| 1 | % (c) 2014-2022 Lehrstuhl fuer Softwaretechnik und Programmiersprachen, | |
| 2 | % Heinrich Heine Universitaet Duesseldorf | |
| 3 | % This software is licenced under EPL 1.0 (http://www.eclipse.org/org/documents/epl-v10.html) | |
| 4 | ||
| 5 | :- module(smtlib2_translation,[smt_type_to_prob_type/3, | |
| 6 | smt_term_to_prob_term/3, | |
| 7 | smt_type_to_prob_type_maplist/3, | |
| 8 | smt_term_to_prob_term_maplist/3, | |
| 9 | bool_to_pred/2, | |
| 10 | typing_constraint/2, | |
| 11 | is_function_constraint/3]). | |
| 12 | ||
| 13 | :- use_module(probsrc(module_information),[module_info/2]). | |
| 14 | :- module_info(group,smtlib). | |
| 15 | :- module_info(description,'The SMT-LIB 2 Interpreter - Translation from SMT-LIB 2 to B'). | |
| 16 | ||
| 17 | :- use_module(library(lists)). | |
| 18 | ||
| 19 | :- use_module(probsrc(bsyntaxtree),[get_texpr_type/2, | |
| 20 | get_texpr_expr/2, | |
| 21 | safe_create_texpr/3, | |
| 22 | create_forall/3, | |
| 23 | create_exists/3, | |
| 24 | create_couple/2, | |
| 25 | create_implication/3, | |
| 26 | conjunct_predicates/2, | |
| 27 | replace_id_by_expr/4]). | |
| 28 | ||
| 29 | :- use_module(smtlib_solver(smtlib2_environment)). | |
| 30 | ||
| 31 | chain(Op,[A,B],BPred) :- !, | |
| 32 | Pred =.. [Op,A,B], | |
| 33 | BPred = b(Pred,pred,[]). | |
| 34 | chain(Op,[First,Second|Further],TermOut) :- | |
| 35 | chain(Op,[First,Second],Pred), | |
| 36 | chain(Op,[Second|Further],FurtherPred), | |
| 37 | conjunct_predicates([Pred,FurtherPred],TermOut). | |
| 38 | ||
| 39 | interleave(_Op,[A],TermOut) :- !, TermOut=A. | |
| 40 | interleave(Op,[First|Further],TermOut) :- | |
| 41 | interleave(Op,Further,FurtherPred), | |
| 42 | get_texpr_type(FurtherPred,FurtherType), | |
| 43 | Pred =.. [Op,First,FurtherPred], | |
| 44 | safe_create_texpr(Pred,FurtherType,TermOut). | |
| 45 | ||
| 46 | :- use_module(probsrc(preferences), [get_preference/2]). | |
| 47 | :- use_module(probsrc(error_manager),[add_error/3]). | |
| 48 | smt_type_to_prob_type(sort('Int'),_,integer) :- !. | |
| 49 | smt_type_to_prob_type(sort('Bool'),_,boolean) :- !. | |
| 50 | smt_type_to_prob_type(sort('Array',[From,sort('Bool')]),E,Out) :- | |
| 51 | get_preference(smtlib2b_arrays_as_sets,true), | |
| 52 | !, % we could translate arrays to Bool as sets | |
| 53 | smt_type_to_prob_type(From,E,FromType), | |
| 54 | Out = set(FromType). | |
| 55 | smt_type_to_prob_type(sort('Array',[From,To]),E,Out) :- !, | |
| 56 | %format('Sort Array ~w to ~w~n',[From,To]),nl, | |
| 57 | smt_type_to_prob_type(From,E,FromType), | |
| 58 | smt_type_to_prob_type(To,E,ToType), | |
| 59 | Out = set(couple(FromType,ToType)). | |
| 60 | smt_type_to_prob_type(sort('BitVec',[_Length]),_E,Out) :- !, | |
| 61 | Out = set(couple(integer,integer)). | |
| 62 | smt_type_to_prob_type(sort('Set',[Sub]),E,Out) :- !, | |
| 63 | smt_type_to_prob_type(Sub,E,SubType), | |
| 64 | Out = set(SubType). | |
| 65 | smt_type_to_prob_type(sort(X),E,global(X)) :- | |
| 66 | is_custom_type(E,X), !. | |
| 67 | smt_type_to_prob_type(X,_,_) :- !, | |
| 68 | add_error(smtlib2_translation,'Unsupported sort in smt_type_to_prob_type:',X), fail. | |
| 69 | ||
| 70 | % special versions for maplist that keeps first argument indexing | |
| 71 | smt_term_to_prob_term_maplist(E,I,O) :- | |
| 72 | smt_term_to_prob_term(I,E,O). | |
| 73 | smt_type_to_prob_type_maplist(E,I,O) :- | |
| 74 | smt_type_to_prob_type(I,E,O). | |
| 75 | ||
| 76 | smt_term_to_prob_term(attributed_term(Term,_Attr),Env,Out) :- !, | |
| 77 | smt_term_to_prob_term(Term,Env,Out). | |
| 78 | smt_term_to_prob_term(id_term(id('not'),[Arg]),Env,Out) :- !, | |
| 79 | smt_term_to_prob_term(Arg,Env,BArg), | |
| 80 | get_texpr_type(BArg,Type), | |
| 81 | (Type = pred | |
| 82 | -> Out = b(negation(BArg),pred,[]) | |
| 83 | ; Out = b(equal(BArg,b(boolean_false,boolean,[])),pred,[])). | |
| 84 | smt_term_to_prob_term(id_term(id('-'),[SingleArg]),Env,Out) :- !, | |
| 85 | % special case for unary minus: can not be interleaved | |
| 86 | smt_term_to_prob_term(SingleArg,Env,BArg), | |
| 87 | Out = b(unary_minus(BArg),integer,[]). | |
| 88 | smt_term_to_prob_term(id_term(id('='),Args),Env,Out) :- !, | |
