq_limit: int Config.T |
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val verbose: bool 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 Trueprop}, _) $ (Const (@{const_name HOL.conj}, _) $ _ $ _) => |
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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 Trueprop}, _)) $ (Const (@{const_name Not}, _) $ t)) = TP $ t |
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| neg_prop ((TP as Const(@{const_name Trueprop}, _)) $ t) = TP $ (HOLogic.Not $t) |
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| neg_prop t = raise TERM ("neg_prop", [t]); |
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fun is_False thm = |
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let val _ $ t = Thm.prop_of thm |
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in t = @{term False} end; |
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fun is_nat t = (fastype_of1 t = HOLogic.natT); |
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fun mk_nat_thm thy t = |
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let |
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val cn = cterm_of thy (Var (("n", 0), HOLogic.natT)) |
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and ct = cterm_of thy t |
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in Drule.instantiate_normalize ([], [(cn, ct)]) @{thm le0} end; |
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end; |
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(* arith context data *) |
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structure Lin_Arith_Data = 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 add_split thm = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} => |
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{splits = update Thm.eq_thm_prop thm splits, |
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inj_consts = inj_consts, discrete = discrete}); |
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fun add_discrete_type d = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} => |
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{splits = splits, inj_consts = inj_consts, |
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discrete = update (op =) d discrete}); |
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fun add_inj_const c = Lin_Arith_Data.map (fn {splits, inj_consts, discrete} => |
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{splits = splits, inj_consts = update (op =) c inj_consts, |
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discrete = discrete}); |
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val split_limit = Attrib.setup_config_int @{binding linarith_split_limit} (K 9); |
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val neq_limit = Attrib.setup_config_int @{binding linarith_neq_limit} (K 9); |
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val verbose = Attrib.setup_config_bool @{binding linarith_verbose} (K true); |
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val trace = Attrib.setup_config_bool @{binding linarith_trace} (K false); |
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structure LA_Data = |
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struct |
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val neq_limit = neq_limit; |
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val verbose = verbose; |
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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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142 |
fun demult (inj_consts : (string * typ) list) : term * Rat.rat -> term option * Rat.rat = |
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143 |
let |
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144 |
fun demult ((mC as Const (@{const_name Groups.times}, _)) $ s $ t, m) = |
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145 |
(case s of Const (@{const_name Groups.times}, _) $ s1 $ s2 => |
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146 |
(* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *) |
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147 |
demult (mC $ s1 $ (mC $ s2 $ t), m) |
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148 |
| _ => |
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149 |
(* product 's * t', where either factor can be 'NONE' *) |
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150 |
(case demult (s, m) of |
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151 |
(SOME s', m') => |
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152 |
(case demult (t, m') of |
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153 |
(SOME t', m'') => (SOME (mC $ s' $ t'), m'') |
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154 |
| (NONE, m'') => (SOME s', m'')) |
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155 |
| (NONE, m') => demult (t, m'))) |
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156 |
| demult ((mC as Const (@{const_name Fields.divide}, _)) $ s $ t, m) = |
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157 |
(* FIXME: Shouldn't we simplify nested quotients, e.g. '(s/t)/u' could |
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|
158 |
become 's/(t*u)', and '(s*t)/u' could become 's*(t/u)' ? Note that |
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|
159 |
if we choose to do so here, the simpset used by arith must be able to |
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|
160 |
perform the same simplifications. *) |
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|
161 |
(* quotient 's / t', where the denominator t can be NONE *) |
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162 |
(* Note: will raise Rat.DIVZERO iff m' is Rat.zero *) |
55375 | 163 |
let val (os',m') = demult (s, m); |
164 |
val (ot',p) = demult (t, Rat.one) |
|
165 |
in (case (os',ot') of |
|
166 |
(SOME s', SOME t') => SOME (mC $ s' $ t') |
|
167 |
| (SOME s', NONE) => SOME s' |
|
168 |
| (NONE, SOME t') => |
|
169 |
let val Const(_,T) = mC |
|
170 |
in SOME (mC $ Const (@{const_name Groups.one}, domain_type T) $ t') end |
|
171 |
| (NONE, NONE) => NONE, |
|
172 |
Rat.mult m' (Rat.inv p)) |
|
173 |
end |
|
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174 |
(* terms that evaluate to numeric constants *) |
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175 |
| demult (Const (@{const_name Groups.uminus}, _) $ t, m) = demult (t, Rat.neg m) |
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176 |
| demult (Const (@{const_name Groups.zero}, _), _) = (NONE, Rat.zero) |
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177 |
| demult (Const (@{const_name Groups.one}, _), m) = (NONE, m) |
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178 |
(*Warning: in rare cases (neg_)numeral encloses a non-numeral, |
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179 |
in which case dest_num raises TERM; hence all the handles below. |
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180 |
Same for Suc-terms that turn out not to be numerals - |
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181 |
although the simplifier should eliminate those anyway ...*) |
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182 |
| demult (t as Const ("Num.numeral_class.numeral", _) $ n, m) = |
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|
183 |
((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_num n))) |
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|
184 |
handle TERM _ => (SOME t, m)) |
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|
185 |
| demult (t as Const (@{const_name Suc}, _) $ _, m) = |
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|
186 |
((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_nat t))) |
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|
187 |
handle TERM _ => (SOME t, m)) |
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|
188 |
(* injection constants are ignored *) |
24092
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parents:
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|
189 |
| demult (t as Const f $ x, m) = |
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|
190 |
if member (op =) inj_consts f then demult (x, m) else (SOME t, m) |
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|
191 |
(* everything else is considered atomic *) |
24092
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|
192 |
| demult (atom, m) = (SOME atom, m) |
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|
193 |
in demult end; |
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|
194 |
|
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|
195 |
fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) : |
