U
    L?hW                     @   s  d dl Z d dlZd dlZd dlZd dlmZ d dlmZ d dlZd dlmZm	Z	m
Z
 d dlmZmZ d dlmZmZmZmZmZmZmZmZmZmZmZmZmZ d dlmZmZmZmZ d dl m!Z! d d	l"m#Z# d d
l$m%Z%m&Z& ed\Z'Z(Z)G dd deZ*e j+ej,e* dddZ-dd Z.dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd  Z5d!d" Z6d#d$ Z7d%d& Z8d'd( Z9d)d* Z:d+d, Z;d-d. Z<d/d0 Z=dS )1    N)Enum)Callable)AddImpliessqrt)MulPow)SpisymbolsFunctionRationalIntegerSymbolEqNeLeLtGtGe)	Piecewiseexpsincos)Qsmtlib_code)raisesFailedzx,y,zc                   @   s6   e Zd ZedejZedejZedejZdS )_Wz2Could not infer type of `.+`. Defaulting to float.z.Non-Symbol/Function `.+` will not be declared.zPNon-Boolean expression `.+` will not be asserted. Converting to SMTLib verbatim.N)	__name__
__module____qualname__recompileIDEFAULTING_TO_FLOATZWILL_NOT_DECLAREWILL_NOT_ASSERT r(   r(   R/var/www/html/venv/lib/python3.8/site-packages/sympy/printing/tests/test_smtlib.pyr      s   r   )expectedc              	   c   s   g }|j }|V  g }tt|| D ]v\}\}}|sN|d| d| dg7 }q$|sn|d| d|j dg7 }q$|j|s$|d| d| d|j dg7 }q$|rtd|d S )	N[z] Received unexpected warning `z`.z$] Did not receive expected warning `z] Warning `z` does not match expected .
)	append	enumerate	itertoolszip_longestnamevaluematchr   join)r*   Zwarnslog_warnerrorsiwer(   r(   r)   _check_warns   s    " r;   c               	   C   s   t tjgd 6} ttd| ddks*tttd| ddksBtW 5 Q R X t g .} ttddksjtttddks~tW 5 Q R X d S )N   C   r6   Z67z-1)r;   r   r'   r   r   AssertionErrorr9   r(   r(   r)   test_Integer-   s    "
rB   c               	   C   s   t tjgd n} ttdd| ddks,tttdd| ddksFtttdd	| dd
ks`tttdd	| ddksztW 5 Q R X t tjtjgd D} tttdd d| ddkstttddt | ddkstW 5 Q R X d S )N         r>   z(/ 3 7)   	   2iz(/ -3 7)r<   FZauto_declarer6   z(+ (/ 3 7) x)z$(declare-const x Real)
(* (/ 3 7) x))r;   r   r'   r   r   r@   r&   xrA   r(   r(   r)   test_Rational6   s    $ rL   c               	   C   s   t tjgd } ttttd| ddks.tttttd| ddksJttt	ttd| ddksfttt
ttd| ddkstttttd| ddkstttttd| dd	kstW 5 Q R X d S )
N   FrJ   (assert (= x y))(assert (not (= x y)))(assert (<= x y))(assert (< x y))(assert (> x y))(assert (>= x y)))r;   r   r&   r   r   rK   yr@   r   r   r   r   r   rA   r(   r(   r)   test_RelationalC   s    rU   c                	      s   t tjgd  ttttd ddks0ttt	ttd ddksNttt
ttd ddksltttttd ddkstttttd ddkstttttd dd	kstW 5 Q R X tt fd
d d S )NrM   FrJ   rN   rO   rQ   rP   rR   rS   c                      s   t tt dS Nr>   )r   r   complexrK   r(   rA   r(   r)   <lambda>V       z,test_AppliedBinaryRelation.<locals>.<lambda>)r;   r   r&   r   r   eqrK   rT   r@   neltlegtger   
ValueErrorr(   r(   rA   r)   test_AppliedBinaryRelationM   s    (ra   c               	   C   s   t tjgd } tttd| ddks.ttttd| ddksJttt	td| ddksfttt
td| ddksttttd| ddksttttd| dd	kstW 5 Q R X d S )
N   FrJ   z(assert (> x 0))z(assert (< x 0))z(assert (= x 0))z(assert (<= x 0))z(assert (>= x 0))z(assert (not (= x 0))))r;   r   r&   r   r   ZpositiverK   r@   negativezerononpositiveZnonnegativeZnonzerorA   r(   r(   r)   test_AppliedPredicateY   s    rf   c               	   C   s  t tjtjg(} ttttt d| ddks4tW 5 Q R X t tjg6} tt	ttt
ttit
