author | wenzelm |
Fri, 25 Sep 2015 20:37:59 +0200 | |
changeset 61268 | abe08fb15a12 |
parent 61144 | 5e94dfead1c2 |
child 61841 | 4d3527b94f2a |
permissions | -rw-r--r-- |
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(* Title: Provers/Arith/fast_lin_arith.ML |
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Author: Tobias Nipkow and Tjark Weber and Sascha Boehme |
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A generic linear arithmetic package. |
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Only take premises and conclusions into account that are already |
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(negated) (in)equations. lin_arith_simproc tries to prove or disprove |
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the term. |
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Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
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*) |
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(*** Data needed for setting up the linear arithmetic package ***) |
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signature LIN_ARITH_LOGIC = |
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sig |
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val conjI : thm (* P ==> Q ==> P & Q *) |
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val ccontr : thm (* (~ P ==> False) ==> P *) |
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val notI : thm (* (P ==> False) ==> ~ P *) |
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val not_lessD : thm (* ~(m < n) ==> n <= m *) |
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val not_leD : thm (* ~(m <= n) ==> n < m *) |
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val sym : thm (* x = y ==> y = x *) |
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val trueI : thm (* True *) |
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val mk_Eq : thm -> thm |
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val atomize : thm -> thm list |
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val mk_Trueprop : term -> term |
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val neg_prop : term -> term |
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val is_False : thm -> bool |
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val is_nat : typ list * term -> bool |
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val mk_nat_thm : theory -> term -> thm |
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end; |
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(* |
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mk_Eq(~in) = `in == False' |
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mk_Eq(in) = `in == True' |
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where `in' is an (in)equality. |
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neg_prop(t) = neg if t is wrapped up in Trueprop and neg is the |
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(logically) negated version of t (again wrapped up in Trueprop), |
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where the negation of a negative term is the term itself (no |
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double negation!); raises TERM ("neg_prop", [t]) if t is not of |
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the form 'Trueprop $ _' |
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is_nat(parameter-types,t) = t:nat |
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mk_nat_thm(t) = "0 <= t" |
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*) |
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signature LIN_ARITH_DATA = |
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sig |
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(*internal representation of linear (in-)equations:*) |
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type decomp = (term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat * bool |
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val decomp: Proof.context -> term -> decomp option |
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val domain_is_nat: term -> bool |
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(*preprocessing, performed on a representation of subgoals as list of premises:*) |
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val pre_decomp: Proof.context -> typ list * term list -> (typ list * term list) list |
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(*preprocessing, performed on the goal -- must do the same as 'pre_decomp':*) |
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val pre_tac: Proof.context -> int -> tactic |
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(*the limit on the number of ~= allowed; because each ~= is split |
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into two cases, this can lead to an explosion*) |
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val neq_limit: int Config.T |
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val trace: bool Config.T |
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end; |
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(* |
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decomp(`x Rel y') should yield (p,i,Rel,q,j,d) |
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where Rel is one of "<", "~<", "<=", "~<=" and "=" and |
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p (q, respectively) is the decomposition of the sum term x |
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(y, respectively) into a list of summand * multiplicity |
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pairs and a constant summand and d indicates if the domain |
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is discrete. |
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domain_is_nat(`x Rel y') t should yield true iff x is of type "nat". |
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The relationship between pre_decomp and pre_tac is somewhat tricky. The |
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internal representation of a subgoal and the corresponding theorem must |
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be modified by pre_decomp (pre_tac, resp.) in a corresponding way. See |
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the comment for split_items below. (This is even necessary for eta- and |
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beta-equivalent modifications, as some of the lin. arith. code is not |
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insensitive to them.) |
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Simpset must reduce contradictory <= to False. |
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It should also cancel common summands to keep <= reduced; |
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otherwise <= can grow to massive proportions. |
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*) |
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signature FAST_LIN_ARITH = |
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sig |
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val prems_lin_arith_tac: Proof.context -> int -> tactic |
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val lin_arith_tac: Proof.context -> int -> tactic |
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val lin_arith_simproc: Proof.context -> cterm -> thm option |
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val map_data: |
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({add_mono_thms: thm list, mult_mono_thms: thm list, inj_thms: thm list, |
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lessD: thm list, neqE: thm list, simpset: simpset, |
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number_of: (Proof.context -> typ -> int -> cterm) option} -> |
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{add_mono_thms: thm list, mult_mono_thms: thm list, inj_thms: thm list, |
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lessD: thm list, neqE: thm list, simpset: simpset, |
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number_of: (Proof.context -> typ -> int -> cterm) option}) -> |
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Context.generic -> Context.generic |
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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 set_number_of: (Proof.context -> typ -> int -> cterm) -> Context.generic -> Context.generic |
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end; |
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functor Fast_Lin_Arith |
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(structure LA_Logic: LIN_ARITH_LOGIC and LA_Data: LIN_ARITH_DATA): FAST_LIN_ARITH = |
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struct |
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(** theory data **) |
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structure Data = Generic_Data |
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( |
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type T = |
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{add_mono_thms: thm list, |
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mult_mono_thms: thm list, |
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inj_thms: thm list, |
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lessD: thm list, |
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neqE: thm list, |
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simpset: simpset, |
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number_of: (Proof.context -> typ -> int -> cterm) option}; |
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val empty : T = |
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{add_mono_thms = [], mult_mono_thms = [], inj_thms = [], |
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lessD = [], neqE = [], simpset = empty_ss, |
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number_of = NONE}; |
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val extend = I; |
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fun merge |