| 89 | maplist(smt_term_to_prob_term_maplist(Env),Args,BArgs), | |
| 90 | maplist(get_texpr_type,BArgs,Types), | |
| 91 | (member(pred,Types) | |
| 92 | -> maplist(bool_to_pred,BArgs,BArgsPreds), | |
| 93 | chain(equivalence,BArgsPreds,Out) | |
| 94 | ; chain(equal,BArgs,Out)). | |
| 95 | smt_term_to_prob_term(id_term(id('ite'),[Test,If,Then]),Env,Out) :- !, | |
| 96 | smt_term_to_prob_term(Test,Env,BTestT), | |
| 97 | smt_term_to_prob_term(If,Env,BIfT), | |
| 98 | smt_term_to_prob_term(Then,Env,BThenT), | |
| 99 | bool_to_pred(BTestT,BTest), | |
| 100 | to_bool_if_necessary(BIfT,BIf), | |
| 101 | to_bool_if_necessary(BThenT,BThen), | |
| 102 | get_texpr_type(BIf,Type), | |
| 103 | Out = b(if_then_else(BTest,BIf,BThen),Type,[]). | |
| 104 | % set logic | |
| 105 | smt_term_to_prob_term(id_term(id(member),[Element,Set]),Env,Out) :- !, | |
| 106 | smt_term_to_prob_term(Set,Env,BSet), | |
| 107 | smt_term_to_prob_term(Element,Env,BElement), | |
| 108 | Out = b(member(BElement,BSet),pred,[]). | |
| 109 | smt_term_to_prob_term(id_term(id(card),[Set]),Env,Out) :- !, | |
| 110 | smt_term_to_prob_term(Set,Env,BSet), | |
| 111 | Out = b(card(BSet),integer,[]). | |
| 112 | smt_term_to_prob_term(id_term(id(singleton),[Element]),Env,Out) :- !, | |
| 113 | smt_term_to_prob_term(Element,Env,BElement), | |
| 114 | get_texpr_type(BElement,ElementType), | |
| 115 | Out = b(set_extension([BElement]),set(ElementType),[]). | |
| 116 | smt_term_to_prob_term(id_term(id(union),[SetA,SetB]),Env,Out) :- !, | |
| 117 | smt_term_to_prob_term(SetA,Env,BSetA), | |
| 118 | smt_term_to_prob_term(SetB,Env,BSetB), | |
| 119 | get_texpr_type(BSetB,Type), | |
| 120 | Out = b(union(BSetA,BSetB),Type,[]). | |
| 121 | smt_term_to_prob_term(id_term(id(intersection),[SetA,SetB]),Env,Out) :- !, | |
| 122 | smt_term_to_prob_term(SetA,Env,BSetA), | |
| 123 | smt_term_to_prob_term(SetB,Env,BSetB), | |
| 124 | get_texpr_type(BSetB,Type), | |
| 125 | Out = b(intersection(BSetA,BSetB),Type,[]). | |
| 126 | smt_term_to_prob_term(id_term(id(subset),[SetA,SetB]),Env,Out) :- !, | |
| 127 | smt_term_to_prob_term(SetA,Env,BSetA), | |
| 128 | smt_term_to_prob_term(SetB,Env,BSetB), | |
| 129 | Out = b(subset(BSetA,BSetB),pred,[]). | |
| 130 | % array logics | |
| 131 | smt_term_to_prob_term(id_term(id('store'),[Array,Index,Element]),Env,Out) :- !, | |
| 132 | smt_term_to_prob_term(Array,Env,BArray), | |
| 133 | get_texpr_type(BArray,ArrayType), | |
| 134 | ArrayType = set(CoupleType), | |
| 135 | smt_term_to_prob_term(Index,Env,BIndex), | |
| 136 | smt_term_to_prob_term(Element,Env,BElement), | |
| 137 | % TO DO: generate union or set_difference depending on Element=true or false when smtlib2b_arrays_as_sets | |
| 138 | % store(X,Index,El) = IF El=TRUE THEN X \/ {Index} ELSE X \ {Index} END | |
| 139 | SetEx = b(set_extension([b(couple(BIndex,BElement),CoupleType,[])]),ArrayType,[]), | |
| 140 | Out = b(overwrite(BArray,SetEx),ArrayType,[]). | |
| 141 | smt_term_to_prob_term(id_term(id('select'),[Array,Index]),Env,Out) :- !, | |
| 142 | smt_term_to_prob_term(Array,Env,BArray), | |
| 143 | smt_term_to_prob_term(Index,Env,BIndex), | |
| 144 | get_texpr_type(BArray,ArrayType), | |
| 145 | %format('select of array ~w (type: ~w) at index ~w~n',[Array,ArrayType,Index]), | |
| 146 | (ArrayType = set(couple(_From,To)) % Array was translated as total function From --> To | |
| 147 | -> Out = b(function(BArray,BIndex),To,[]) | |
| 148 | ; ArrayType = set(_From), % Array was translated as set (smtlib2b_arrays_as_sets=true) | |
| 149 | MEM = b(member(BIndex,BArray),pred,[]), | |
| 150 | Out = b(convert_bool(MEM),boolean,[]) | |
| 151 | ). | |
| 152 | % bitvector logics | |
| 153 | smt_term_to_prob_term(id_term(id('concat'),[A,B]),Env,Out) :- !, | |
| 154 | smt_term_to_prob_term(A,Env,BA), | |
| 155 | smt_term_to_prob_term(B,Env,BB), | |
| 156 | bvwidth(BA,WidthA), | |
| 157 | bvwidth(BB,WidthB), | |
| 158 | WidthBP1 = b(add(WidthB,Int1),integer,[]), | |
| 159 | Int0 = b(integer(0),integer,[]), | |
| 160 | Int1 = b(integer(1),integer,[]), | |
| 161 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 162 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 163 | FullWidth = b(add(b(add(WidthA,WidthB),integer,[]),Int1),integer,[]), | |