ditjdi| ddks|tW 5 Q R X td}t tjg.} t|t|ttgtf i| d	d
kstW 5 Q R X t g } t|t|ttgtf i| d	dksttt|ttt|tt
tgtf i| d	dks6ttt|ttt|tt
tgtf i|dtdi| ddksttW 5 Q R X t tjgd 2} tt|ttt|dtdi| ddkstW 5 Q R X d S )NFrJ   z(pow (sin x) (cos x))ZINTEGER_TYPEZABSOLUTE_VALUE_OF)symbol_tableZknown_typesknown_functionsr6   z4(declare-const x INTEGER_TYPE)
(ABSOLUTE_VALUE_OF x)f1rg   r6   z:(declare-const x Bool)
(declare-fun f1 (Bool) Real)
(f1 x)zC(declare-const x Bool)
(declare-fun f1 (Bool) Bool)
(assert (f1 x))z|(declare-const x Int)
(declare-const y Bool)
(declare-const z Bool)
(declare-fun f1 (Int Bool) Bool)
(assert (= (f1 x z) y))ZMY_KNOWN_FUNz==)rg   rh   r6   zf(declare-const x Int)
(declare-const y Bool)
(declare-const z Bool)
(assert (== (MY_KNOWN_FUN x z) y))rD   )rh   r6   zg(declare-const x Real)
(declare-const y Real)
(declare-const z Real)
(assert (== (MY_KNOWN_FUN x z) y)))r;   r   r&   r'   r   r   rK   r   r@   absintrT   boolsympyZAbsr   r   floatr   z)r9   Zmy_fun1r(   r(   r)   test_Functionb   sh    ,
	






rq   c                  C   s  t tjtjg } ttd d| ddks,tW 5 Q R X t tjtjtjg$} tttd  d| ddksjtW 5 Q R X t tjtjgv} tttdd d| ddkstt	dd	d
}t	dd	d}t	d}dd }d||d |||    |d |  }W 5 Q R X t g L} tt
|dk |t
||k||d	@ t
|dtdd g| ddksPtW 5 Q R X t tjtjg<} ttd|tt||ddddddd| ddkstW 5 Q R X d S )NrD   FrJ   z	(pow x 3)z(pow x (pow y 3))r<   z(pow x (/ 2 3))aTintegerbrealcc                 S   s   d|  S )Nr<   r(   )rK   r(   r(   r)   g   rY   ztest_Pow.<locals>.g   g      @r>   z(declare-const a Int)
(declare-const b Real)
(declare-const c Bool)
(assert (= (< a 2) c))
(assert (= (> b a) c))
(assert c)
(assert (= (* (pow (* 7.0 a) (+ (pow b a) (* -1 a))) (pow (+ b (pow a 2)) -1)) (/ 7 3)))evaluater?   zG(declare-const b Real)
(declare-const c Real)
(* -2 c (pow (* b b) -1)))r;   r   r&   r'   r   rK   r@   rT   r   r   r   r   r   )r9   rr   ru   rx   ry   exprr(   r(   r)   test_Pow   s:    $( 2
"r   c               	   C   s   t tjtjtjg } ttt d| ddks0tW 5 Q R X t tjtjtjg } ttt d| ddksjtW 5 Q R X t tjtjg} tt d| ddkstW 5 Q R X d S )NFrJ   z(* x y)z(+ x y)z(* -1 x))r;   r   r&   r'   r   rK   rT   r@   rA   r(   r(   r)   test_basic_ops   s    $$r   c                     s  ddl m  ddlmmm G  fddd td} ttj	gD}t
tddft| t| t| ttgtf i|d	d
kstW 5 Q R X ttj	gd X}t
tddftddfttttt| t| t| ttgtf i|d	dkstW 5 Q R X tddd}tddd}td}tg J}t
|ddf|ddft||k t||k |B |ddksvtW 5 Q R X d S )Nr   )Boolean)IntervalTuplesympifyc                       sB   e Zd ZfddZedd Zedd Z fddZd	S )
z*test_quantifier_extensions.<locals>.ForAllc                    s0    fdd| j D } d d|| jgS )Nc              	      s6   g | ].\}}} |jjj|   ||gqS r(   )_s_exprr2   Z_known_typesrg   ).0symstartend)r   printerr(   r)   
<listcomp>   s
   zFtest_quantifier_extensions.<locals>.ForAll._smtlib.<locals>.<listcomp>forall )limitsr   function)selfr   Zbound_symbol_declarations)r   )r   r)   _smtlib   s    
z2test_quantifier_extensions.<locals>.ForAll._smtlibc                 S   s   dd | j D S )Nc                 S   s   h | ]\}}}|qS r(   r(   )r   s_r(   r(   r)   	<setcomp>   s     zKtest_quantifier_extensions.<locals>.ForAll.bound_symbols.<locals>.<setcomp>)r   r   r(   r(   r)   bound_symbols   s    z8test_quantifier_extensions.<locals>.ForAll.bound_symbolsc                    s&   dd | j D   fdd| jjD S )Nc                 S   s   h | ]