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({add_mono_thms = add_mono_thms1, mult_mono_thms = mult_mono_thms1, inj_thms = inj_thms1, |
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lessD = lessD1, neqE = neqE1, simpset = simpset1, number_of = number_of1}, |
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{add_mono_thms = add_mono_thms2, mult_mono_thms = mult_mono_thms2, inj_thms = inj_thms2, |
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lessD = lessD2, neqE = neqE2, simpset = simpset2, number_of = number_of2}) : T = |
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{add_mono_thms = Thm.merge_thms (add_mono_thms1, add_mono_thms2), |
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mult_mono_thms = Thm.merge_thms (mult_mono_thms1, mult_mono_thms2), |
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inj_thms = Thm.merge_thms (inj_thms1, inj_thms2), |
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lessD = Thm.merge_thms (lessD1, lessD2), |
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neqE = Thm.merge_thms (neqE1, neqE2), |
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simpset = merge_ss (simpset1, simpset2), |
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number_of = merge_options (number_of1, number_of2)}; |
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); |
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val map_data = Data.map; |
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val get_data = Data.get o Context.Proof; |
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fun get_neqE ctxt = map (Thm.transfer (Proof_Context.theory_of ctxt)) (#neqE (get_data ctxt)); |
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fun map_inj_thms f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} = |
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{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = f inj_thms, |
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lessD = lessD, neqE = neqE, simpset = simpset, number_of = number_of}; |
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fun map_lessD f {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} = |
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{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, |
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lessD = f lessD, neqE = neqE, simpset = simpset, number_of = number_of}; |
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fun map_simpset f context = |
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map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, number_of} => |
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{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, |
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lessD = lessD, neqE = neqE, simpset = simpset_map (Context.proof_of context) f simpset, |
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number_of = number_of}) context; |
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161 |
|
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fun add_inj_thms thms = map_data (map_inj_thms (append (map Thm.trim_context thms))); |
163 |
fun add_lessD thm = map_data (map_lessD (fn thms => thms @ [Thm.trim_context thm])); |
|
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fun add_simps thms = map_simpset (fn ctxt => ctxt addsimps thms); |
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fun add_simprocs procs = map_simpset (fn ctxt => ctxt addsimprocs procs); |
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166 |
|
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167 |
fun set_number_of f = |
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168 |
map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset, ...} => |
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{add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms, |
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170 |
lessD = lessD, neqE = neqE, simpset = simpset, number_of = SOME f}); |
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171 |
|
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172 |
fun number_of ctxt = |
61097 | 173 |
(case get_data ctxt of |
59996 | 174 |
{number_of = SOME f, ...} => f ctxt |
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175 |
| _ => fn _ => fn _ => raise CTERM ("number_of", [])); |
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176 |
|
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|
178 |
||
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179 |
(*** A fast decision procedure ***) |
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(*** Code ported from HOL Light ***) |
6056 | 181 |
(* possible optimizations: |
182 |
use (var,coeff) rep or vector rep tp save space; |
|
183 |
treat non-negative atoms separately rather than adding 0 <= atom |
|
184 |
*) |
|
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185 |
|
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186 |
datatype lineq_type = Eq | Le | Lt; |
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|
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datatype injust = Asm of int |
189 |
| Nat of int (* index of atom *) |
|
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| LessD of injust |
191 |
| NotLessD of injust |
|
192 |
| NotLeD of injust |
|
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| NotLeDD of injust |
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| Multiplied of int * injust |
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| Added of injust * injust; |
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|
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datatype lineq = Lineq of int * lineq_type * int list * injust; |
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|
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(* ------------------------------------------------------------------------- *) |
200 |
(* Finding a (counter) example from the trace of a failed elimination *) |
|
201 |
(* ------------------------------------------------------------------------- *) |
|
202 |
(* Examples are represented as rational numbers, *) |
|
203 |
(* Dont blame John Harrison for this code - it is entirely mine. TN *) |
|
204 |
||
205 |
exception NoEx; |
|
206 |
||
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207 |
(* Coding: (i,true,cs) means i <= cs and (i,false,cs) means i < cs. |
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208 |
In general, true means the bound is included, false means it is excluded. |
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209 |
Need to know if it is a lower or upper bound for unambiguous interpretation! |
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210 |
*) |
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211 |
|
13498 | 212 |
(* ------------------------------------------------------------------------- *) |
23197 | 213 |
(* End of counterexample finder. The actual decision procedure starts here. *) |
13498 | 214 |
(* ------------------------------------------------------------------------- *) |
215 |
||
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(* ------------------------------------------------------------------------- *) |
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217 |
(* Calculate new (in)equality type after addition. *) |
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(* ------------------------------------------------------------------------- *) |
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219 |
|
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fun find_add_type(Eq,x) = x |
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| find_add_type(x,Eq) = x |
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| find_add_type(_,Lt) = Lt |
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| find_add_type(Lt,_) = Lt |
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| find_add_type(Le,Le) = Le; |
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225 |
|
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226 |
(* ------------------------------------------------------------------------- *) |
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|
227 |
(* Multiply out an (in)equation. *) |
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228 |
(* ------------------------------------------------------------------------- *) |
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229 |
|
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230 |
fun multiply_ineq n (i as Lineq(k,ty,l,just)) = |
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231 |
if n = 1 then i |
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|
232 |
else if n = 0 andalso ty = Lt then raise Fail "multiply_ineq" |
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233 |
else if n < 0 andalso (ty=Le orelse ty=Lt) then raise Fail "multiply_ineq" |
33002 | 234 |
else Lineq (n * k, ty, map (Integer.mult n) l, Multiplied (n, just)); |
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235 |
|
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|
236 |
(* ------------------------------------------------------------------------- *) |
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|
237 |
(* Add together (in)equations. *) |
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|
238 |
(* ------------------------------------------------------------------------- *) |
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|
239 |
|
38052 | 240 |
fun add_ineq (Lineq (k1,ty1,l1,just1)) (Lineq (k2,ty2,l2,just2)) = |
33002 | 241 |
let val l = map2 Integer.add l1 l2 |
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242 |
in Lineq(k1+k2,find_add_type(ty1,ty2),l,Added(just1,just2)) end; |
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|
243 |
|
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|
244 |
(* ------------------------------------------------------------------------- *) |
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|
245 |
(* Elimination of variable between a single pair of (in)equations. *) |
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|
246 |
(* If they're both inequalities, 1st coefficient must be +ve, 2nd -ve. *) |