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|
196 |
((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option = |
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|
197 |
let |
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|
198 |
(* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of |
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parents:
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changeset
|
199 |
summands and associated multiplicities, plus a constant 'i' (with implicit |
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parents:
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changeset
|
200 |
multiplicity 1) *) |
35267
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|
201 |
fun poly (Const (@{const_name Groups.plus}, _) $ s $ t, |
24092
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wenzelm
parents:
diff
changeset
|
202 |
m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi)) |
35267
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haftmann
parents:
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diff
changeset
|
203 |
| poly (all as Const (@{const_name Groups.minus}, T) $ s $ t, m, pi) = |
24092
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wenzelm
parents:
diff
changeset
|
204 |
if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi)) |
35267
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haftmann
parents:
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diff
changeset
|
205 |
| poly (all as Const (@{const_name Groups.uminus}, T) $ t, m, pi) = |
24092
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wenzelm
parents:
diff
changeset
|
206 |
if nT T then add_atom all m pi else poly (t, Rat.neg m, pi) |
35267
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haftmann
parents:
35092
diff
changeset
|
207 |
| poly (Const (@{const_name Groups.zero}, _), _, pi) = |
24092
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wenzelm
parents:
diff
changeset
|
208 |
pi |
35267
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moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
209 |
| poly (Const (@{const_name Groups.one}, _), m, (p, i)) = |
24092
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HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
210 |
(p, Rat.add i m) |
54489
03ff4d1e6784
eliminiated neg_numeral in favour of - (numeral _)
haftmann
parents:
54249
diff
changeset
|
211 |
| poly (all as Const ("Num.numeral_class.numeral", Type(_,[_,_])) $ t, m, pi as (p, i)) = |
03ff4d1e6784
eliminiated neg_numeral in favour of - (numeral _)
haftmann
parents:
54249
diff
changeset
|
212 |
(let val k = HOLogic.dest_num t |
03ff4d1e6784
eliminiated neg_numeral in favour of - (numeral _)
haftmann
parents:
54249
diff
changeset
|
213 |
in (p, Rat.add i (Rat.mult m (Rat.rat_of_int k))) end |
03ff4d1e6784
eliminiated neg_numeral in favour of - (numeral _)
haftmann
parents:
54249
diff
changeset
|
214 |
handle TERM _ => add_atom all m pi) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
215 |
| poly (Const (@{const_name Suc}, _) $ t, m, (p, i)) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
216 |
poly (t, m, (p, Rat.add i m)) |
35267
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moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
217 |
| poly (all as Const (@{const_name Groups.times}, _) $ _ $ _, m, pi as (p, i)) = |
24092
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parents:
diff
changeset
|
218 |
(case demult inj_consts (all, m) of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
219 |
(NONE, m') => (p, Rat.add i m') |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
220 |
| (SOME u, m') => add_atom u m' pi) |
44064
5bce8ff0d9ae
moved division ring stuff from Rings.thy to Fields.thy
huffman
parents:
43609
diff
changeset
|
221 |
| poly (all as Const (@{const_name Fields.divide}, _) $ _ $ _, m, pi as (p, i)) = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
222 |
(case demult inj_consts (all, m) of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
223 |
(NONE, m') => (p, Rat.add i m') |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
224 |
| (SOME u, m') => add_atom u m' pi) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
225 |
| 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
|
226 |
if member (op =) inj_consts f then poly (x, m, pi) else add_atom all m pi |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
227 |
| poly (all, m, pi) = |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
228 |
add_atom all m pi |
71c27b320610
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wenzelm
parents:
diff
changeset
|
229 |
val (p, i) = poly (lhs, Rat.one, ([], Rat.zero)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
230 |
val (q, j) = poly (rhs, Rat.one, ([], Rat.zero)) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
231 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
232 |
case rel of |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
233 |
@{const_name Orderings.less} => SOME (p, i, "<", q, j) |
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
234 |
| @{const_name Orderings.less_eq} => SOME (p, i, "<=", q, j) |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
235 |
| @{const_name HOL.eq} => SOME (p, i, "=", q, j) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
236 |
| _ => NONE |
24328
83afe527504d
fixed a bug in demult: -a in (-a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset
|
237 |
end handle Rat.DIVZERO => NONE; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
238 |
|
24271 | 239 |
fun of_lin_arith_sort thy U = |
35050
9f841f20dca6
renamed OrderedGroup to Groups; split theory Ring_and_Field into Rings Fields
haftmann
parents:
35028
diff
changeset
|
240 |
Sign.of_sort thy (U, @{sort Rings.linordered_idom}); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
241 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
242 |
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
|
243 |
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
|
244 |
else if member (op =) discrete D then (true, true) else (false, false) |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
245 |
| allows_lin_arith sg discrete U = (of_lin_arith_sort sg U, false); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
246 |
|
26942 | 247 |
fun decomp_typecheck (thy, discrete, inj_consts) (T : typ, xxx) : decomp option = |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
248 |
case T of |
71c27b320610
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wenzelm
parents:
diff
changeset
|
249 |
Type ("fun", [U, _]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
250 |
(case allows_lin_arith thy discrete U of |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
251 |
(true, d) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
252 |
(case decomp0 inj_consts xxx of |
71c27b320610
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wenzelm
parents:
diff
changeset
|
253 |
NONE => NONE |
71c27b320610
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wenzelm
parents:
diff
changeset
|
254 |
| 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
|
255 |
| (false, _) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
256 |
NONE) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
257 |
| _ => NONE; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
258 |
|
71c27b320610
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wenzelm
parents:
diff
changeset
|
259 |
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
|
260 |
| negate NONE = NONE; |
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|
261 |
|
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262 |
fun decomp_negation data |
38558 | 263 |
((Const (@{const_name Trueprop}, _)) $ (Const (rel, T) $ lhs $ rhs)) : decomp option = |
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|
264 |
decomp_typecheck data (T, (rel, lhs, rhs)) |
38558 | 265 |
| decomp_negation data ((Const (@{const_name Trueprop}, _)) $ |
266 |
(Const (@{const_name Not}, _) $ (Const (rel, T) $ lhs $ rhs))) = |
|
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|
267 |
negate (decomp_typecheck data (T, (rel, lhs, rhs))) |
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|
268 |
| decomp_negation data _ = |
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|
269 |
NONE; |
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|
270 |
|
26942 | 271 |
fun decomp ctxt : term -> decomp option = |
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272 |
let |
42361 | 273 |
val thy = Proof_Context.theory_of ctxt |
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|
274 |
val {discrete, inj_consts, ...} = get_arith_data ctxt |
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|