}|j qS r(   r2   r   r   r(   r(   r)   r      s     zJtest_quantifier_extensions.<locals>.ForAll.free_symbols.<locals>.<setcomp>c                    s   h | ]}|j  kr|qS r(   r   r   Zbound_symbol_namesr(   r)   r      s   
)r   r   free_symbolsr   r(   r   r)   r      s    
z7test_quantifier_extensions.<locals>.ForAll.free_symbolsc                    s   fdd|D } fdd|D }t |t | t |ksDtt |dksTt|d }t|rjf||j |jf S  | }t||g |_||_||_|S )Nc                    s"   g | ]}t |t fr|qS r(   )
isinstancetupler   rr   )r   r   r(   r)   r      s      zFtest_quantifier_extensions.<locals>.ForAll.__new__.<locals>.<listcomp>c                    s   g | ]}t | r|qS r(   )r   r   )r   r   r(   r)   r      s     
 rz   r   )lenr@   r   __new__r   r   r   _args)clsargsr   r   inst)r   ForAllr   r   r(   r)   r      s"    
  
z2test_quantifier_extensions.<locals>.ForAll.__new__N)r    r!   r"   r   propertyr   r   r   r(   r   r   r   r   r   r(   r)   r      s   

r   fi   rj   z,(assert (forall ( (x Real [-42, 21])) true))r<   irD   zs(declare-fun f (Real) Real)
(assert (forall ( (x Real [-42, 21]) (y Real [-100, 3])) (=> (= x y) (= (f x) (f y)))))rr   Trs   ru   rv   rx   d   r>   zx(declare-const c Bool)
(assert (forall ( (a Int [2, 100]) (b Real [2, 100])) (or c (=> (< a b) (< (pow a (/ 1 2)) b))))))Zsympy.logic.boolalgr   rn   r   r   r   r   r;   r   r&   r   rK   r   r   ro   r@   rT   r   r   r   )r   r9   rr   ru   rx   r(   r   r)   test_quantifier_extensions   sP    + 
 r   c                  C   s  t tjg$} tdt tdi| ddks,tW 5 Q R X t tjg2} tttddddt gtdi| ddksptW 5 Q R X t tjg\} tttj	tj
tjtjtjtjtjddtjd	tjd
tjditdtdid| ddkstW 5 Q R X t tjgR} tttj	tj
tjtjtjtjtjddtjd	itdtdid| ddksBtW 5 Q R X t tjgF} tttj	tj
tjtjtjtjtjddtdid| ddkstW 5 Q R X t tjgN} tttj	tj
tjtjtjtjtjddtjditdid| ddkstW 5 Q R X d S )Nrz   ZMY_PI)known_constantsr6   z(pow MY_PI -1)gQ	@Fr|   z&(assert (= MY_PI 3.14))
(pow MY_PI -1)pry   r:   plusr   rD   )r   rh   	precisionr6   z!(plus 0 1 -1 (/ 1 2) (exp 1) p g)z$(plus 0 1 -1 (/ 1 2) (exp 1) p 1.62))rh   r   r6   z$(plus 0 1 -1 (/ 1 2) 2.72 3.14 1.62)z!(plus 0 1 -1 (/ 1 2) e 3.14 1.62))r;   r   r'   r   r
   r@   r   r   r	   ZZeroZOneZNegativeOneZHalfZExp1PiZGoldenRatior   rA   r(   r(   r)   test_mix_number_mult_symbols7  s    
                     r   c                  C   s  t g h} ttt@ | ddks"ttttB | ddks:ttt | ddksPtttt@ t@ | ddksltW 5 Q R X t tjg(} ttt @ tdkB | ddkstW 5 Q R X td}td	}td
}t tjgR} tt	|ttt
t|tg|ttgtf |ttgtf i| ddks"tW 5 Q R X t g R} tt|ttt
t|tg|ttgtf |ttgtf i| ddkstW 5 Q R X t g x} tt|ttt||ttt|||ttg|ttgtf |ttgtf |ttgtf i| ddkstW 5 Q R X d S )Nr>   z@(declare-const x Bool)
(declare-const y Bool)
(assert (and x y))z?(declare-const x Bool)
(declare-const y Bool)
(assert (or x y))z'(declare-const x Bool)
(assert (not x))zY(declare-const x Bool)
(declare-const y Bool)
(declare-const z Bool)
(assert (and x y z))rD   zj(declare-const x Bool)
(declare-const y Bool)
(declare-const z Real)