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|
247 |
(* ------------------------------------------------------------------------- *) |
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|
248 |
|
49387 | 249 |
fun elim_var v (i1 as Lineq(_,ty1,l1,_)) (i2 as Lineq(_,ty2,l2,_)) = |
23063 | 250 |
let val c1 = nth l1 v and c2 = nth l2 v |
23261 | 251 |
val m = Integer.lcm (abs c1) (abs c2) |
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|
252 |
val m1 = m div (abs c1) and m2 = m div (abs c2) |
aeb97860d352
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|
253 |
val (n1,n2) = |
aeb97860d352
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|
254 |
if (c1 >= 0) = (c2 >= 0) |
aeb97860d352
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changeset
|
255 |
then if ty1 = Eq then (~m1,m2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
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changeset
|
256 |
else if ty2 = Eq then (m1,~m2) |
40316
665862241968
replaced ancient sys_error by raise Fail, assuming that the latter is not handled specifically by the environment;
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|
257 |
else raise Fail "elim_var" |
5982
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|
258 |
else (m1,m2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
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|
259 |
val (p1,p2) = if ty1=Eq andalso ty2=Eq andalso (n1 = ~1 orelse n2 = ~1) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
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|
260 |
then (~n1,~n2) else (n1,n2) |
31510
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diff
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|
261 |
in add_ineq (multiply_ineq p1 i1) (multiply_ineq p2 i2) end; |
5982
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|
262 |
|
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|
263 |
(* ------------------------------------------------------------------------- *) |
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|
264 |
(* The main refutation-finding code. *) |
aeb97860d352
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|
265 |
(* ------------------------------------------------------------------------- *) |
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|
266 |
|
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|
267 |
fun is_trivial (Lineq(_,_,l,_)) = forall (fn i => i=0) l; |
aeb97860d352
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|
268 |
|
38052 | 269 |
fun is_contradictory (Lineq(k,ty,_,_)) = |
5982
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|
270 |
case ty of Eq => k <> 0 | Le => k > 0 | Lt => k >= 0; |
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|
271 |
|
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simplified type int (eliminated IntInf.int, integer);
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|
272 |
fun calc_blowup l = |
33317 | 273 |
let val (p,n) = List.partition (curry (op <) 0) (filter (curry (op <>) 0) l) |
24630
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|
274 |
in length p * length n end; |
5982
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|
275 |
|
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|
276 |
(* ------------------------------------------------------------------------- *) |
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|
277 |
(* Main elimination code: *) |
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|
278 |
(* *) |
aeb97860d352
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|
279 |
(* (1) Looks for immediate solutions (false assertions with no variables). *) |
aeb97860d352
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|
280 |
(* *) |
aeb97860d352
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|
281 |
(* (2) If there are any equations, picks a variable with the lowest absolute *) |
aeb97860d352
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|
282 |
(* coefficient in any of them, and uses it to eliminate. *) |
aeb97860d352
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|
283 |
(* *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
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changeset
|
284 |
(* (3) Otherwise, chooses a variable in the inequality to minimize the *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
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|
285 |
(* blowup (number of consequences generated) and eliminates it. *) |
aeb97860d352
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|
286 |
(* ------------------------------------------------------------------------- *) |
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|
287 |
|
aeb97860d352
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|
288 |
fun extract_first p = |
31510
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|
289 |
let |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
290 |
fun extract xs (y::ys) = if p y then (y, xs @ ys) else extract (y::xs) ys |
47060
e2741ec9ae36
prefer explicitly qualified exception List.Empty;
wenzelm
parents:
46709
diff
changeset
|
291 |
| extract xs [] = raise List.Empty |
5982
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|
292 |
in extract [] end; |
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changeset
|
293 |
|
44654 | 294 |
fun print_ineqs ctxt ineqs = |
295 |
if Config.get ctxt LA_Data.trace then |
|
12262 | 296 |
tracing(cat_lines(""::map (fn Lineq(c,t,l,_) => |
24630
351a308ab58d
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wenzelm
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|
297 |
string_of_int c ^ |
9073 | 298 |
(case t of Eq => " = " | Lt=> " < " | Le => " <= ") ^ |
24630
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wenzelm
parents:
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changeset
|
299 |
commas(map string_of_int l)) ineqs)) |
9073 | 300 |
else (); |
6056 | 301 |
|
13498 | 302 |
type history = (int * lineq list) list; |
303 |
datatype result = Success of injust | Failure of history; |
|
304 |
||
44654 | 305 |
fun elim ctxt (ineqs, hist) = |
306 |
let val _ = print_ineqs ctxt ineqs |
|
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
307 |
val (triv, nontriv) = List.partition is_trivial ineqs in |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
308 |
if not (null triv) |
59584 | 309 |
then case find_first is_contradictory triv of |
44654 | 310 |
NONE => elim ctxt (nontriv, hist) |
15531 | 311 |
| SOME(Lineq(_,_,_,j)) => Success j |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
312 |
else |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
313 |
if null nontriv then Failure hist |
13498 | 314 |
else |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
315 |
let val (eqs, noneqs) = List.partition (fn (Lineq(_,ty,_,_)) => ty=Eq) nontriv in |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
316 |
if not (null eqs) then |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
317 |
let val c = |
33042 | 318 |
fold (fn Lineq(_,_,l,_) => fn cs => union (op =) l cs) eqs [] |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
319 |
|> filter (fn i => i <> 0) |
59058
a78612c67ec0
renamed "pairself" to "apply2", in accordance to @{apply 2};
wenzelm
parents:
58839
diff
changeset
|
320 |
|> sort (int_ord o apply2 abs) |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
321 |
|> hd |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
322 |
val (eq as Lineq(_,_,ceq,_),othereqs) = |
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:
35872
diff
changeset
|
323 |
extract_first (fn Lineq(_,_,l,_) => member (op =) l c) eqs |
31986 | 324 |
val v = find_index (fn v => v = c) ceq |
23063 | 325 |
val (ioth,roth) = List.partition (fn (Lineq(_,_,l,_)) => nth l v = 0) |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
326 |
(othereqs @ noneqs) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
327 |
val others = map (elim_var v eq) roth @ ioth |
44654 | 328 |
in elim ctxt (others,(v,nontriv)::hist) end |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
329 |
else |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
330 |
let val lists = map (fn (Lineq(_,_,l,_)) => l) noneqs |
23063 | 331 |
val numlist = 0 upto (length (hd lists) - 1) |
332 |
val coeffs = map (fn i => map (fn xs => nth xs i) lists) numlist |
|
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
333 |
val blows = map calc_blowup coeffs |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
334 |
val iblows = blows ~~ numlist |
23063 | 335 |
val nziblows = filter_out (fn (i, _) => i = 0) iblows |
13498 | 336 |
in if null nziblows then Failure((~1,nontriv)::hist) |
337 |
else |
|
60348 | 338 |
let val (_,v) = hd(sort (fn (x,y) => int_ord(fst(x),fst(y))) nziblows) |
23063 | 339 |
val (no,yes) = List.partition (fn (Lineq(_,_,l,_)) => nth l v = 0) ineqs |
340 |
val (pos,neg) = List.partition(fn (Lineq(_,_,l,_)) => nth l v > 0) yes |
|
44654 | 341 |
in elim ctxt (no @ map_product (elim_var v) pos neg, (v,nontriv)::hist) end |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
342 |
end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
343 |
end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
344 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
345 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
346 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
347 |
(* Translate back a proof. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
348 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
349 |
|
44654 | 350 |
fun trace_thm ctxt msgs th = |
351 |
(if Config.get ctxt LA_Data.trace |
|
61268 | 352 |
then tracing (cat_lines (msgs @ [Thm.string_of_thm ctxt th])) |
44654 | 353 |
else (); th); |
9073 | 354 |
|
44654 | 355 |
fun trace_term ctxt msgs t = |
356 |
(if Config.get ctxt LA_Data.trace |
|
357 |
then tracing (cat_lines (msgs @ [Syntax.string_of_term ctxt t])) |
|
358 |
else (); t); |
|
24076 | 359 |
|
44654 | 360 |
fun trace_msg ctxt msg = |
361 |
if Config.get ctxt LA_Data.trace then tracing msg else (); |
|
9073 | 362 |
|
52131 | 363 |
val union_term = union Envir.aeconv; |
26835
404550067389
Lookup and union operations on terms are now modulo eta conversion.
