You are an expert in program synthesis. You are tasked with solving a Syntax-Guided Synthesis (SyGuS) problem. Your goal is to output a function that should produce outputs that satisfy a series of constraints when given specific inputs.

Question:
(set-logic SLIA)

(synth-fun f ((firstname String) (lastname String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (firstname lastname "," " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.to_int ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString) (str.contains ntString ntString)))))

(declare-var firstname String)
(declare-var lastname String)
(constraint (= (f "Launa" "Withers") "Withers, L."))
(constraint (= (f "Lakenya" "Edison") "Edison, L."))
(constraint (= (f "Brendan" "Hage") "Hage, B."))
(constraint (= (f "Bradford" "Lango") "Lango, B."))
(constraint (= (f "Rudolf" "Akiyama") "Akiyama, R."))

(check-synth)
Solution:
(define-fun f ((firstname String) (lastname String)) String (str.++ lastname (str.++ "," (str.++ " " (str.++ (str.at firstname 0) ".")))))

Question:
(set-logic SLIA)

(synth-fun f ((firstname String) (lastname String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (firstname lastname " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.to_int ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString) (str.contains ntString ntString)))))

(declare-var firstname String)
(declare-var lastname String)
(constraint (= (f "Nancy" "FreeHafer") "Nancy F."))
(constraint (= (f "Andrew" "Cencici") "Andrew C."))
(constraint (= (f "Jan" "Kotas") "Jan K."))
(constraint (= (f "Mariya" "Sergienko") "Mariya S."))

(check-synth)
Solution:
(define-fun f ((firstname String) (lastname String)) String (str.++ (str.++ (str.++ firstname " ") (str.at lastname 0)) "."))

Question:
(set-logic SLIA)

(synth-fun f ((firstname String) (lastname String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (firstname lastname " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (str.len ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString)))))

(declare-var firstname String)
(declare-var lastname String)
(constraint (= (f "Launa" "Withers") "L. Withers"))
(constraint (= (f "Lakenya" "Edison") "L. Edison"))
(constraint (= (f "Brendan" "Hage") "B. Hage"))
(constraint (= (f "Bradford" "Lango") "B. Lango"))
(constraint (= (f "Rudolf" "Akiyama") "R. Akiyama"))
(constraint (= (f "Lara" "Constable") "L. Constable"))

(check-synth)
Solution:
(define-fun f ((firstname String) (lastname String)) String (str.++ (str.++ (str.++ (str.at firstname 0) ".") " ") lastname))

Question:
(set-logic SLIA)

(synth-fun f ((firstname String) (lastname String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (firstname lastname " " "." (str.++ ntString ntString) (str.replace ntString ntString ntString) (str.at ntString ntInt) (str.from_int ntInt) (str.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- ntInt ntInt) (str.len ntString) (str.to_int ntString) (str.indexof ntString ntString ntInt)))
    (ntBool Bool (true false (str.prefixof ntString ntString) (str.suffixof ntString ntString) (str.contains ntString ntString)))))

(declare-var firstname String)
(declare-var lastname String)
(constraint (= (f "Nancy" "FreeHafer") "Nancy F."))
(constraint (= (f "Andrew" "Cencici") "Andrew C."))
(constraint (= (f "Jan" "Kotas") "Jan K."))
(constraint (= (f "Mariya" "Sergienko") "Mariya S."))

(check-synth)
Solution:


Output grammar:
root ::= "(define-fun f ((firstname String) (lastname String)) String " Start ")"
Start ::= ntString
ntString ::= "firstname" | "lastname" | "\" \"" | "\".\"" | "(" "str.++" " " ntString " " ntString ")" | "(" "str.replace" " " ntString " " ntString " " ntString ")" | "(" "str.at" " " ntString " " ntInt ")" | "(" "str.from_int" " " ntInt ")" | "(" "str.substr" " " ntString " " ntInt " " ntInt ")"
ntInt ::= "0" | "1" | "2" | "(" "+" " " ntInt " " ntInt ")" | "(" "-" " " ntInt " " ntInt ")" | "(" "str.len" " " ntString ")" | "(" "str.to_int" " " ntString ")" | "(" "str.indexof" " " ntString " " ntString " " ntInt ")"
ntBool ::= "true" | "false" | "(" "str.prefixof" " " ntString " " ntString ")" | "(" "str.suffixof" " " ntString " " ntString ")" | "(" "str.contains" " " ntString " " ntString ")"