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mathematical_expr.h
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1/*******************************************************************\
2
3Module: API to expression classes for 'mathematical' expressions
4
5Author: Daniel Kroening, kroening@kroening.com
6
7\*******************************************************************/
8
9#ifndef CPROVER_UTIL_MATHEMATICAL_EXPR_H
10#define CPROVER_UTIL_MATHEMATICAL_EXPR_H
11
14
15#include "mathematical_types.h"
16#include "std_expr.h"
17
20class transt : public ternary_exprt
21{
22public:
24 const irep_idt &_id,
25 const exprt &_op0,
26 const exprt &_op1,
27 const exprt &_op2,
28 const typet &_type)
29 : ternary_exprt(_id, _op0, _op1, _op2, _type)
30 {
31 }
32
34 {
35 return op0();
36 }
38 {
39 return op1();
40 }
42 {
43 return op2();
44 }
45
46 const exprt &invar() const
47 {
48 return op0();
49 }
50 const exprt &init() const
51 {
52 return op1();
53 }
54 const exprt &trans() const
55 {
56 return op2();
57 }
58};
59
60template <>
61inline bool can_cast_expr<transt>(const exprt &base)
62{
63 return base.id() == ID_trans;
64}
65
66inline void validate_expr(const transt &value)
67{
68 validate_operands(value, 3, "Transition systems must have three operands");
69}
70
75inline const transt &to_trans_expr(const exprt &expr)
76{
77 PRECONDITION(expr.id() == ID_trans);
78 const transt &ret = static_cast<const transt &>(expr);
80 return ret;
81}
82
85{
86 PRECONDITION(expr.id() == ID_trans);
87 transt &ret = static_cast<transt &>(expr);
89 return ret;
90}
91
94{
95public:
98 {
99 }
100};
101
102template <>
103inline bool can_cast_expr<power_exprt>(const exprt &base)
104{
105 return base.id() == ID_power;
106}
107
108inline void validate_expr(const power_exprt &value)
109{
110 validate_operands(value, 2, "Power must have two operands");
111}
112
119inline const power_exprt &to_power_expr(const exprt &expr)
120{
121 PRECONDITION(expr.id() == ID_power);
122 const power_exprt &ret = static_cast<const power_exprt &>(expr);
124 return ret;
125}
126
129{
130 PRECONDITION(expr.id() == ID_power);
131 power_exprt &ret = static_cast<power_exprt &>(expr);
133 return ret;
134}
135
138{
139public:
144};
145
146template <>
148{
149 return base.id() == ID_factorial_power;
150}
151
152inline void validate_expr(const factorial_power_exprt &value)
153{
154 validate_operands(value, 2, "Factorial power must have two operands");
155}
156
164{
167 static_cast<const factorial_power_exprt &>(expr);
169 return ret;
170}
171
174{
176 factorial_power_exprt &ret = static_cast<factorial_power_exprt &>(expr);
178 return ret;
179}
180
182{
183public:
188
193};
194
197{
198public:
200
204
206 {
207 return op0();
208 }
209
210 const exprt &function() const
211 {
212 return op0();
213 }
214
217
219 {
220 return op1().operands();
221 }
222
223 const argumentst &arguments() const
224 {
225 return op1().operands();
226 }
227};
228
229template <>
231{
232 return base.id() == ID_function_application;
233}
234
236{
237 validate_operands(value, 2, "Function application must have two operands");
238}
239
246inline const function_application_exprt &
248{
251 static_cast<const function_application_exprt &>(expr);
253 return ret;
254}
255
265
268{
269public:
275
281
282 // for the special case of one variable
284 {
285 auto &variables = this->variables();
286 PRECONDITION(variables.size() == 1);
287 return variables.front();
288 }
289
290 // for the special case of one variable
291 const symbol_exprt &symbol() const
292 {
293 auto &variables = this->variables();
294 PRECONDITION(variables.size() == 1);
295 return variables.front();
296 }
297};
298
299template <>
301{
302 return base.id() == ID_forall || base.id() == ID_exists;
303}
304
305inline void validate_expr(const quantifier_exprt &value)
306{
307 validate_operands(value, 2, "quantifier expressions must have two operands");