berghofe
parents:
24920
diff
changeset
|
364 |
|
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
365 |
fun add_atoms (lhs, _, _, rhs, _, _) = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
366 |
union_term (map fst lhs) o union_term (map fst rhs); |
6056 | 367 |
|
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
368 |
fun atoms_of ds = fold add_atoms ds []; |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
369 |
|
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
370 |
(* |
6056 | 371 |
Simplification may detect a contradiction 'prematurely' due to type |
372 |
information: n+1 <= 0 is simplified to False and does not need to be crossed |
|
373 |
with 0 <= n. |
|
374 |
*) |
|
375 |
local |
|
24076 | 376 |
exception FalseE of thm |
6056 | 377 |
in |
27020
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
378 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
379 |
fun mkthm ctxt asms (just: injust) = |
24076 | 380 |
let |
42361 | 381 |
val thy = Proof_Context.theory_of ctxt; |
61097 | 382 |
val {add_mono_thms = add_mono_thms0, mult_mono_thms = mult_mono_thms0, |
383 |
inj_thms = inj_thms0, lessD = lessD0, simpset, ...} = get_data ctxt; |
|
384 |
val add_mono_thms = map (Thm.transfer thy) add_mono_thms0; |
|
385 |
val mult_mono_thms = map (Thm.transfer thy) mult_mono_thms0; |
|
386 |
val inj_thms = map (Thm.transfer thy) inj_thms0; |
|
387 |
val lessD = map (Thm.transfer thy) lessD0; |
|
388 |
||
38763
283f1f9969ba
Fast_Lin_Arith.number_of: more conventional merge that prefers the left side -- note that former ordering wrt. serial numbers makes it depend on accidental load order;
wenzelm
parents:
38762
diff
changeset
|
389 |
val number_of = number_of ctxt; |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
390 |
val simpset_ctxt = put_simpset simpset ctxt; |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
391 |
fun only_concl f thm = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
392 |
if Thm.no_prems thm then f (Thm.concl_of thm) else NONE; |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
393 |
val atoms = atoms_of (map_filter (only_concl (LA_Data.decomp ctxt)) asms); |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
394 |
|
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
395 |
fun use_first rules thm = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
396 |
get_first (fn th => SOME (thm RS th) handle THM _ => NONE) rules |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
397 |
|
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
398 |
fun add2 thm1 thm2 = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
399 |
use_first add_mono_thms (thm1 RS (thm2 RS LA_Logic.conjI)); |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
400 |
fun try_add thms thm = get_first (fn th => add2 th thm) thms; |
6056 | 401 |
|
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
402 |
fun add_thms thm1 thm2 = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
403 |
(case add2 thm1 thm2 of |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
404 |
NONE => |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
405 |
(case try_add ([thm1] RL inj_thms) thm2 of |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
406 |
NONE => |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
407 |
(the (try_add ([thm2] RL inj_thms) thm1) |
51930
52fd62618631
prefer explicitly qualified exceptions, which is particular important for robust handlers;
wenzelm
parents:
51717
diff
changeset
|
408 |
handle Option.Option => |
44654 | 409 |
(trace_thm ctxt [] thm1; trace_thm ctxt [] thm2; |
40316
665862241968
replaced ancient sys_error by raise Fail, assuming that the latter is not handled specifically by the environment;
wenzelm
parents:
38763
diff
changeset
|
410 |
raise Fail "Linear arithmetic: failed to add thms")) |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
411 |
| SOME thm => thm) |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
412 |
| SOME thm => thm); |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
413 |
|
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
414 |
fun mult_by_add n thm = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
415 |
let fun mul i th = if i = 1 then th else mul (i - 1) (add_thms thm th) |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
416 |
in mul n thm end; |
10575 | 417 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
418 |
val rewr = Simplifier.rewrite simpset_ctxt; |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
419 |
val rewrite_concl = Conv.fconv_rule (Conv.concl_conv ~1 (Conv.arg_conv |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
420 |
(Conv.binop_conv rewr))); |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
421 |
fun discharge_prem thm = if Thm.nprems_of thm = 0 then thm else |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
422 |
let val cv = Conv.arg1_conv (Conv.arg_conv rewr) |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
423 |
in Thm.implies_elim (Conv.fconv_rule cv thm) LA_Logic.trueI end |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
424 |
|
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
425 |
fun mult n thm = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
426 |
(case use_first mult_mono_thms thm of |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
427 |
NONE => mult_by_add n thm |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
428 |
| SOME mth => |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
429 |
let |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
430 |
val cv = mth |> Thm.cprop_of |> Drule.strip_imp_concl |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
431 |
|> Thm.dest_arg |> Thm.dest_arg1 |> Thm.dest_arg1 |
59586 | 432 |
val T = Thm.typ_of_cterm cv |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
433 |
in |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
434 |
mth |
60642
48dd1cefb4ae
simplified Thm.instantiate and derivatives: the LHS refers to non-certified variables -- this merely serves as index into already certified structures (or is ignored);
wenzelm
parents:
60348
diff
changeset
|
435 |
|> Thm.instantiate ([], [(dest_Var (Thm.term_of cv), number_of T n)]) |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
436 |
|> rewrite_concl |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
437 |
|> discharge_prem |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
438 |
handle CTERM _ => mult_by_add n thm |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
439 |
| THM _ => mult_by_add n thm |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
440 |
end); |
10691 | 441 |
|
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
442 |
fun mult_thm (n, thm) = |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
443 |
if n = ~1 then thm RS LA_Logic.sym |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
444 |
else if n < 0 then mult (~n) thm RS LA_Logic.sym |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