275 |
in decomp_negation (thy, discrete, inj_consts) end; |
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|
276 |
|
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|
277 |
fun domain_is_nat (_ $ (Const (_, T) $ _ $ _)) = nT T |
38558 | 278 |
| domain_is_nat (_ $ (Const (@{const_name Not}, _) $ (Const (_, T) $ _ $ _))) = nT T |
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|
279 |
| domain_is_nat _ = false; |
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|
280 |
|
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|
281 |
|
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|
282 |
(*---------------------------------------------------------------------------*) |
32369 | 283 |
(* the following code performs splitting of certain constants (e.g., min, *) |
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|
284 |
(* max) in a linear arithmetic problem; similar to what split_tac later does *) |
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|
285 |
(* to the proof state *) |
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|
286 |
(*---------------------------------------------------------------------------*) |
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|
287 |
|
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|
288 |
(* checks if splitting with 'thm' is implemented *) |
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|
289 |
|
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|
290 |
fun is_split_thm ctxt thm = |
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|
291 |
(case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => |
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|
292 |
(* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *) |
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|
293 |
(case head_of lhs of |
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|
294 |
Const (a, _) => |
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|
295 |
member (op =) |
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|
296 |
[@{const_name Orderings.max}, |
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|
297 |
@{const_name Orderings.min}, |
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|
298 |
@{const_name Groups.abs}, |
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|
299 |
@{const_name Groups.minus}, |
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|
300 |
"Int.nat" (*DYNAMIC BINDING!*), |
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|
301 |
"Divides.div_class.mod" (*DYNAMIC BINDING!*), |
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|
302 |
"Divides.div_class.div" (*DYNAMIC BINDING!*)] a |
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|
303 |
| _ => |
59352
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|
304 |
(if Context_Position.is_visible ctxt then |
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|
305 |
warning ("Lin. Arith.: wrong format for split rule " ^ Display.string_of_thm ctxt thm) |
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|
306 |
else (); false)) |
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|
307 |
| _ => |
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|
308 |
(if Context_Position.is_visible ctxt then |
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|
309 |
warning ("Lin. Arith.: wrong format for split rule " ^ Display.string_of_thm ctxt thm) |
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|
310 |
else (); false)); |
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|
311 |
|
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|
312 |
(* substitute new for occurrences of old in a term, incrementing bound *) |
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|
313 |
(* variables as needed when substituting inside an abstraction *) |
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|
314 |
|
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|
315 |
fun subst_term ([] : (term * term) list) (t : term) = t |
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|
316 |
| subst_term pairs t = |
52131 | 317 |
(case AList.lookup Envir.aeconv pairs t of |
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|
318 |
SOME new => |
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|
319 |
new |
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|
320 |
| NONE => |
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|
321 |
(case t of Abs (a, T, body) => |
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renamed "pairself" to "apply2", in accordance to @{apply 2};
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changeset
|
322 |
let val pairs' = map (apply2 (incr_boundvars 1)) pairs |
24092
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|
323 |
in Abs (a, T, subst_term pairs' body) end |
59058
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renamed "pairself" to "apply2", in accordance to @{apply 2};
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|
324 |
| t1 $ t2 => subst_term pairs t1 $ subst_term pairs t2 |
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|
325 |
| _ => t)); |
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changeset
|
326 |
|
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|
327 |
(* approximates the effect of one application of split_tac (followed by NNF *) |
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|
328 |
(* normalization) on the subgoal represented by '(Ts, terms)'; returns a *) |
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|
329 |
(* list of new subgoals (each again represented by a typ list for bound *) |
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|
330 |
(* variables and a term list for premises), or NONE if split_tac would fail *) |
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|
331 |
(* on the subgoal *) |
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|
332 |
|
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parents:
diff
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|
333 |
(* FIXME: currently only the effect of certain split theorems is reproduced *) |
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changeset
|
334 |
(* (which is why we need 'is_split_thm'). A more canonical *) |
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changeset
|
335 |
(* implementation should analyze the right-hand side of the split *) |
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|
336 |
(* theorem that can be applied, and modify the subgoal accordingly. *) |
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|
337 |
(* Or even better, the splitter should be extended to provide *) |
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diff
changeset
|
338 |
(* splitting on terms as well as splitting on theorems (where the *) |
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changeset
|
339 |
(* former can have a faster implementation as it does not need to be *) |
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|
340 |
(* proof-producing). *) |
71c27b320610
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parents:
diff
changeset
|
341 |
|
71c27b320610
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parents:
diff
changeset
|
342 |
fun split_once_items ctxt (Ts : typ list, terms : term list) : |
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changeset
|
343 |
(typ list * term list) list option = |
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|
344 |
let |
42361 | 345 |
val thy = Proof_Context.theory_of ctxt |
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|
346 |
(* takes a list [t1, ..., tn] to the term *) |
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changeset
|
347 |
(* tn' --> ... --> t1' --> False , *) |
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parents:
diff
changeset
|
348 |
(* where ti' = HOLogic.dest_Trueprop ti *) |
32369 | 349 |
fun REPEAT_DETERM_etac_rev_mp tms = |
350 |
fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop tms) |
|
45740 | 351 |
@{term False} |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
352 |
val split_thms = filter (is_split_thm ctxt) (#splits (get_arith_data ctxt)) |
32369 | 353 |
val cmap = Splitter.cmap_of_split_thms split_thms |
354 |
val goal_tm = REPEAT_DETERM_etac_rev_mp terms |
|
355 |
val splits = Splitter.split_posns cmap thy Ts goal_tm |
|
31082 | 356 |
val split_limit = Config.get ctxt split_limit |
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
357 |
in |
32369 | 358 |
if length splits > split_limit then ( |
359 |
tracing ("linarith_split_limit exceeded (current value is " ^ |
|
360 |
string_of_int split_limit ^ ")"); |
|
361 |
NONE |
|
362 |
) else case splits of |
|
363 |
[] => |
|
24092
71c27b320610
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wenzelm