| 164 | TypeOfX1 = b(member(IdX1,b(interval(Int0,FullWidth),set(integer),[])),pred,[]), | |
| 165 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 166 | ValOfX2 = b(if_then_else(b(less_equal(IdX1,WidthB),pred,[]), | |
| 167 | b(function(BB,IdX1),integer,[]), | |
| 168 | b(function(BA,b(minus(IdX1,WidthBP1),integer,[])),integer,[])),integer,[]), | |
| 169 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 170 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 171 | smt_term_to_prob_term(id_term(id(zero_extend(NewLength)),[A]),Env,Out) :- !, | |
| 172 | smt_term_to_prob_term(A,Env,BA), | |
| 173 | bvwidth(BA,WidthA), | |
| 174 | WidthAP1 = b(add(WidthA,Int1),integer,[]), | |
| 175 | Int0 = b(integer(0),integer,[]), | |
| 176 | Int1 = b(integer(1),integer,[]), | |
| 177 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 178 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 179 | FullWidth = b(add(WidthA,b(integer(NewLength),integer,[])),integer,[]), | |
| 180 | TypeOfX1 = b(member(IdX1,b(interval(Int0,FullWidth),set(integer),[])),pred,[]), | |
| 181 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 182 | ValOfX2 = b(if_then_else(b(less_equal(IdX1,WidthA),pred,[]), | |
| 183 | b(integer(0),integer,[]), | |
| 184 | b(function(BA,b(minus(IdX1,WidthAP1),integer,[])),integer,[])),integer,[]), | |
| 185 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 186 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 187 | smt_term_to_prob_term(id_term(id(sign_extend(NewLength)),[A]),Env,Out) :- !, | |
| 188 | smt_term_to_prob_term(A,Env,BA), | |
| 189 | bvwidth(BA,WidthA), | |
| 190 | Int0 = b(integer(0),integer,[]), | |
| 191 | Int1 = b(integer(1),integer,[]), | |
| 192 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 193 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 194 | WidthAP1 = b(add(WidthA,Int1),integer,[]), | |
| 195 | FullWidth = b(add(WidthA,b(integer(NewLength),integer,[])),integer,[]), | |
| 196 | TypeOfX1 = b(member(IdX1,b(interval(Int0,FullWidth),set(integer),[])),pred,[]), | |
| 197 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 198 | ValOfX2 = b(if_then_else(b(less_equal(IdX1,WidthA),pred,[]), | |
| 199 | b(function(BA,IdX1),integer,[]), | |
| 200 | b(function(BA,b(minus(IdX1,WidthAP1),integer,[])),integer,[])),integer,[]), | |
| 201 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 202 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 203 | smt_term_to_prob_term(id_term(id(extract(I,J)),[S]),Env,Out) :- !, | |
| 204 | BI = b(integer(I),integer,[]), | |
| 205 | BJ = b(integer(J),integer,[]), | |
| 206 | smt_term_to_prob_term(S,Env,BS), | |
| 207 | Int0 = b(integer(0),integer,[]), | |
| 208 | Int1 = b(integer(1),integer,[]), | |
| 209 | DomX1 = b(add(b(minus(BI,BJ),integer,[]),Int1),integer,[]), | |
| 210 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 211 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 212 | TypeOfX1 = b(member(IdX1,b(interval(Int0,DomX1),set(integer),[])),pred,[]), | |
| 213 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 214 | ValOfX2 = b(function(BS,IdX1),integer,[]), | |
| 215 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 216 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 217 | smt_term_to_prob_term(id_term(id('bvnot'),[A]),Env,Out) :- !, | |
| 218 | smt_term_to_prob_term(A,Env,BA), | |
| 219 | bvwidth(BA,Width), | |
| 220 | Int0 = b(integer(0),integer,[]), | |
| 221 | Int1 = b(integer(1),integer,[]), | |
| 222 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 223 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 224 | TypeOfX1 = b(member(IdX1,b(interval(Int0,Width),set(integer),[])),pred,[]), | |
| 225 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 226 | ValOfX2 = b(if_then_else(b(equal(b(function(BA,IdX1),integer,[]),Int0),pred,[]),Int1,Int0),integer,[]), | |
| 227 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 228 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 229 | smt_term_to_prob_term(id_term(id('bvand'),[A,B]),Env,Out) :- !, | |
| 230 | smt_term_to_prob_term(A,Env,BA), | |
| 231 | smt_term_to_prob_term(B,Env,BB), | |