445 |
else mult n thm; |
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
446 |
|
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
447 |
fun simp thm = |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
448 |
let val thm' = trace_thm ctxt ["Simplified:"] (full_simplify simpset_ctxt thm) |
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
449 |
in if LA_Logic.is_False thm' then raise FalseE thm' else thm' end; |
6056 | 450 |
|
44654 | 451 |
fun mk (Asm i) = trace_thm ctxt ["Asm " ^ string_of_int i] (nth asms i) |
452 |
| mk (Nat i) = trace_thm ctxt ["Nat " ^ string_of_int i] (LA_Logic.mk_nat_thm thy (nth atoms i)) |
|
453 |
| mk (LessD j) = trace_thm ctxt ["L"] (hd ([mk j] RL lessD)) |
|
454 |
| mk (NotLeD j) = trace_thm ctxt ["NLe"] (mk j RS LA_Logic.not_leD) |
|
455 |
| mk (NotLeDD j) = trace_thm ctxt ["NLeD"] (hd ([mk j RS LA_Logic.not_leD] RL lessD)) |
|
456 |
| mk (NotLessD j) = trace_thm ctxt ["NL"] (mk j RS LA_Logic.not_lessD) |
|
457 |
| mk (Added (j1, j2)) = simp (trace_thm ctxt ["+"] (add_thms (mk j1) (mk j2))) |
|
32091
30e2ffbba718
proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents:
31986
diff
changeset
|
458 |
| mk (Multiplied (n, j)) = |
44654 | 459 |
(trace_msg ctxt ("*" ^ string_of_int n); trace_thm ctxt ["*"] (mult_thm (n, mk j))) |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
460 |
|
27020
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
461 |
in |
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
462 |
let |
44654 | 463 |
val _ = trace_msg ctxt "mkthm"; |
464 |
val thm = trace_thm ctxt ["Final thm:"] (mk just); |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
465 |
val fls = simplify simpset_ctxt thm; |
44654 | 466 |
val _ = trace_thm ctxt ["After simplification:"] fls; |
27020
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
467 |
val _ = |
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
468 |
if LA_Logic.is_False fls then () |
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
469 |
else |
35872
9b579860d59b
removed warning_count (known causes for warnings have been resolved)
boehmes
parents:
35861
diff
changeset
|
470 |
(tracing (cat_lines |
61268 | 471 |
(["Assumptions:"] @ map (Thm.string_of_thm ctxt) asms @ [""] @ |
472 |
["Proved:", Thm.string_of_thm ctxt fls, ""])); |
|
35872
9b579860d59b
removed warning_count (known causes for warnings have been resolved)
boehmes
parents:
35861
diff
changeset
|
473 |
warning "Linear arithmetic should have refuted the assumptions.\n\ |
9b579860d59b
removed warning_count (known causes for warnings have been resolved)
boehmes
parents:
35861
diff
changeset
|
474 |
\Please inform Tobias Nipkow.") |
27020
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
475 |
in fls end |
44654 | 476 |
handle FalseE thm => trace_thm ctxt ["False reached early:"] thm |
27020
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
477 |
end; |
b5b8afc9fdcd
added warning_count for issued reconstruction failure messages (limit 10);
wenzelm
parents:
26945
diff
changeset
|
478 |
|
6056 | 479 |
end; |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
480 |
|
23261 | 481 |
fun coeff poly atom = |
52131 | 482 |
AList.lookup Envir.aeconv poly atom |> the_default 0; |
10691 | 483 |
|
484 |
fun integ(rlhs,r,rel,rrhs,s,d) = |
|
17951 | 485 |
let val (rn,rd) = Rat.quotient_of_rat r and (sn,sd) = Rat.quotient_of_rat s |
24630
351a308ab58d
simplified type int (eliminated IntInf.int, integer);
wenzelm
parents:
24112
diff
changeset
|
486 |
val m = Integer.lcms(map (abs o snd o Rat.quotient_of_rat) (r :: s :: map snd rlhs @ map snd rrhs)) |
22846 | 487 |
fun mult(t,r) = |
17951 | 488 |
let val (i,j) = Rat.quotient_of_rat r |
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15922
diff
changeset
|
489 |
in (t,i * (m div j)) end |
12932 | 490 |
in (m,(map mult rlhs, rn*(m div rd), rel, map mult rrhs, sn*(m div sd), d)) end |
10691 | 491 |
|
38052 | 492 |
fun mklineq atoms = |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
493 |
fn (item, k) => |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
494 |
let val (m, (lhs,i,rel,rhs,j,discrete)) = integ item |
13498 | 495 |
val lhsa = map (coeff lhs) atoms |
496 |
and rhsa = map (coeff rhs) atoms |
|
18330 | 497 |
val diff = map2 (curry (op -)) rhsa lhsa |
13498 | 498 |
val c = i-j |
499 |
val just = Asm k |
|
31511 | 500 |
fun lineq(c,le,cs,j) = Lineq(c,le,cs, if m=1 then j else Multiplied(m,j)) |
13498 | 501 |
in case rel of |
502 |
"<=" => lineq(c,Le,diff,just) |
|
503 |
| "~<=" => if discrete |
|
504 |
then lineq(1-c,Le,map (op ~) diff,NotLeDD(just)) |
|
505 |
else lineq(~c,Lt,map (op ~) diff,NotLeD(just)) |
|
506 |
| "<" => if discrete |
|
507 |
then lineq(c+1,Le,diff,LessD(just)) |
|
508 |
else lineq(c,Lt,diff,just) |
|
509 |
| "~<" => lineq(~c,Le,map (op~) diff,NotLessD(just)) |
|
510 |
| "=" => lineq(c,Eq,diff,just) |
|
40316
665862241968
replaced ancient sys_error by raise Fail, assuming that the latter is not handled specifically by the environment;
wenzelm
parents:
38763
diff
changeset
|
511 |
| _ => raise Fail ("mklineq" ^ rel) |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
512 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
513 |
|
13498 | 514 |
(* ------------------------------------------------------------------------- *) |
515 |
(* Print (counter) example *) |
|
516 |
(* ------------------------------------------------------------------------- *) |
|
517 |
||
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
518 |
(* ------------------------------------------------------------------------- *) |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
519 |
|
20268 | 520 |
fun mknat (pTs : typ list) (ixs : int list) (atom : term, i : int) : lineq option = |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
521 |
if LA_Logic.is_nat (pTs, atom) |
6056 | 522 |
then let val l = map (fn j => if j=i then 1 else 0) ixs |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
523 |
in SOME (Lineq (0, Le, l, Nat i)) end |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
524 |
else NONE; |
6056 | 525 |
|
13186
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
526 |
(* This code is tricky. It takes a list of premises in the order they occur |
15531 | 527 |
in the subgoal. Numerical premises are coded as SOME(tuple), non-numerical |
528 |
ones as NONE. Going through the premises, each numeric one is converted into |
|
13186
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
529 |
a Lineq. The tricky bit is to convert ~= which is split into two cases < and |
13498 | 530 |
>. Thus split_items returns a list of equation systems. This may blow up if |
13186
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
531 |
there are many ~=, but in practice it does not seem to happen. The really |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
532 |