(assert (or (> z 3) (and x (not y))))r   ry   hrj   z(declare-const x Bool)
(declare-const y Real)
(declare-const z Bool)
(declare-fun f (Bool) Int)
(declare-fun g (Bool) Int)
(assert (> (f x) y))
(assert (< y (g z)))z(declare-const x Bool)
(declare-const y Int)
(declare-const z Bool)
(declare-fun f (Bool) Int)
(declare-fun g (Bool) Int)
(assert (= (f x) y))
(assert (< y (g z)))z(declare-const x Real)
(declare-const y Int)
(declare-const z Bool)
(declare-fun f (Real) Int)
(declare-fun g (Int) Bool)
(declare-fun h (Bool) Real)
(assert (= (f x) y))
(assert (= (g (f x)) z))
(assert (= (h (g (f x))) x)))r;   r   rK   rT   r@   rp   r   r&   r   r   r   r   rm   rl   r   ro   )r9   r   ry   r   r(   r(   r)   test_boolean}  sn    
&,   
   
   
r   c                	      s  t tjtjg2ttttdk ftd dfdddks>tW 5 Q R X t tjtjgRtttd tdk ftd tdk ftd tdk ftd	 dfddd
kstW 5 Q R X tttdk ftd tdkftttdkf t tjtjgt	t fdd W 5 Q R X d S )Nrz   r<   TFrJ   z(ite (< x 1) x (pow x 2))rD   rC      zQ(ite (< x 1) (pow x 2) (ite (< x 2) (pow x 3) (ite (< x 3) (pow x 4) (pow x 5))))r   c                      s   t  dS rV   r   r(   r~   r9   r(   r)   rX     rY   z'test_smtlib_piecewise.<locals>.<lambda>)
r;   r   r&   r'   r   r   rK   r@   r   r   r(   r(   r   r)   test_smtlib_piecewise  s2    

,r   c               	   C   s   t ttdk ftd df} ttjtjg}td|  |ddksDtW 5 Q R X ttjtjg}t| t |ddksxtW 5 Q R X ttjtjtjg"}t| tt  |ddkstW 5 Q R X ttjtjg}t| d |dd	kstW 5 Q R X d S )
Nrz   r<   Tr>   z6(declare-const x Real)
(* 2 (ite (< x 1) x (pow x 2)))z?(declare-const x Real)
(* (pow x -1) (ite (< x 1) x (pow x 2)))za(declare-const x Real)
(declare-const y Real)
(* (pow x -1) (pow y -1) (ite (< x 1) x (pow x 2)))rD   z<(declare-const x Real)
(* (/ 1 3) (ite (< x 1) x (pow x 2))))	r   rK   r;   r   r&   r'   r   r@   rT   )pwr9   r(   r(   r)   !test_smtlib_piecewise_times_const  s    ""&r   c               	   C   s   t g } tdd| ddks ttd| ddks4tttj| ddksJtttj| ddks`ttd| ddkstttdd| ddkstW 5 Q R X d S )	NTF)Zauto_assertr6   truer>   z(assert true)z(assert false)false)r;   r   r@   r	   r   r   rA   r(   r(   r)   test_smtlib_boolean  s    
r   c                	      sf   t d ttjtjgtt fdd W 5 Q R X ttjgttfdd W 5 Q R X d S )Nr   c                      s&   t  tt ttgtf idS )Nrj   )r   rK   diffr   ro   r(   r   r9   r(   r)   rX   !  rY   z$test_not_supported.<locals>.<lambda>c                      s   t tj dS rV   )r   r	   ZComplexInfinityr(   rA   r(   r)   rX   #  rY   )r   r;   r   r&   r'   r   KeyErrorr(   r(   r   r)   test_not_supported  s
    r   c                   C   s4   t ddkstt ddks tt ddks0td S )Ng        z0.0geK<z(* 3.0 (pow 10 -18))g333333@z5.3)r   r@   r(   r(   r(   r)   
test_Float&  s    r   )>
contextlibr0   r#   typingenumr   r   rn   r   r   r   Z
sympy.corer   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   Zsympy.functionsr   r   r   r   Zsympy.assumptions.askr   Zsympy.printing.smtlibr   Zsympy.testing.pytestr   r   rK   rT   rp   r   contextmanagerIterabler;   rB   rL   rU   ra   rf   rq   r   r   r   r   r   r   r   r   r   r   r(   r(   r(   r)   <module>   sB   <	
	@.XFX#