| 232 | bvwidth(BA,Width), | |
| 233 | Int0 = b(integer(0),integer,[]), | |
| 234 | Int1 = b(integer(1),integer,[]), | |
| 235 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 236 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 237 | TypeOfX1 = b(member(IdX1,b(interval(Int0,Width),set(integer),[])),pred,[]), | |
| 238 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 239 | ValOfX2 = b(if_then_else(b(equal(b(function(BA,IdX1),integer,[]),Int0),pred,[]),Int0,b(function(BB,IdX1),integer,[])),integer,[]), | |
| 240 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 241 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 242 | smt_term_to_prob_term(id_term(id('bvor'),[A,B]),Env,Out) :- !, | |
| 243 | smt_term_to_prob_term(A,Env,BA), | |
| 244 | smt_term_to_prob_term(B,Env,BB), | |
| 245 | bvwidth(BA,Width), | |
| 246 | Int0 = b(integer(0),integer,[]), | |
| 247 | Int1 = b(integer(1),integer,[]), | |
| 248 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 249 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 250 | TypeOfX1 = b(member(IdX1,b(interval(Int0,Width),set(integer),[])),pred,[]), | |
| 251 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 252 | ValOfX2 = b(if_then_else(b(equal(b(function(BA,IdX1),integer,[]),Int1),pred,[]),Int1,b(function(BB,IdX1),integer,[])),integer,[]), | |
| 253 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 254 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 255 | smt_term_to_prob_term(id_term(id('bvxor'),[A,B]),Env,Out) :- !, | |
| 256 | smt_term_to_prob_term(A,Env,BA), | |
| 257 | smt_term_to_prob_term(B,Env,BB), | |
| 258 | bvwidth(BA,Width), | |
| 259 | Int0 = b(integer(0),integer,[]), | |
| 260 | Int1 = b(integer(1),integer,[]), | |
| 261 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 262 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 263 | TypeOfX1 = b(member(IdX1,b(interval(Int0,Width),set(integer),[])),pred,[]), | |
| 264 | TypeOfX2 = b(member(IdX2,b(interval(Int0,Int1),set(integer),[])),pred,[]), | |
| 265 | ValOfX2 = b(if_then_else(b(equal(b(function(BA,IdX1),integer,[]),b(function(BB,IdX1),integer,[])),pred,[]),Int0,Int1),integer,[]), | |
| 266 | conjunct_predicates([TypeOfX1,TypeOfX2,b(equal(IdX2,ValOfX2),pred,[])],Pred), | |
| 267 | Out = b(comprehension_set([IdX1,IdX2],Pred),set(couple(integer,integer)),[]). | |
| 268 | smt_term_to_prob_term(id_term(id('bvult'),[A,B]),Env,Out) :- !, | |
| 269 | bv_to_nat_and_compare(A,B,less,Env,Out). | |
| 270 | smt_term_to_prob_term(id_term(id('bvule'),[A,B]),Env,Out) :- !, | |
| 271 | bv_to_nat_and_compare(A,B,less_equal,Env,Out). | |
| 272 | smt_term_to_prob_term(id_term(id('bvuge'),[A,B]),Env,Out) :- !, | |
| 273 | bv_to_nat_and_compare(A,B,greater_equal,Env,Out). | |
| 274 | smt_term_to_prob_term(id_term(id('bvugt'),[A,B]),Env,Out) :- !, | |
| 275 | bv_to_nat_and_compare(A,B,greater,Env,Out). | |
| 276 | smt_term_to_prob_term(id_term(id('bvslt'),[A,B]),Env,Out) :- !, | |
| 277 | signed_bv_to_nat_and_compare(A,B,less,Env,Out). | |
| 278 | smt_term_to_prob_term(id_term(id('bvsle'),[A,B]),Env,Out) :- !, | |
| 279 | signed_bv_to_nat_and_compare(A,B,less_equal,Env,Out). | |
| 280 | smt_term_to_prob_term(id_term(id('bvsge'),[A,B]),Env,Out) :- !, | |
| 281 | signed_bv_to_nat_and_compare(A,B,greater_equal,Env,Out). | |
| 282 | smt_term_to_prob_term(id_term(id('bvsgt'),[A,B]),Env,Out) :- !, | |
| 283 | signed_bv_to_nat_and_compare(A,B,greater,Env,Out). | |
| 284 | smt_term_to_prob_term(id_term(id('bvneg'),[A]),Env,Out) :- !, | |
| 285 | smt_term_to_prob_term(A,Env,BA), | |
| 286 | bvwidth(BA,Width), | |
| 287 | WidthP1 = b(add(Width,b(integer(1),integer,[])),integer,[]), | |
| 288 | bv2nat(BA,BANat), | |
| 289 | Int2 = b(integer(2),integer,[]), | |
| 290 | Pow = b(power_of(Int2,WidthP1),integer,[]), | |
| 291 | Differenz = b(minus(Pow,BANat),integer,[]), | |
| 292 | nat2bv(Differenz,Width,Out). | |
| 293 | smt_term_to_prob_term(id_term(id('bvadd'),[A,B]),Env,Out) :- !, | |
| 294 | smt_term_to_prob_term(A,Env,BA), | |
| 295 | smt_term_to_prob_term(B,Env,BB), | |
| 296 | bvwidth(BA,Width), | |
| 297 | bv2nat(BA,BANat), | |
| 298 | bv2nat(BB,BBNat), | |
| 299 | Sum = b(add(BANat,BBNat),integer,[]), | |