tricky bit is to arrange the order of the cases such that they coincide with |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
533 |
the order in which the cases are in the end generated by the tactic that |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
534 |
applies the generated refutation thms (see function 'refute_tac'). |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
535 |
|
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
536 |
For variables n of type nat, a constraint 0 <= n is added. |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
537 |
*) |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
538 |
|
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
539 |
(* FIXME: To optimize, the splitting of cases and the search for refutations *) |
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
540 |
(* could be intertwined: separate the first (fully split) case, *) |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
541 |
(* refute it, continue with splitting and refuting. Terminate with *) |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
542 |
(* failure as soon as a case could not be refuted; i.e. delay further *) |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
543 |
(* splitting until after a refutation for other cases has been found. *) |
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
544 |
|
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
545 |
fun split_items ctxt do_pre split_neq (Ts, terms) : (typ list * (LA_Data.decomp * int) list) list = |
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
546 |
let |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
547 |
(* splits inequalities '~=' into '<' and '>'; this corresponds to *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
548 |
(* 'REPEAT_DETERM (eresolve_tac neqE i)' at the theorem/tactic *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
549 |
(* level *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
550 |
(* FIXME: this is currently sensitive to the order of theorems in *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
551 |
(* neqE: The theorem for type "nat" must come first. A *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
552 |
(* better (i.e. less likely to break when neqE changes) *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
553 |
(* implementation should *test* which theorem from neqE *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
554 |
(* can be applied, and split the premise accordingly. *) |
26945 | 555 |
fun elim_neq (ineqs : (LA_Data.decomp option * bool) list) : |
556 |
(LA_Data.decomp option * bool) list list = |
|
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
557 |
let |
26945 | 558 |
fun elim_neq' nat_only ([] : (LA_Data.decomp option * bool) list) : |
559 |
(LA_Data.decomp option * bool) list list = |
|
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
560 |
[[]] |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
561 |
| elim_neq' nat_only ((NONE, is_nat) :: ineqs) = |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
562 |
map (cons (NONE, is_nat)) (elim_neq' nat_only ineqs) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
563 |
| elim_neq' nat_only ((ineq as (SOME (l, i, rel, r, j, d), is_nat)) :: ineqs) = |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
564 |
if rel = "~=" andalso (not nat_only orelse is_nat) then |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
565 |
(* [| ?l ~= ?r; ?l < ?r ==> ?R; ?r < ?l ==> ?R |] ==> ?R *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
566 |
elim_neq' nat_only (ineqs @ [(SOME (l, i, "<", r, j, d), is_nat)]) @ |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
567 |
elim_neq' nat_only (ineqs @ [(SOME (r, j, "<", l, i, d), is_nat)]) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
568 |
else |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
569 |
map (cons ineq) (elim_neq' nat_only ineqs) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
570 |
in |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
571 |
ineqs |> elim_neq' true |
26945 | 572 |
|> maps (elim_neq' false) |
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
573 |
end |
13464 | 574 |
|
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
575 |
fun ignore_neq (NONE, bool) = (NONE, bool) |
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
576 |
| ignore_neq (ineq as SOME (_, _, rel, _, _, _), bool) = |
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
577 |
if rel = "~=" then (NONE, bool) else (ineq, bool) |
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
578 |
|
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
579 |
fun number_hyps _ [] = [] |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
580 |
| number_hyps n (NONE::xs) = number_hyps (n+1) xs |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
581 |
| number_hyps n ((SOME x)::xs) = (x, n) :: number_hyps (n+1) xs |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
582 |
|
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
583 |
val result = (Ts, terms) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
584 |
|> (* user-defined preprocessing of the subgoal *) |
24076 | 585 |
(if do_pre then LA_Data.pre_decomp ctxt else Library.single) |
44654 | 586 |
|> tap (fn subgoals => trace_msg ctxt ("Preprocessing yields " ^ |
23195 | 587 |
string_of_int (length subgoals) ^ " subgoal(s) total.")) |
22846 | 588 |
|> (* produce the internal encoding of (in-)equalities *) |
24076 | 589 |
map (apsnd (map (fn t => (LA_Data.decomp ctxt t, LA_Data.domain_is_nat t)))) |
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
590 |
|> (* splitting of inequalities *) |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
591 |
map (apsnd (if split_neq then elim_neq else |
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
592 |
Library.single o map ignore_neq)) |
22846 | 593 |
|> maps (fn (Ts, subgoals) => map (pair Ts o map fst) subgoals) |
20276
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
594 |
|> (* numbering of hypotheses, ignoring irrelevant ones *) |
d94dc40673b1
possible disagreement between proof search and proof reconstruction when eliminating inequalities over different types fixed
webertj
parents:
20268
diff
changeset
|
595 |
map (apsnd (number_hyps 0)) |
23195 | 596 |
in |
44654 | 597 |
trace_msg ctxt ("Splitting of inequalities yields " ^ |
23195 | 598 |
string_of_int (length result) ^ " subgoal(s) total."); |
599 |
result |
|
600 |
end; |
|
13464 | 601 |
|
59656 | 602 |
fun refutes ctxt : |
26945 | 603 |
(typ list * (LA_Data.decomp * int) list) list -> injust list -> injust list option = |
604 |
let |
|
605 |
fun refute ((Ts, initems : (LA_Data.decomp * int) list) :: initemss) (js: injust list) = |
|
606 |
let |
|
31510
e0f2bb4b0021
fast_lin_arith uses proper multiplication instead of unfolding to additions
boehmes
parents:
31102
diff
changeset
|
607 |
val atoms = atoms_of (map fst initems) |
26945 | 608 |
val n = length atoms |