parents:
diff
changeset
|
364 |
(* split_tac would fail: no possible split *) |
71c27b320610
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wenzelm
parents:
diff
changeset
|
365 |
NONE |
32369 | 366 |
| (_, _::_, _, _, _) :: _ => |
367 |
(* disallow a split that involves non-locally bound variables (except *) |
|
368 |
(* when bound by outermost meta-quantifiers) *) |
|
369 |
NONE |
|
370 |
| (_, [], _, split_type, split_term) :: _ => |
|
371 |
(* ignore all but the first possible split *) |
|
372 |
(case strip_comb split_term of |
|
24092
71c27b320610
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parents:
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changeset
|
373 |
(* ?P (max ?i ?j) = ((?i <= ?j --> ?P ?j) & (~ ?i <= ?j --> ?P ?i)) *) |
71c27b320610
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parents:
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changeset
|
374 |
(Const (@{const_name Orderings.max}, _), [t1, t2]) => |
71c27b320610
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parents:
diff
changeset
|
375 |
let |
71c27b320610
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wenzelm
parents:
diff
changeset
|
376 |
val rev_terms = rev terms |
71c27b320610
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wenzelm
parents:
diff
changeset
|
377 |
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
|
378 |
val terms2 = map (subst_term [(split_term, t2)]) rev_terms |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
379 |
val t1_leq_t2 = Const (@{const_name Orderings.less_eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
380 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
381 |
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 |
45740 | 382 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
383 |
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
|
384 |
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
|
385 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
386 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
387 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
388 |
(* ?P (min ?i ?j) = ((?i <= ?j --> ?P ?i) & (~ ?i <= ?j --> ?P ?j)) *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
389 |
| (Const (@{const_name Orderings.min}, _), [t1, t2]) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
390 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
391 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
392 |
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
|
393 |
val terms2 = map (subst_term [(split_term, t2)]) rev_terms |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
394 |
val t1_leq_t2 = Const (@{const_name Orderings.less_eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
395 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
396 |
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 |
45740 | 397 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
398 |
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
|
399 |
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
|
400 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
401 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
402 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
403 |
(* ?P (abs ?a) = ((0 <= ?a --> ?P ?a) & (?a < 0 --> ?P (- ?a))) *) |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
404 |
| (Const (@{const_name Groups.abs}, _), [t1]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
405 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
406 |
val rev_terms = rev terms |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
407 |
val terms1 = map (subst_term [(split_term, t1)]) rev_terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
408 |
val terms2 = map (subst_term [(split_term, Const (@{const_name Groups.uminus}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
409 |
split_type --> split_type) $ t1)]) rev_terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
410 |
val zero = Const (@{const_name Groups.zero}, split_type) |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
411 |
val zero_leq_t1 = Const (@{const_name Orderings.less_eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
412 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t1 |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
413 |
val t1_lt_zero = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
414 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ zero |
45740 | 415 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
416 |
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
|
417 |
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
|
418 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
419 |
SOME [(Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
420 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
421 |
(* ?P (?a - ?b) = ((?a < ?b --> ?P 0) & (ALL d. ?a = ?b + d --> ?P d)) *) |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
422 |
| (Const (@{const_name Groups.minus}, _), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
423 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
424 |
(* "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
|
425 |
(* transformation, therefore some adjustment of indices is necessary *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
426 |
val rev_terms = rev terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
427 |
val zero = Const (@{const_name Groups.zero}, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
428 |
val d = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
429 |
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
|
430 |
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
|
431 |
(map (incr_boundvars 1) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
432 |
val t1' = incr_boundvars 1 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
433 |
val t2' = incr_boundvars 1 t2 |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
434 |
val t1_lt_t2 = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
435 |
split_type --> split_type --> HOLogic.boolT) $ t1 $ t2 |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
436 |
val t1_eq_t2_plus_d = Const (@{const_name HOL.eq}, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
437 |
(Const (@{const_name Groups.plus}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
438 |
split_type --> split_type --> split_type) $ t2' $ d) |
45740 | 439 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
440 |
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
|
441 |
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
|
442 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
443 |
SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
444 |
end |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
445 |
(* ?P (nat ?i) = ((ALL n. ?i = of_nat n --> ?P n) & (?i < 0 --> ?P 0)) *) |
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset
|
446 |
| (Const ("Int.nat", _), [t1]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
447 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
448 |
val rev_terms = rev terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
449 |
val zero_int = Const (@{const_name Groups.zero}, HOLogic.intT) |
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
450 |
val zero_nat = Const (@{const_name Groups.zero}, HOLogic.natT) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
451 |
val n = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
452 |
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
|
453 |
(map (incr_boundvars 1) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
454 |
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
|
455 |
val t1' = incr_boundvars 1 t1 |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
456 |
val t1_eq_nat_n = Const (@{const_name HOL.eq}, HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1' $ |
24196 | 457 |
(Const (@{const_name of_nat}, HOLogic.natT --> HOLogic.intT) $ n) |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
458 |
val t1_lt_zero = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
459 |
HOLogic.intT --> HOLogic.intT --> HOLogic.boolT) $ t1 $ zero_int |
45740 | 460 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
461 |
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
|
462 |
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
|
463 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
464 |
SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
465 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
466 |
(* ?P ((?n::nat) mod (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
467 |
((numeral ?k = 0 --> ?P ?n) & (~ (numeral ?k = 0) --> |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
468 |
(ALL i j. j < numeral ?k --> ?n = numeral ?k * i + j --> ?P j))) *) |