| 300 | nat2bv(Sum,Width,Out). | |
| 301 | smt_term_to_prob_term(id_term(id('bvsub'),[A,B]),Env,Out) :- !, | |
| 302 | smt_term_to_prob_term(A,Env,BA), | |
| 303 | smt_term_to_prob_term(B,Env,BB), | |
| 304 | bvwidth(BA,Width), | |
| 305 | bv2nat(BA,BANat), | |
| 306 | bv2nat(BB,BBNat), | |
| 307 | Sum = b(minus(BANat,BBNat),integer,[]), | |
| 308 | nat2bv(Sum,Width,Out). | |
| 309 | smt_term_to_prob_term(id_term(id('bvmul'),[A,B]),Env,Out) :- !, | |
| 310 | smt_term_to_prob_term(A,Env,BA), | |
| 311 | smt_term_to_prob_term(B,Env,BB), | |
| 312 | bvwidth(BA,Width), | |
| 313 | bv2nat(BA,BANat), | |
| 314 | bv2nat(BB,BBNat), | |
| 315 | Prod = b(multiplication(BANat,BBNat),integer,[]), | |
| 316 | nat2bv(Prod,Width,Out). | |
| 317 | smt_term_to_prob_term(id_term(id('bvudiv'),[A,B]),Env,Out) :- !, | |
| 318 | smt_term_to_prob_term(A,Env,BA), | |
| 319 | smt_term_to_prob_term(B,Env,BB), | |
| 320 | bvwidth(BA,Width), | |
| 321 | bv2nat(BA,BANat), | |
| 322 | bv2nat(BB,BBNat), | |
| 323 | Div = b(div(BANat,BBNat),integer,[]), | |
| 324 | nat2bv(Div,Width,Out). | |
| 325 | smt_term_to_prob_term(id_term(id('bvurem'),[A,B]),Env,Out) :- !, | |
| 326 | smt_term_to_prob_term(A,Env,BA), | |
| 327 | smt_term_to_prob_term(B,Env,BB), | |
| 328 | bvwidth(BA,Width), | |
| 329 | bv2nat(BA,BANat), | |
| 330 | bv2nat(BB,BBNat), | |
| 331 | Rem = b(modulo(BANat,BBNat),integer,[]), | |
| 332 | nat2bv(Rem,Width,Out). | |
| 333 | smt_term_to_prob_term(id_term(id('bvshl'),[A,B]),Env,Out) :- !, | |
| 334 | smt_term_to_prob_term(A,Env,BA), | |
| 335 | smt_term_to_prob_term(B,Env,BB), | |
| 336 | bvwidth(BA,Width), | |
| 337 | bv2nat(BA,BANat), | |
| 338 | bv2nat(BB,BBNat), | |
| 339 | Int2 = b(integer(2),integer,[]), | |
| 340 | Exp = b(power_of(Int2,BBNat),integer,[]), | |
| 341 | Res = b(multiplication(BANat,Exp),integer,[]), | |
| 342 | nat2bv(Res,Width,Out). | |
| 343 | smt_term_to_prob_term(id_term(id('bvlshr'),[A,B]),Env,Out) :- !, | |
| 344 | smt_term_to_prob_term(A,Env,BA), | |
| 345 | smt_term_to_prob_term(B,Env,BB), | |
| 346 | bvwidth(BA,Width), | |
| 347 | bv2nat(BA,BANat), | |
| 348 | bv2nat(BB,BBNat), | |
| 349 | Int2 = b(integer(2),integer,[]), | |
| 350 | Exp = b(power_of(Int2,BBNat),integer,[]), | |
| 351 | Res = b(div(BANat,Exp),integer,[]), | |
| 352 | nat2bv(Res,Width,Out). | |
| 353 | % division is a special case, because it has a different | |
| 354 | % semantic in B and SMT-LIB | |
| 355 | smt_term_to_prob_term(id_term(id(div),[Dividend|Divisors]),Env,Out) :- !, | |
| 356 | smt_term_to_prob_term(id_term(id('*'),Divisors),Env,BDivisor), | |
| 357 | smt_term_to_prob_term(Dividend,Env,BDividend), | |
| 358 | Zero = b(integer(0),integer,[]), | |
| 359 | DividendLessZero = b(less(BDividend,Zero),pred,[]), | |
| 360 | DivisorLessZero = b(less(BDivisor,Zero),pred,[]), | |
| 361 | DivisorGreaterZero = b(greater(BDivisor,Zero),pred,[]), | |
| 362 | DivisorMinusOne = b(minus(BDivisor,b(integer(1),integer,[])),integer,[]), | |
| 363 | DivisorPlusOne = b(add(BDivisor,b(integer(1),integer,[])),integer,[]), | |
| 364 | MinusDivisorPlusOne = b(unary_minus(DivisorPlusOne),integer,[]), | |
| 365 | ||
| 366 | conjunct_predicates([DividendLessZero,DivisorGreaterZero],If1), | |
| 367 | conjunct_predicates([DividendLessZero,DivisorLessZero],If2), | |
| 368 | ||
| 369 | FixInner = b(if_then_else(If2,MinusDivisorPlusOne,Zero),integer,[]), | |
| 370 | Fix = b(if_then_else(If1,DivisorMinusOne,FixInner),integer,[]), | |
| 371 | NewBDividend = b(minus(BDividend,Fix),integer,[]), | |
| 372 | Out = b(div(NewBDividend,BDivisor),integer,[]). | |
| 373 | % general cases | |
| 374 | smt_term_to_prob_term(id_term(id(Id),Args),Env,Out) :- | |
| 375 | smt_id_to_prob_id_preds(Id,BId), !, | |
| 376 | maplist(smt_term_to_prob_term_maplist(Env),Args,BArgs), | |
| 377 | maplist(bool_to_pred,BArgs,PredBArgs), | |
| 378 | interleave(BId,PredBArgs,Out). | |
| 379 | smt_term_to_prob_term(id_term(id(Id),Args),Env,Out) :- | |
| 380 | smt_id_to_prob_id(Id,BId,ConnectingPred), !, | |
| 381 | maplist(smt_term_to_prob_term_maplist(Env),Args,BArgs), | |
| 382 | call(ConnectingPred,BId,BArgs,Out). | |
| 383 | smt_term_to_prob_term(id_term(id(Id),Args),Env,Out) :- | |