38052 | 609 |
val mkleq = mklineq atoms |
26945 | 610 |
val ixs = 0 upto (n - 1) |
611 |
val iatoms = atoms ~~ ixs |
|
32952 | 612 |
val natlineqs = map_filter (mknat Ts ixs) iatoms |
26945 | 613 |
val ineqs = map mkleq initems @ natlineqs |
59656 | 614 |
in |
615 |
(case elim ctxt (ineqs, []) of |
|
26945 | 616 |
Success j => |
44654 | 617 |
(trace_msg ctxt ("Contradiction! (" ^ string_of_int (length js + 1) ^ ")"); |
26945 | 618 |
refute initemss (js @ [j])) |
59656 | 619 |
| Failure _ => NONE) |
26945 | 620 |
end |
621 |
| refute [] js = SOME js |
|
622 |
in refute end; |
|
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
623 |
|
59656 | 624 |
fun refute ctxt params do_pre split_neq terms : injust list option = |
625 |
refutes ctxt (split_items ctxt do_pre split_neq (map snd params, terms)) []; |
|
20254
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
626 |
|
22950 | 627 |
fun count P xs = length (filter P xs); |
20254
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
628 |
|
59656 | 629 |
fun prove ctxt params do_pre Hs concl : bool * injust list option = |
20254
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
630 |
let |
44654 | 631 |
val _ = trace_msg ctxt "prove:" |
20254
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
632 |
(* append the negated conclusion to 'Hs' -- this corresponds to *) |
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
633 |
(* 'DETERM (resolve_tac [LA_Logic.notI, LA_Logic.ccontr] i)' at the *) |
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
634 |
(* theorem/tactic level *) |
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
635 |
val Hs' = Hs @ [LA_Logic.neg_prop concl] |
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
636 |
fun is_neq NONE = false |
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
637 |
| is_neq (SOME (_,_,r,_,_,_)) = (r = "~=") |
44654 | 638 |
val neq_limit = Config.get ctxt LA_Data.neq_limit |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
639 |
val split_neq = count is_neq (map (LA_Data.decomp ctxt) Hs') <= neq_limit |
20254
58b71535ed00
lin_arith_prover splits certain operators (e.g. min, max, abs)
webertj
parents:
20217
diff
changeset
|
640 |
in |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
641 |
if split_neq then () |
24076 | 642 |
else |
44654 | 643 |
trace_msg ctxt ("neq_limit exceeded (current value is " ^ |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
644 |
string_of_int neq_limit ^ "), ignoring all inequalities"); |
59656 | 645 |
(split_neq, refute ctxt params do_pre split_neq Hs') |
23190 | 646 |
end handle TERM ("neg_prop", _) => |
647 |
(* since no meta-logic negation is available, we can only fail if *) |
|
648 |
(* the conclusion is not of the form 'Trueprop $ _' (simply *) |
|
649 |
(* dropping the conclusion doesn't work either, because even *) |
|
650 |
(* 'False' does not imply arbitrary 'concl::prop') *) |
|
44654 | 651 |
(trace_msg ctxt "prove failed (cannot negate conclusion)."; |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
652 |
(false, NONE)); |
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
653 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
654 |
fun refute_tac ctxt (i, split_neq, justs) = |
6074 | 655 |
fn state => |
24076 | 656 |
let |
32091
30e2ffbba718
proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents:
31986
diff
changeset
|
657 |
val _ = trace_thm ctxt |
44654 | 658 |
["refute_tac (on subgoal " ^ string_of_int i ^ ", with " ^ |
659 |
string_of_int (length justs) ^ " justification(s)):"] state |
|
61097 | 660 |
val neqE = get_neqE ctxt; |
24076 | 661 |
fun just1 j = |
662 |
(* eliminate inequalities *) |
|
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
663 |
(if split_neq then |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59058
diff
changeset
|
664 |
REPEAT_DETERM (eresolve_tac ctxt neqE i) |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
665 |
else |
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
666 |
all_tac) THEN |
44654 | 667 |
PRIMITIVE (trace_thm ctxt ["State after neqE:"]) THEN |
24076 | 668 |
(* use theorems generated from the actual justifications *) |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59058
diff
changeset
|
669 |
Subgoal.FOCUS (fn {prems, ...} => resolve_tac ctxt [mkthm ctxt prems j] 1) ctxt i |
24076 | 670 |
in |
671 |
(* rewrite "[| A1; ...; An |] ==> B" to "[| A1; ...; An; ~B |] ==> False" *) |
|
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
59058
diff
changeset
|
672 |
DETERM (resolve_tac ctxt [LA_Logic.notI, LA_Logic.ccontr] i) THEN |
24076 | 673 |
(* user-defined preprocessing of the subgoal *) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
674 |
DETERM (LA_Data.pre_tac ctxt i) THEN |
44654 | 675 |
PRIMITIVE (trace_thm ctxt ["State after pre_tac:"]) THEN |
24076 | 676 |
(* prove every resulting subgoal, using its justification *) |
677 |
EVERY (map just1 justs) |
|
20217
25b068a99d2b
linear arithmetic splits certain operators (e.g. min, max, abs)
webertj
parents:
19618
diff
changeset
|
678 |
end state; |
6074 | 679 |
|
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
680 |
(* |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
681 |
Fast but very incomplete decider. Only premises and conclusions |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
682 |
that are already (negated) (in)equations are taken into account. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
683 |
*) |
59656 | 684 |
fun simpset_lin_arith_tac ctxt = SUBGOAL (fn (A, i) => |
24076 | 685 |
let |
686 |
val params = rev (Logic.strip_params A) |
|
687 |
val Hs = Logic.strip_assums_hyp A |
|
688 |
val concl = Logic.strip_assums_concl A |
|
44654 | 689 |
val _ = trace_term ctxt ["Trying to refute subgoal " ^ string_of_int i] A |
24076 | 690 |
in |
59656 | 691 |
case prove ctxt params true Hs concl of |
44654 | 692 |
(_, NONE) => (trace_msg ctxt "Refutation failed."; no_tac) |
693 |
| (split_neq, SOME js) => (trace_msg ctxt "Refutation succeeded."; |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
694 |
refute_tac ctxt (i, split_neq, js)) |
24076 | 695 |
end); |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
696 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
697 |
fun prems_lin_arith_tac ctxt = |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
698 |
Method.insert_tac (Simplifier.prems_of ctxt) THEN' |
59656 | 699 |
simpset_lin_arith_tac ctxt; |
17613 | 700 |
|
24076 | 701 |
fun lin_arith_tac ctxt = |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
702 |
simpset_lin_arith_tac (empty_simpset ctxt); |
24076 | 703 |
|
704 |
||
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
705 |
|
13186
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
706 |
(** Forward proof from theorems **) |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
707 |
|
20433
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
708 |