37388 | 469 |
| (Const ("Divides.div_class.mod", Type ("fun", [@{typ nat}, _])), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
470 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
471 |
val rev_terms = rev terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
472 |
val zero = Const (@{const_name Groups.zero}, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
473 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
474 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
475 |
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
|
476 |
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
|
477 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
478 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
479 |
val t2' = incr_boundvars 2 t2 |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
480 |
val t2_eq_zero = Const (@{const_name HOL.eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
481 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
482 |
val t2_neq_zero = HOLogic.mk_not (Const (@{const_name HOL.eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
483 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero) |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
484 |
val j_lt_t2 = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
485 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
486 |
val t1_eq_t2_times_i_plus_j = Const (@{const_name HOL.eq}, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
487 |
(Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $ |
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
488 |
(Const (@{const_name Groups.times}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
489 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
45740 | 490 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
491 |
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
|
492 |
val subgoal2 = (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
493 |
[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
|
494 |
@ terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
495 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
496 |
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
|
497 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
498 |
(* ?P ((?n::nat) div (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
499 |
((numeral ?k = 0 --> ?P 0) & (~ (numeral ?k = 0) --> |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
500 |
(ALL i j. j < numeral ?k --> ?n = numeral ?k * i + j --> ?P i))) *) |
37388 | 501 |
| (Const ("Divides.div_class.div", Type ("fun", [@{typ nat}, _])), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
502 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
503 |
val rev_terms = rev terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
504 |
val zero = Const (@{const_name Groups.zero}, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
505 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
506 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
507 |
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
|
508 |
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
|
509 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
510 |
val t1' = incr_boundvars 2 t1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
511 |
val t2' = incr_boundvars 2 t2 |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
512 |
val t2_eq_zero = Const (@{const_name HOL.eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
513 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
514 |
val t2_neq_zero = HOLogic.mk_not (Const (@{const_name HOL.eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
515 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero) |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
516 |
val j_lt_t2 = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
517 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
518 |
val t1_eq_t2_times_i_plus_j = Const (@{const_name HOL.eq}, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
519 |
(Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $ |
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
520 |
(Const (@{const_name Groups.times}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
521 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
45740 | 522 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
523 |
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
|
524 |
val subgoal2 = (map HOLogic.mk_Trueprop |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
525 |
[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
|
526 |
@ terms2 @ [not_false] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
527 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
528 |
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
|
529 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
530 |
(* ?P ((?n::int) mod (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
531 |
((numeral ?k = 0 --> ?P ?n) & |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
532 |
(0 < numeral ?k --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
533 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
534 |
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
|
535 |
(numeral ?k < 0 --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
536 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
537 |
numeral ?k < j & j <= 0 & ?n = numeral ?k * i + j --> ?P j))) *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
538 |
| (Const ("Divides.div_class.mod", |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
539 |
Type ("fun", [Type ("Int.int", []), _])), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
540 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
541 |
val rev_terms = rev terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
542 |
val zero = Const (@{const_name Groups.zero}, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
543 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
544 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
545 |
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
|
546 |
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
|
547 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
548 |
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
|
549 |
val t2' = incr_boundvars 2 t2 |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
550 |
val t2_eq_zero = Const (@{const_name HOL.eq}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
551 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
552 |
val zero_lt_t2 = Const (@{const_name Orderings.less}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
553 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t2' |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
554 |
val t2_lt_zero = Const (@{const_name Orderings.less}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
555 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
556 |
val zero_leq_j = Const (@{const_name Orderings.less_eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
557 |
split_type --> split_type --> HOLogic.boolT) $ zero $ j |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
558 |
val j_leq_zero = Const (@{const_name Orderings.less_eq}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
559 |
split_type --> split_type --> HOLogic.boolT) $ j $ zero |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
560 |
val j_lt_t2 = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
561 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
562 |
val t2_lt_j = Const (@{const_name Orderings.less}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
563 |
split_type --> split_type--> HOLogic.boolT) $ t2' $ j |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
564 |
val t1_eq_t2_times_i_plus_j = Const (@{const_name HOL.eq}, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
565 |
(Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $ |
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
566 |
(Const (@{const_name Groups.times}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
567 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
45740 | 568 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
569 |
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
|
570 |
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
|
571 |
@ hd terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
572 |
:: (if tl terms2_3 = [] then [not_false] else []) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
573 |
@ (map HOLogic.mk_Trueprop [j_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
|
574 |
@ (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
|
575 |
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
|
576 |
@ hd terms2_3 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