| 384 | get_function(Id,Env,Params,_Results,Definition), !, | |
| 385 | replace_identifiers(Params,Args,Definition,Out,Env). | |
| 386 | smt_term_to_prob_term(id_term(id(Id),Args),Env,Out) :- | |
| 387 | get_type(Id,Env,set(couple(_X,Y))), !, | |
| 388 | smt_term_to_prob_term(id(Id),Env,BId), | |
| 389 | maplist(smt_term_to_prob_term_maplist(Env),Args,BArgs), | |
| 390 | create_couple(BArgs,BArg), | |
| 391 | Out = b(function(BId,BArg),Y,[]). | |
| 392 | smt_term_to_prob_term(id(true),_,b(boolean_true,boolean,[])) :- !. | |
| 393 | smt_term_to_prob_term(id(false),_,b(boolean_false,boolean,[])) :- !. | |
| 394 | smt_term_to_prob_term(id(Id),Env,OutId) :- !, | |
| 395 | get_type(Id,Env,Type), | |
| 396 | OutId = b(identifier(Id),Type,[]).%, | |
| 397 | %(Type = boolean | |
| 398 | % -> bool_to_pred(OutId,Out) | |
| 399 | % ; Out = OutId). | |
| 400 | smt_term_to_prob_term(id(Id,Sort),Env,OutId) :- !, | |
| 401 | smt_type_to_prob_type(Sort,Env,Type), | |
| 402 | OutId = b(identifier(Id),Type,[]). | |
| 403 | smt_term_to_prob_term(svar(Id,Sort),Env,Out) :- !, | |
| 404 | smt_type_to_prob_type(Sort,Env,Type), | |
| 405 | Out = b(identifier(Id),Type,[]). | |
| 406 | smt_term_to_prob_term(integer(I),_,b(integer(I),integer,[])) :- !. | |
| 407 | smt_term_to_prob_term(let(Bindings,Term),Env,BTerm) :- !, | |
| 408 | let_equalities_and_bids(Bindings,BIDs,Assignments,Env), | |
| 409 | create_local_env(Env,BIDs,LocalEnv), | |
| 410 | smt_term_to_prob_term(Term,LocalEnv,InnerBTerm), | |
| 411 | get_texpr_type(InnerBTerm,InnerType), | |
| 412 | (InnerType = pred | |
| 413 | -> safe_create_texpr(let_predicate(BIDs,Assignments,InnerBTerm),pred,BTerm) | |
| 414 | ; safe_create_texpr(let_expression(BIDs,Assignments,InnerBTerm),InnerType,BTerm)). | |
| 415 | smt_term_to_prob_term(forall(IDs,Term),Env,Forall) :- !, | |
| 416 | maplist(smt_term_to_prob_term_maplist(Env),IDs,Identifiers), | |
| 417 | create_local_env(Env,Identifiers,LocalEnv), | |
| 418 | smt_term_to_prob_term(Term,LocalEnv,InnerTerm), | |
| 419 | convlist(typing_constraint,IDs,InnerConstraints), | |
| 420 | bool_to_pred(InnerTerm,InnerTermAsPred), % necessary ?? | |
| 421 | conjunct_predicates(InnerConstraints,LHS), | |
| 422 | create_implication(LHS,InnerTermAsPred,Body), | |
| 423 | create_forall(Identifiers,Body,Forall). | |
| 424 | smt_term_to_prob_term(exists(IDs,Term),Env,Forall) :- !, | |
| 425 | maplist(smt_term_to_prob_term_maplist(Env),IDs,Identifiers), | |
| 426 | create_local_env(Env,Identifiers,LocalEnv), | |
| 427 | smt_term_to_prob_term(Term,LocalEnv,InnerTerm), | |
| 428 | convlist(typing_constraint,IDs,InnerConstraints), | |
| 429 | append(InnerConstraints,[InnerTerm],IList), | |
| 430 | conjunct_predicates(IList,Inner), | |
| 431 | bool_to_pred(Inner,InnerAsPred), | |
| 432 | create_exists(Identifiers,InnerAsPred,Forall). | |
| 433 | smt_term_to_prob_term(bitvector(Value,Length),_Env,Out) :- !, | |
| 434 | integer_to_binary_couples(Value,Length,Couples), | |
| 435 | Out = b(set_extension(Couples),set(couple(integer,integer)),[]). | |
| 436 | smt_term_to_prob_term(bitvector(Bits),_Env,Out) :- !, | |
| 437 | binary_to_binary_couples(Bits,Couples), | |
| 438 | Out = b(set_extension(Couples),set(couple(integer,integer)),[]). | |
| 439 | smt_term_to_prob_term(X,_,_) :- | |
| 440 | add_error(smtlib2_translation,'Unsupported term in smt_term_to_prob_term:',X), fail. | |
| 441 | ||
| 442 | ||
| 443 | bool_to_pred(Bool,Pred) :- | |
| 444 | get_texpr_expr(Bool,convert_bool(Pred)), !. | |
| 445 | bool_to_pred(Bool,Pred) :- | |
| 446 | get_texpr_type(Bool,boolean), !, | |
| 447 | safe_create_texpr(equal(Bool,b(boolean_true,boolean,[])),pred,Pred). | |
| 448 | bool_to_pred(Bool,Bool) :- | |
| 449 | get_texpr_type(Bool,pred), !. | |
| 450 | ||
| 451 | to_bool_if_necessary(PossiblePred,Bool) :- | |
| 452 | get_texpr_type(PossiblePred,pred), !, | |
| 453 | safe_create_texpr(convert_bool(PossiblePred),boolean,Bool). | |
| 454 | to_bool_if_necessary(NonPred,NonPred). | |
| 455 | ||
| 456 | let_equalities_and_bids([bind(ID,Term)],[IDTerm],[AssOut],Env) :- !, | |
| 457 | smt_term_to_prob_term(Term,Env,Ass), | |
| 458 | get_texpr_type(Ass,IdentifierType), | |