(* More tricky code. Needs to arrange the proofs of the multiple cases (due |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
709 |
to splits of ~= premises) such that it coincides with the order of the cases |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
710 |
generated by function split_items. *) |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
711 |
|
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
712 |
datatype splittree = Tip of thm list |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
713 |
| Spl of thm * cterm * splittree * cterm * splittree; |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
714 |
|
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
715 |
(* "(ct1 ==> ?R) ==> (ct2 ==> ?R) ==> ?R" is taken to (ct1, ct2) *) |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
716 |
|
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
717 |
fun extract (imp : cterm) : cterm * cterm = |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
718 |
let val (Il, r) = Thm.dest_comb imp |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
719 |
val (_, imp1) = Thm.dest_comb Il |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
720 |
val (Ict1, _) = Thm.dest_comb imp1 |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
721 |
val (_, ct1) = Thm.dest_comb Ict1 |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
722 |
val (Ir, _) = Thm.dest_comb r |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
723 |
val (_, Ict2r) = Thm.dest_comb Ir |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
724 |
val (Ict2, _) = Thm.dest_comb Ict2r |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
725 |
val (_, ct2) = Thm.dest_comb Ict2 |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
726 |
in (ct1, ct2) end; |
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
727 |
|
24076 | 728 |
fun splitasms ctxt (asms : thm list) : splittree = |
61097 | 729 |
let val neqE = get_neqE ctxt |
35693
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
730 |
fun elim_neq [] (asms', []) = Tip (rev asms') |
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
731 |
| elim_neq [] (asms', asms) = Tip (rev asms' @ asms) |
49387 | 732 |
| elim_neq (_ :: neqs) (asms', []) = elim_neq neqs ([],rev asms') |
35693
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
733 |
| elim_neq (neqs as (neq :: _)) (asms', asm::asms) = |
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
734 |
(case get_first (fn th => SOME (asm COMP th) handle THM _ => NONE) [neq] of |
20433
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
735 |
SOME spl => |
59582 | 736 |
let val (ct1, ct2) = extract (Thm.cprop_of spl) |
36945 | 737 |
val thm1 = Thm.assume ct1 |
738 |
val thm2 = Thm.assume ct2 |
|
35693
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
739 |
in Spl (spl, ct1, elim_neq neqs (asms', asms@[thm1]), |
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
740 |
ct2, elim_neq neqs (asms', asms@[thm2])) |
20433
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
741 |
end |
35693
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
742 |
| NONE => elim_neq neqs (asm::asms', asms)) |
d58a4ac1ca1c
Use same order of neq-elimination as in proof search.
hoelzl
parents:
35230
diff
changeset
|
743 |
in elim_neq neqE ([], asms) end; |
20433
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
744 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
745 |
fun fwdproof ctxt (Tip asms : splittree) (j::js : injust list) = (mkthm ctxt asms j, js) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
746 |
| fwdproof ctxt (Spl (thm, ct1, tree1, ct2, tree2)) js = |
24076 | 747 |
let |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
748 |
val (thm1, js1) = fwdproof ctxt tree1 js |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
749 |
val (thm2, js2) = fwdproof ctxt tree2 js1 |
36945 | 750 |
val thm1' = Thm.implies_intr ct1 thm1 |
751 |
val thm2' = Thm.implies_intr ct2 thm2 |
|
24076 | 752 |
in (thm2' COMP (thm1' COMP thm), js2) end; |
753 |
(* FIXME needs handle THM _ => NONE ? *) |
|
20433
55471f940e5c
lin_arith_prover: splitting reverted because of performance loss
webertj
parents:
20280
diff
changeset
|
754 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
755 |
fun prover ctxt thms Tconcl (js : injust list) split_neq pos : thm option = |
24076 | 756 |
let |
757 |
val nTconcl = LA_Logic.neg_prop Tconcl |
|
59642 | 758 |
val cnTconcl = Thm.cterm_of ctxt nTconcl |
36945 | 759 |
val nTconclthm = Thm.assume cnTconcl |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
760 |
val tree = (if split_neq then splitasms ctxt else Tip) (thms @ [nTconclthm]) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
761 |
val (Falsethm, _) = fwdproof ctxt tree js |
24076 | 762 |
val contr = if pos then LA_Logic.ccontr else LA_Logic.notI |
36945 | 763 |
val concl = Thm.implies_intr cnTconcl Falsethm COMP contr |
44654 | 764 |
in SOME (trace_thm ctxt ["Proved by lin. arith. prover:"] (LA_Logic.mk_Eq concl)) end |
24076 | 765 |
(*in case concl contains ?-var, which makes assume fail:*) (* FIXME Variable.import_terms *) |
766 |
handle THM _ => NONE; |
|
13186
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
767 |
|
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
768 |
(* PRE: concl is not negated! |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
769 |
This assumption is OK because |
24076 | 770 |
1. lin_arith_simproc tries both to prove and disprove concl and |
771 |
2. lin_arith_simproc is applied by the Simplifier which |
|
13186
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
772 |
dives into terms and will thus try the non-negated concl anyway. |
ef8ed6adcb38
Big update. Allows case splitting on ~= now (trying both < and >).
nipkow
parents:
13105
diff
changeset
|
773 |
*) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
774 |
fun lin_arith_simproc ctxt concl = |
24076 | 775 |
let |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
776 |
val thms = maps LA_Logic.atomize (Simplifier.prems_of ctxt) |
24076 | 777 |
val Hs = map Thm.prop_of thms |
61144 | 778 |
val Tconcl = LA_Logic.mk_Trueprop (Thm.term_of concl) |
24076 | 779 |
in |
59656 | 780 |
case prove ctxt [] false Hs Tconcl of (* concl provable? *) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
781 |
(split_neq, SOME js) => prover ctxt thms Tconcl js split_neq true |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
782 |
| (_, NONE) => |
24076 | 783 |
let val nTconcl = LA_Logic.neg_prop Tconcl in |
59656 | 784 |
case prove ctxt [] false Hs nTconcl of (* ~concl provable? *) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49387
diff
changeset
|
785 |
(split_neq, SOME js) => prover ctxt thms nTconcl js split_neq false |
30406
15dc25f8a0e2
Instead of giving up entirely, arith now ignores all inequalities when there are too many.
webertj
parents:
27020
diff
changeset
|
786 |
| (_, NONE) => NONE |
24076 | 787 |
end |
788 |
end; |
|
6074 | 789 |
|
790 |
end; |