577 |
:: (if tl terms2_3 = [] then [not_false] else []) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
578 |
@ (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
|
579 |
@ (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
|
580 |
val Ts' = split_type :: split_type :: Ts |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
581 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
582 |
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
583 |
end |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
584 |
(* ?P ((?n::int) div (numeral ?k)) = |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
585 |
((numeral ?k = 0 --> ?P 0) & |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
586 |
(0 < numeral ?k --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
587 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
588 |
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
|
589 |
(numeral ?k < 0 --> |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
590 |
(ALL i j. |
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
46709
diff
changeset
|
591 |
numeral ?k < j & j <= 0 & ?n = numeral ?k * i + j --> ?P i))) *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
592 |
| (Const ("Divides.div_class.div", |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
593 |
Type ("fun", [Type ("Int.int", []), _])), [t1, t2]) => |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
594 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
595 |
val rev_terms = rev terms |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
596 |
val zero = Const (@{const_name Groups.zero}, split_type) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
597 |
val i = Bound 1 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
598 |
val j = Bound 0 |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
599 |
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
|
600 |
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
|
601 |
(map (incr_boundvars 2) rev_terms) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
602 |
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
|
603 |
val t2' = incr_boundvars 2 t2 |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
604 |
val t2_eq_zero = Const (@{const_name HOL.eq}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
605 |
split_type --> split_type --> HOLogic.boolT) $ t2 $ zero |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
606 |
val zero_lt_t2 = Const (@{const_name Orderings.less}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
607 |
split_type --> split_type --> HOLogic.boolT) $ zero $ t2' |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
608 |
val t2_lt_zero = Const (@{const_name Orderings.less}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
609 |
split_type --> split_type --> HOLogic.boolT) $ t2' $ zero |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
610 |
val zero_leq_j = Const (@{const_name Orderings.less_eq}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
611 |
split_type --> split_type --> HOLogic.boolT) $ zero $ j |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
612 |
val j_leq_zero = Const (@{const_name Orderings.less_eq}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
613 |
split_type --> split_type --> HOLogic.boolT) $ j $ zero |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
614 |
val j_lt_t2 = Const (@{const_name Orderings.less}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
615 |
split_type --> split_type--> HOLogic.boolT) $ j $ t2' |
35092
cfe605c54e50
moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents:
35084
diff
changeset
|
616 |
val t2_lt_j = Const (@{const_name Orderings.less}, |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
617 |
split_type --> split_type--> HOLogic.boolT) $ t2' $ j |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38797
diff
changeset
|
618 |
val t1_eq_t2_times_i_plus_j = Const (@{const_name HOL.eq}, split_type --> split_type --> HOLogic.boolT) $ t1' $ |
35267
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
619 |
(Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $ |
8dfd816713c6
moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents:
35092
diff
changeset
|
620 |
(Const (@{const_name Groups.times}, |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
621 |
split_type --> split_type --> split_type) $ t2' $ i) $ j) |
45740 | 622 |
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ @{term False}) |
33728
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
623 |
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
|
624 |
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
|
625 |
@ hd terms2_3 |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
626 |
:: (if tl terms2_3 = [] then [not_false] else []) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
627 |
@ (map HOLogic.mk_Trueprop [j_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
|
628 |
@ (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
|
629 |
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
|
630 |
@ hd terms2_3 |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
631 |
:: (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
|
632 |
@ (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
|
633 |
@ (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
|
634 |
val Ts' = split_type :: split_type :: Ts |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
635 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
636 |
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
637 |
end |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
638 |
(* 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
|
639 |
(* 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
|
640 |
(* 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
|
641 |
(* out *) |
59352
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
642 |
| (t, ts) => |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
643 |
(if Context_Position.is_visible ctxt then |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
644 |
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
|
645 |
" (with " ^ string_of_int (length ts) ^ |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
646 |
" argument(s)) not implemented; proof reconstruction is likely to fail") |
63c02d051661
tuned warnings: observe Context_Position.is_visible;
wenzelm
parents:
59058
diff
changeset
|
647 |
else (); NONE)) |
32369 | 648 |
end; (* split_once_items *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
649 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
650 |
(* 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
|
651 |
(* 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
|
652 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
653 |
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
|
654 |
let |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
655 |
fun filter_prems t (left, right) = |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
656 |
if p t then (left, right @ [t]) else (left @ right, []) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
657 |
val (left, right) = fold filter_prems terms ([], []) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
658 |
in |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
659 |
right @ left |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
660 |
end; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
661 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
662 |
(* 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
|
663 |
(* subgoal that has 'terms' as premises *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
664 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
665 |
fun negated_term_occurs_positively (terms : term list) : bool = |
58412 | 666 |
exists |
38558 | 667 |
(fn (Trueprop $ (Const (@{const_name Not}, _) $ t)) => |
52131 | 668 |
member Envir.aeconv terms (Trueprop $ t) |
32369 | 669 |
| _ => false) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
670 |
terms; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
671 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
672 |
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
|
673 |
let |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
674 |
(* repeatedly split (including newly emerging subgoals) until no further *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
675 |
(* splitting is possible *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
676 |
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
|
677 |
| split_loop (subgoal::subgoals) = |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
678 |
(case split_once_items ctxt subgoal of |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
679 |