| 459 | (IdentifierType == pred | |
| 460 | -> IDTerm = b(identifier(ID),boolean,[]), | |
| 461 | safe_create_texpr(convert_bool(Ass),boolean,AssOut) | |
| 462 | ; IDTerm = b(identifier(ID),IdentifierType,[]), | |
| 463 | AssOut = Ass). | |
| 464 | let_equalities_and_bids([bind(ID,Term)|Further],[IDTerm|FurtherIdentifiers],Assignments,Env) :- | |
| 465 | let_equalities_and_bids([bind(ID,Term)],[IDTerm],FirstAssignment,Env), | |
| 466 | let_equalities_and_bids(Further,FurtherIdentifiers,FurtherAssignments,Env), | |
| 467 | append(FirstAssignment,FurtherAssignments,Assignments). | |
| 468 | ||
| 469 | replace_identifiers([],[],D,D,_Env). | |
| 470 | replace_identifiers([b(identifier(I),_,_)|T1],[Term|Terms],In,Out,Env) :- | |
| 471 | smt_term_to_prob_term(Term,Env,BTerm), | |
| 472 | replace_id_by_expr(In,I,BTerm,TOut), | |
| 473 | replace_identifiers(T1,Terms,TOut,Out,Env). | |
| 474 | ||
| 475 | % certain sorts enforce an inner constrait to strengthen their type | |
| 476 | typing_constraint(svar(Name,sort('Array',[Index,Element])),Constraint) :- | |
| 477 | smt_type_to_prob_type(Index,EIn,BIndex), | |
| 478 | smt_type_to_prob_type(Element,EIn,BElement), | |
| 479 | Identifier = b(identifier(Name),FullType,[]), | |
| 480 | Constraint = b(member(Identifier,b(EXPR,set(FullType),[])),pred,[]), | |
| 481 | type_to_expr(BIndex,From), | |
| 482 | (BElement=boolean,get_preference(smtlib2b_arrays_as_sets,true) % we translate boolean Array as Set | |
| 483 | -> EXPR = pow_subset(From), | |
| 484 | FullType = set(BIndex) | |
| 485 | ; type_to_expr(BElement,To), | |
| 486 | EXPR=total_function(From,To), | |
| 487 | FullType = set(couple(BIndex,BElement)) | |
| 488 | ). | |
| 489 | typing_constraint(svar(Name,sort('BitVec',[Length])),Constraint) :- | |
| 490 | Zero = b(integer(0),integer,[]), | |
| 491 | One = b(integer(1),integer,[]), | |
| 492 | L2 is Length - 1, | |
| 493 | LengthMinusOne = b(integer(L2),integer,[]), | |
| 494 | FullType = set(couple(integer,integer)), | |
| 495 | Identifier = b(identifier(Name),FullType,[]), | |
| 496 | From = b(interval(Zero,LengthMinusOne),set(integer),[]), | |
| 497 | To = b(interval(Zero,One),set(integer),[]), | |
| 498 | Constraint = b(member(Identifier,b(total_function(From,To),set(FullType),[])),pred,[]). | |
| 499 | ||
| 500 | is_function_constraint(Id,FullType,Constraint) :- | |
| 501 | FullType = set(couple(From,To)), | |
| 502 | Identifier = b(identifier(Id),FullType,[]), | |
| 503 | type_to_expr(From,FromExpr), | |
| 504 | type_to_expr(To,ToExpr), | |
| 505 | Constraint = b(member(Identifier,b(partial_function(FromExpr,ToExpr),set(FullType),[])),pred,[]). | |
| 506 | ||
| 507 | integer_to_binary_couples(Value,Length,Couples) :- | |
| 508 | PLength is Length - 1, | |
| 509 | integer_to_binary_couples(Value,0,PLength,Couples). | |
| 510 | integer_to_binary_couples(Value,Current,Current,[b(couple(A,B),couple(integer,integer),[])]) :- !, | |
| 511 | A = b(integer(Current),integer,[]), | |
| 512 | BVal is mod(Value,2), | |
| 513 | B = b(integer(BVal),integer,[]). | |
| 514 | integer_to_binary_couples(Value,Current,PLength,[b(couple(A,B),couple(integer,integer),[])|Cs]) :- | |
| 515 | A = b(integer(Current),integer,[]), | |
| 516 | BVal is mod(Value,2), | |
| 517 | B = b(integer(BVal),integer,[]), | |
| 518 | NValue is Value // 2, | |
| 519 | NCurrent is Current + 1, | |
| 520 | integer_to_binary_couples(NValue,NCurrent,PLength,Cs). | |
| 521 | ||
| 522 | binary_to_binary_couples(Bits,Couples) :- | |
| 523 | length(Bits,L), FirstL is L - 1, | |
| 524 | binary_to_binary_couples(FirstL,Bits,Couples). | |
| 525 | binary_to_binary_couples(-1,[],[]). | |
| 526 | binary_to_binary_couples(L,[Bit|Bits],[Couple|Couples]) :- | |
| 527 | A = b(integer(L),integer,[]), | |
| 528 | B = b(integer(Bit),integer,[]), | |
| 529 | Couple = b(couple(A,B),couple(integer,integer),[]), | |
| 530 | L2 is L - 1, | |
| 531 | binary_to_binary_couples(L2,Bits,Couples). | |
| 532 | ||
| 533 | smt_id_to_prob_id('<=',less_equal,chain). | |
| 534 | smt_id_to_prob_id('>=',greater_equal,chain). | |
| 535 | smt_id_to_prob_id('<',less,chain). | |
| 536 | smt_id_to_prob_id('>',greater,chain). | |
| 537 | smt_id_to_prob_id('distinct',not_equal,chain). | |