308 for(auto &op : value.variables())
310 op.id() == ID_symbol, "quantified variable shall be a symbol");
311}
312
319inline const quantifier_exprt &to_quantifier_expr(const exprt &expr)
320{
322 const quantifier_exprt &ret = static_cast<const quantifier_exprt &>(expr);
324 return ret;
325}
326
329{
331 quantifier_exprt &ret = static_cast<quantifier_exprt &>(expr);
333 return ret;
334}
335
350
351template <>
352inline bool can_cast_expr<forall_exprt>(const exprt &base)
353{
354 return base.id() == ID_forall;
355}
356
357inline void validate_expr(const forall_exprt &value)
358{
359 validate_expr(static_cast<const quantifier_exprt &>(value));
360}
361
362inline const forall_exprt &to_forall_expr(const exprt &expr)
363{
364 PRECONDITION(expr.id() == ID_forall);
365 const forall_exprt &ret = static_cast<const forall_exprt &>(expr);
366 validate_expr(static_cast<const quantifier_exprt &>(ret));
367 return ret;
368}
369
371{
372 PRECONDITION(expr.id() == ID_forall);
373 forall_exprt &ret = static_cast<forall_exprt &>(expr);
374 validate_expr(static_cast<const quantifier_exprt &>(ret));
375 return ret;
376}
377
392
393template <>
394inline bool can_cast_expr<exists_exprt>(const exprt &base)
395{
396 return base.id() == ID_exists;
397}
398
399inline void validate_expr(const exists_exprt &value)
400{
401 validate_expr(static_cast<const quantifier_exprt &>(value));
402}
403
404inline const exists_exprt &to_exists_expr(const exprt &expr)
405{
406 PRECONDITION(expr.id() == ID_exists);
407 const exists_exprt &ret = static_cast<const exists_exprt &>(expr);
408 validate_expr(static_cast<const quantifier_exprt &>(ret));
409 return ret;
410}
411
413{
414 PRECONDITION(expr.id() == ID_exists);
415 exists_exprt &ret = static_cast<exists_exprt &>(expr);
416 validate_expr(static_cast<const quantifier_exprt &>(ret));
417 return ret;
418}
419
422{
423public:
424 lambda_exprt(const variablest &, const exprt &_where);
425
430
432 {
433 return static_cast<const mathematical_function_typet &>(
435 }
436
437 // apply the function to the given arguments
438 exprt application(const operandst &arguments) const
439 {
440 return instantiate(arguments);
441 }
442};
443
444template <>
445inline bool can_cast_expr<lambda_exprt>(const exprt &base)
446{
447 return base.id() == ID_lambda;
448}
449
450inline void validate_expr(const lambda_exprt &value)
451{
452 validate_operands(value, 2, "lambda must have two operands");
453}
454
461inline const lambda_exprt &to_lambda_expr(const exprt &expr)
462{
463 PRECONDITION(expr.id() == ID_lambda);
464 DATA_INVARIANT(expr.operands().size() == 2, "lambda must have two operands");
466 expr.type().id() == ID_mathematical_function,
467 "lambda must have right type");
468 return static_cast<const lambda_exprt &>(expr);
469}
470
473{
474 PRECONDITION(expr.id() == ID_lambda);
475 DATA_INVARIANT(expr.operands().size() == 2, "lambda must have two operands");
477 expr.type().id() == ID_mathematical_function,
478 "lambda must have right type");
479 return static_cast<lambda_exprt &>(expr);
480}
481
482#endif // CPROVER_UTIL_MATHEMATICAL_EXPR_H
ait supplies three of the four components needed: an abstract interpreter (in this case handling func...
Definition ai.h:563
A base class for binary expressions.
Definition std_expr.h:583
exprt & op0()
Definition expr.h:125
exprt & op1()
Definition expr.h:128
A base class for variable bindings (quantifiers, let, lambda)
Definition std_expr.h:3052
variablest & variables()
Definition std_expr.h:3073
exprt instantiate(const exprt::operandst &) const
substitute free occurrences of the variables in where() by the given values
Definition std_expr.cpp:169
std::vector< symbol_exprt > variablest
Definition std_expr.h:3054
The Boolean type.
Definition std_types.h:36
dstringt has one field, an unsigned integer no which is an index into a static table of strings.