SOME new_subgoals => split_loop (new_subgoals @ subgoals) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
680 |
| NONE => subgoal :: split_loop subgoals) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
681 |
fun is_relevant t = is_some (decomp ctxt t) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
682 |
(* filter_prems_tac is_relevant: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
683 |
val relevant_terms = filter_prems_tac_items is_relevant terms |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
684 |
(* split_tac, NNF normalization: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
685 |
val split_goals = split_loop [(Ts, relevant_terms)] |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
686 |
(* necessary because split_once_tac may normalize terms: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
687 |
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
|
688 |
split_goals |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
689 |
(* TRY (etac notE) THEN eq_assume_tac: *) |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
690 |
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
|
691 |
in |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
692 |
result |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
693 |
end; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
694 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
695 |
(* 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
|
696 |
(* 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
|
697 |
(* (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
|
698 |
(* performs NNF-normalization of ~P, and eliminates conjunctions, *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
699 |
(* 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
|
700 |
(* 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
|
701 |
(* general form [| Q1; ...; Qm |] ==> False. Fails if more than *) |
31082 | 702 |
(* !split_limit splits are possible. *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
703 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
704 |
local |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
705 |
fun nnf_simpset ctxt = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
706 |
(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
|
707 |
|> 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
|
708 |
|> Simplifier.set_mksimps (mksimps mksimps_pairs)) |
35410 | 709 |
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, |
710 |
@{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
|
711 |
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
|
712 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
713 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
714 |
fun split_once_tac ctxt split_thms = |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
715 |
let |
42361 | 716 |
val thy = Proof_Context.theory_of ctxt |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
717 |
val cond_split_tac = SUBGOAL (fn (subgoal, i) => |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
718 |
let |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
719 |
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
|
720 |
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
|
721 |
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
|
722 |
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
|
723 |
in |
32369 | 724 |
if null splits orelse length splits > Config.get ctxt split_limit then |
725 |
no_tac |
|
726 |
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
|
727 |
split_tac ctxt split_thms i |
32369 | 728 |
else |
729 |
(* disallow a split that involves non-locally bound variables *) |
|
730 |
(* (except when bound by outermost meta-quantifiers) *) |
|
731 |
no_tac |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
732 |
end) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
733 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
734 |
EVERY' [ |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
735 |
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
|
736 |
cond_split_tac, |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
737 |
resolve_tac ctxt @{thms ccontr}, |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
738 |
prem_nnf_tac ctxt, |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
739 |
TRY o REPEAT_ALL_NEW |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
740 |
(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
|
741 |
] |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
742 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
743 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
744 |
end; (* local *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
745 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
746 |
(* 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
|
747 |
(* 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
|
748 |
(* subgoals and finally attempt to solve them by finding an immediate *) |
32369 | 749 |
(* 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
|
750 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
751 |
fun pre_tac ctxt i = |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
752 |
let |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
753 |
val split_thms = filter (is_split_thm ctxt) (#splits (get_arith_data ctxt)) |
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 |
in |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
756 |
DETERM ( |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
757 |
TRY (filter_prems_tac ctxt is_relevant i) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
758 |
THEN ( |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
759 |
(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
|
760 |
THEN_ALL_NEW |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
761 |
(CONVERSION Drule.beta_eta_conversion |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
762 |
THEN' |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
763 |
(TRY o (eresolve_tac ctxt [notE] THEN' eq_assume_tac))) |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
764 |
) i |
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
765 |
) |
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 |
|
31100 | 768 |
end; (* LA_Data *) |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
769 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
770 |
|
31100 | 771 |
val pre_tac = LA_Data.pre_tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
772 |
|
31100 | 773 |
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
|
774 |
|
38762
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
775 |
val add_inj_thms = Fast_Arith.add_inj_thms; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
776 |
val add_lessD = Fast_Arith.add_lessD; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
777 |
val add_simps = Fast_Arith.add_simps; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
778 |
val add_simprocs = Fast_Arith.add_simprocs; |
996afaa9254a
slightly more abstract data handling in Fast_Lin_Arith;
wenzelm
parents:
38715
diff
changeset
|
779 |
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
|
780 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
781 |
fun simple_tac ctxt = Fast_Arith.lin_arith_tac ctxt false; |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
782 |
val lin_arith_tac = Fast_Arith.lin_arith_tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
783 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
784 |
(* reduce contradictory <= to False. |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
785 |
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
|
786 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
787 |
val init_arith_data = |
54249 | 788 |
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, number_of, ...} => |
789 |
{add_mono_thms = @{thms add_mono_thms_linordered_semiring} |
|
790 |
@ @{thms add_mono_thms_linordered_field} @ add_mono_thms, |
|
791 |
mult_mono_thms = @{thm mult_strict_left_mono} :: @{thm mult_left_mono} |
|
792 |
:: @{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
|
793 |
inj_thms = inj_thms, |
54249 | 794 |
lessD = lessD, |
795 |
neqE = @{thm linorder_neqE_nat} :: @{thm linorder_neqE_linordered_idom} :: neqE, |
|
796 |
simpset = put_simpset HOL_basic_ss @{context} |> Simplifier.add_cong @{thm if_weak_cong} |> simpset_of, |
|
797 |
number_of = number_of}); |
|
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
798 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
799 |
(* FIXME !?? *) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
800 |
fun add_arith_facts ctxt = |
57955 | 801 |
Simplifier.add_prems (rev (Named_Theorems.get ctxt @{named_theorems arith})) ctxt; |
29849
a2baf1b221be
new attribute "arith" for facts supplied to arith.