| 538 | smt_id_to_prob_id('*',multiplication,interleave). | |
| 539 | smt_id_to_prob_id('+',add,interleave). | |
| 540 | smt_id_to_prob_id('-',minus,interleave). | |
| 541 | ||
| 542 | smt_id_to_prob_id_preds('or',disjunct). | |
| 543 | smt_id_to_prob_id_preds('and',conjunct). | |
| 544 | smt_id_to_prob_id_preds('=>',implication). | |
| 545 | ||
| 546 | bvwidth(BV,Width) :- | |
| 547 | Width = b(max(b(domain(BV),set(integer),[])),integer,[]). | |
| 548 | ||
| 549 | bv2nat(BV,Nat) :- | |
| 550 | IntOne = b(integer(1),integer,[]), | |
| 551 | IntTwo = b(integer(2),integer,[]), | |
| 552 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 553 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 554 | PowerOf = b(power_of(IntTwo,b(minus(IdX1,IntOne),integer,[])),integer,[]), | |
| 555 | Nat = b(general_sum([IdX1,IdX2],b(member(b(couple(IdX1,IdX2),couple(integer,integer),[]),BV),pred,[]),b(multiplication(IdX2,PowerOf),integer,[])),integer,[]). | |
| 556 | signed_bv2nat(BV,Nat) :- | |
| 557 | IntOne = b(integer(1),integer,[]), | |
| 558 | IntTwo = b(integer(2),integer,[]), | |
| 559 | IntMinusOne = b(integer(-1),integer,[]), | |
| 560 | % todo: make sure identifiers do not collide | |
| 561 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 562 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 563 | NotZeroIndex = b(not_equal(IdX1,b(integer(0),integer,[])),pred,[]), | |
| 564 | MemberConstraint = b(member(b(couple(IdX1,IdX2),couple(integer,integer),[]),BV),pred,[]), | |
| 565 | conjunct_predicates([NotZeroIndex,MemberConstraint],Const), | |
| 566 | PowerOf = b(power_of(IntTwo,b(minus(IdX1,IntOne),integer,[])),integer,[]), | |
| 567 | Sum = b(general_sum([IdX1,IdX2],Const,b(multiplication(IdX2,PowerOf),integer,[])),integer,[]), | |
| 568 | ZeroIndex = b(function(BV,b(integer(0),integer,[])),integer,[]), | |
| 569 | Sign = b(power_of(IntMinusOne,ZeroIndex),integer,[]), | |
| 570 | Nat = b(multiplication(Sign,Sum),integer,[]). | |
| 571 | ||
| 572 | nat2bv(Nat,Width,BV) :- | |
| 573 | IntOne = b(integer(1),integer,[]), | |
| 574 | IntTwo = b(integer(2),integer,[]), | |
| 575 | % todo: make sure identifiers do not collide | |
| 576 | IdX1 = b(identifier('\\tmp1'),integer,[]), | |
| 577 | IdX2 = b(identifier('\\tmp2'),integer,[]), | |
| 578 | TypeId1 = b(member(IdX1,b(interval(b(integer(1),integer,[]),Width),set(integer),[])),pred,[]), | |
| 579 | TypeId2 = b(member(IdX2,b(interval(b(integer(0),integer,[]),b(integer(1),integer,[])),set(integer),[])),pred,[]), | |
| 580 | PowerOf = b(power_of(IntTwo,b(minus(IdX1,IntOne),integer,[])),integer,[]), | |
| 581 | ValueOfId2 = b(equal(IdX2,b(modulo(b(div(Nat,PowerOf),integer,[]),IntTwo),integer,[])),pred,[]), | |
| 582 | conjunct_predicates([TypeId1,TypeId2,ValueOfId2],InnerPred), | |
| 583 | BV = b(comprehension_set([IdX1,IdX2],InnerPred),set(couple(integer,integer)),[]). | |
| 584 | ||
| 585 | type_to_expr(set(A),Res) :- !, Res = b(pow_subset(AE),set(set(A)),[]), | |
| 586 | type_to_expr(A,AE). | |
| 587 | type_to_expr(couple(A,B),b(cartesian_product(AE,BE),set(couple(AET,BET)),[])) :- !, | |
| 588 | type_to_expr(A,AE), type_to_expr(B,BE), | |
| 589 | get_texpr_type(AE,AET), get_texpr_type(BE,BET). | |
| 590 | type_to_expr(integer,b(integer_set('INTEGER'),set(integer),[])) :- !. | |
| 591 | type_to_expr(boolean,b(bool_set,set(boolean),[])) :- !. | |
| 592 | type_to_expr(global(E),b(identifier(E),set(global(E)),[])) :- !. | |
| 593 | type_to_expr(T,_) :- | |
| 594 | add_error(smtlib2_translation,'Unsupported type in type_to_expr:',T), fail. | |
| 595 | ||
| 596 | signed_bv_to_nat_and_compare(A,B,Op,Env,Out) :- | |
| 597 | smt_term_to_prob_term(A,Env,BA), | |
| 598 | smt_term_to_prob_term(B,Env,BB), | |
| 599 | signed_bv2nat(BA,BANat), | |
| 600 | signed_bv2nat(BB,BBNat), | |
| 601 | Operation =.. [Op,BANat,BBNat], | |
| 602 | Out = b(Operation,pred,[]). | |
| 603 | ||
| 604 | bv_to_nat_and_compare(A,B,Op,Env,Out) :- | |
| 605 | smt_term_to_prob_term(A,Env,BA), | |
| 606 | smt_term_to_prob_term(B,Env,BB), | |
| 607 | bv2nat(BA,BANat), | |
| 608 | bv2nat(BB,BBNat), | |
| 609 | Operation =.. [Op,BANat,BBNat], | |
| 610 | Out = b(Operation,pred,[]). |