Definition dstring.h:39
An exists expression.
exists_exprt(const symbol_exprt &_symbol, const exprt &_where)
exists_exprt(const binding_exprt::variablest &_variables, const exprt &_where)
Base class for all expressions.
Definition expr.h:56
std::vector< exprt > operandst
Definition expr.h:58
typet & type()
Return the type of the expression.
Definition expr.h:84
operandst & operands()
Definition expr.h:94
Falling factorial power.
factorial_power_exprt(const exprt &_base, const exprt &_exp)
A forall expression.
forall_exprt(const binding_exprt::variablest &_variables, const exprt &_where)
forall_exprt(const symbol_exprt &_symbol, const exprt &_where)
Application of (mathematical) function.
const exprt & function() const
const mathematical_function_typet & function_type() const
This helper method provides the type of the expression returned by function.
const argumentst & arguments() const
const irep_idt & id() const
Definition irep.h:396
A (mathematical) lambda expression.
mathematical_function_typet & type()
exprt application(const operandst &arguments) const
const mathematical_function_typet & type() const
A type for mathematical functions (do not confuse with functions/methods in code)
A base class for multi-ary expressions Associativity is not specified.
Definition std_expr.h:857
Exponentiation.
power_exprt(const exprt &_base, const exprt &_exp)
A base class for quantifier expressions.
quantifier_exprt(irep_idt _id, symbol_exprt _symbol, exprt _where)
constructor for single variable
quantifier_exprt(irep_idt _id, const variablest &_variables, exprt _where)
constructor for multiple variables
const symbol_exprt & symbol() const
symbol_exprt & symbol()
Expression to hold a symbol (variable)
Definition std_expr.h:113
An expression with three operands.
Definition std_expr.h:49
exprt & op0()
Definition expr.h:125
exprt & op1()
Definition expr.h:128
exprt & op2()
Definition expr.h:131
Transition system, consisting of state invariant, initial state predicate, and transition predicate.
const exprt & init() const
exprt & init()
exprt & invar()
transt(const irep_idt &_id, const exprt &_op0, const exprt &_op1, const exprt &_op2, const typet &_type)
const exprt & trans() const
exprt & trans()
const exprt & invar() const
tuple_exprt(exprt::operandst operands, typet type)
tuple_exprt(exprt::operandst operands)
The type of an expression, extends irept.
Definition type.h:29
void validate_operands(const exprt &value, exprt::operandst::size_type number, const char *message, bool allow_more=false)
Definition expr_cast.h:250
const quantifier_exprt & to_quantifier_expr(const exprt &expr)
Cast an exprt to a quantifier_exprt.
bool can_cast_expr< forall_exprt >(const exprt &base)
const factorial_power_exprt & to_factorial_power_expr(const exprt &expr)
Cast an exprt to a factorial_power_exprt.
bool can_cast_expr< quantifier_exprt >(const exprt &base)
bool can_cast_expr< exists_exprt >(const exprt &base)
void validate_expr(const transt &value)
bool can_cast_expr< function_application_exprt >(const exprt &base)
bool can_cast_expr< factorial_power_exprt >(const exprt &base)
factorial_power_exprt & to_factorial_expr(exprt &expr)
Cast an exprt to a factorial_power_exprt.
const exists_exprt & to_exists_expr(const exprt &expr)
bool can_cast_expr< lambda_exprt >(const exprt &base)
const power_exprt & to_power_expr(const exprt &expr)
Cast an exprt to a power_exprt.
const forall_exprt & to_forall_expr(const exprt &expr)
const transt & to_trans_expr(const exprt &expr)
Cast an exprt to a transt expr must be known to be transt.
const function_application_exprt & to_function_application_expr(const exprt &expr)
Cast an exprt to a function_application_exprt.
bool can_cast_expr< transt >(const exprt &base)
const lambda_exprt & to_lambda_expr(const exprt &expr)
Cast an exprt to a lambda_exprt.
bool can_cast_expr< power_exprt >(const exprt &base)
Mathematical types.
STL namespace.
#define DATA_INVARIANT(CONDITION, REASON)
This condition should be used to document that assumptions that are made on goto_functions,...
Definition invariant.h:534
#define PRECONDITION(CONDITION)
Definition invariant.h:463
API to expression classes.