nipkow
parents:
29548
diff
changeset
|
802 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
803 |
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
|
804 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
805 |
|
26110 | 806 |
(* generic refutation procedure *) |
807 |
||
808 |
(* parameters: |
|
809 |
||
810 |
test: term -> bool |
|
811 |
tests if a term is at all relevant to the refutation proof; |
|
812 |
if not, then it can be discarded. Can improve performance, |
|
813 |
esp. if disjunctions can be discarded (no case distinction needed!). |
|
814 |
||
815 |
prep_tac: int -> tactic |
|
816 |
A preparation tactic to be applied to the goal once all relevant premises |
|
817 |
have been moved to the conclusion. |
|
818 |
||
819 |
ref_tac: int -> tactic |
|
820 |
the actual refutation tactic. Should be able to deal with goals |
|
821 |
[| A1; ...; An |] ==> False |
|
822 |
where the Ai are atomic, i.e. no top-level &, | or EX |
|
823 |
*) |
|
824 |
||
825 |
local |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
826 |
fun nnf_simpset ctxt = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
827 |
(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
|
828 |
|> 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
|
829 |
|> Simplifier.set_mksimps (mksimps mksimps_pairs)) |
26110 | 830 |
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, |
831 |
@{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}]; |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
832 |
fun prem_nnf_tac ctxt = full_simp_tac (nnf_simpset ctxt); |
26110 | 833 |
in |
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
834 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
835 |
fun refute_tac ctxt test prep_tac ref_tac = |
26110 | 836 |
let val refute_prems_tac = |
837 |
REPEAT_DETERM |
|
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
838 |
(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
|
839 |
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
|
840 |
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
|
841 |
(DETERM (eresolve_tac ctxt @{thms notE} 1 THEN eq_assume_tac 1) ORELSE |
26110 | 842 |
ref_tac 1); |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
843 |
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
|
844 |
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
|
845 |
resolve_tac ctxt @{thms ccontr}, prem_nnf_tac ctxt, |
26110 | 846 |
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] |
847 |
end; |
|
42439
9efdd0af15ac
eliminated Display.string_of_thm_without_context;
wenzelm
parents:
42361
diff
changeset
|
848 |
|
26110 | 849 |
end; |
850 |
||
851 |
||
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
852 |
(* arith proof method *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
853 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
854 |
local |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
855 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
856 |
fun raw_tac ctxt ex = |
33035 | 857 |
(* 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
|
858 |
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
|
859 |
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
|
860 |
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
|
861 |
(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
|
862 |
(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
|
863 |
*) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
864 |
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
|
865 |
(* 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
|
866 |
(* 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
|
867 |
(* 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
|
868 |
(* split_limit may trigger. *) |
cb4235333c30
Fixed splitting of div and mod on integers (split theorem differed from implementation).
webertj
parents:
33719
diff
changeset
|
869 |
(* 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
|
870 |
(* some goals that simple_tac alone would fail on. *) |
58956
a816aa3ff391
proper context for compose_tac, Splitter.split_tac (relevant for unify trace options);
wenzelm
parents:
58839
diff
changeset
|
871 |
(REPEAT_DETERM o split_tac ctxt (#splits (get_arith_data ctxt))) |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
872 |
(lin_arith_tac ctxt ex); |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
873 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
874 |
in |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
875 |
|
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
54489
diff
changeset
|
876 |
fun gen_tac ex ctxt = |
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
54489
diff
changeset
|
877 |
FIRST' [simple_tac ctxt, |
58839 | 878 |
Object_Logic.full_atomize_tac ctxt THEN' |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59352
diff
changeset
|
879 |
(REPEAT_DETERM o resolve_tac ctxt [impI]) THEN' raw_tac ctxt ex]; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
880 |
|
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
881 |
val tac = gen_tac true; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
882 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
883 |
end; |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
884 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
885 |
|
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
886 |
(* context setup *) |
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
887 |
|
31100 | 888 |
val global_setup = |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
889 |
map_theory_simpset (fn ctxt => ctxt |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
48560
diff
changeset
|
890 |
addSolver (mk_solver "lin_arith" (add_arith_facts #> Fast_Arith.prems_lin_arith_tac))) #> |
31100 | 891 |
Attrib.setup @{binding arith_split} (Scan.succeed (Thm.declaration_attribute add_split)) |
892 |
"declaration of split rules for arithmetic procedure" #> |
|
893 |
Method.setup @{binding linarith} |
|
33554 | 894 |
(Scan.succeed (fn ctxt => |
31100 | 895 |
METHOD (fn facts => |
57955 | 896 |
HEADGOAL (Method.insert_tac (rev (Named_Theorems.get ctxt @{named_theorems arith}) @ facts) |
31101
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
897 |
THEN' tac ctxt)))) "linear arithmetic" #> |
26c7bb764a38
qualified names for Lin_Arith tactics and simprocs
haftmann
parents:
31100
diff
changeset
|
898 |
Arith_Data.add_tactic "linear arithmetic" gen_tac; |
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
899 |
|
54249 | 900 |
val setup = |
901 |
init_arith_data |
|
902 |
#> add_discrete_type @{type_name nat} |
|
903 |
#> add_lessD @{thm Suc_leI} |
|
904 |
#> add_simps (@{thms simp_thms} @ @{thms ring_distribs} @ [@{thm if_True}, @{thm if_False}, |
|
905 |
@{thm add_0_left}, @{thm add_0_right}, @{thm order_less_irrefl}, |
|
906 |
@{thm zero_neq_one}, @{thm zero_less_one}, @{thm zero_le_one}, |
|
907 |
@{thm zero_neq_one} RS not_sym, @{thm not_one_le_zero}, @{thm not_one_less_zero}]) |
|
908 |
#> add_simps [@{thm add_Suc}, @{thm add_Suc_right}, @{thm nat.inject}, |
|
909 |
@{thm Suc_le_mono}, @{thm Suc_less_eq}, @{thm Zero_not_Suc}, |
|
910 |
@{thm Suc_not_Zero}, @{thm le_0_eq}, @{thm One_nat_def}] |
|
911 |
#> add_simprocs [@{simproc group_cancel_add}, @{simproc group_cancel_diff}, |
|
912 |
@{simproc group_cancel_eq}, @{simproc group_cancel_le}, |
|
913 |
@{simproc group_cancel_less}] |
|
914 |
(*abel_cancel helps it work in abstract algebraic domains*) |
|
915 |
#> add_simprocs [@{simproc nateq_cancel_sums},@{simproc natless_cancel_sums}, |
|
916 |
@{simproc natle_cancel_sums}]; |
|
917 |
||
24092
71c27b320610
HOL setup for linear arithmetic -- moved here from arith_data.ML;
wenzelm
parents:
diff
changeset
|
918 |
end; |