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;; The background theory
(set-logic NRA)
(define-fun sqr ((x Real)) Real (* x x))
;(define-fun sqr ((x Real)) Real (ite (>= x 0) x (- x) ))
(define-fun error ((x Real)) Real (ite (> x 0) x (* (- 1) x) ) )
(define-fun transitionX ((x Real) (xP Real)) Real
(ite (> xP 0) (- x 1) (ite (= xP 0) x (+ x 1)))
)
(define-fun transitionY ((y Real) (yP Real)) Real
(ite (> yP 0) (- y 1) (ite (= yP 0) y (+ y 1)))
)
(synth-fun inCircle ((x Real) (y Real) (x_p Real) (y_p Real)) Bool
;; Declare the non-terminals that would be used in the grammar
( (B Bool) (R Real) (C Real))
(
(B Bool ( (<= R (sqr C)) ))
(R Real (
(+ (sqr (- x_p (+ (* C x) (* C y) 0 ) ))
(sqr (- y_p (+ (* C x) (* C y) 0 ) ))
)
)
)
(C Real ( (Constant Real) )
)
)
)
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(synth-fun inCircle2 ((x Real) (y Real) (x_p Real) (y_p Real)) Bool
;; Declare the non-terminals that would be used in the grammar
( (B Bool) (R Real) (C Real))
(
(B Bool ( (= R (sqr C)) ))
(R Real (
(+ (sqr (- x_p (+ (* C x) (* C y) 0 ) ))
(sqr (- y_p (+ (* C x) (* C y) 0 ) ))
)
)
)
(C Real ( (Constant Real) )
)
)
)
(synth-fun inShape ((x Real) (y Real) (x_p Real) (y_p Real)) Bool
;; Declare the non-terminals that would be used in the grammar
;((B Bool))
(
(B Bool ( (inCircle x y x_p y_p ) (inCircle2 x y x_p y_p) )
)
)
)
;; Define the semantic constraints on the function
(constraint (= (inShape 10 (- 10) 11 (- 11) ) true ) )
(constraint (= (inShape 10 (- 10) 9 (- 9) ) true ) )
(constraint (= (inShape 1 1 2 2 ) false) )