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.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- 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") "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.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- 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 "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.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 name 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."))
(constraint (= (f "Lara" "Constable") "Constable, L."))
(constraint (= (f "Madelaine" "Ghoston") "Ghoston, M."))
(constraint (= (f "Salley" "Hornak") "Hornak, S."))
(constraint (= (f "Micha" "Junkin") "Junkin, M."))
(constraint (= (f "Teddy" "Bobo") "Bobo, T."))
(constraint (= (f "Coralee" "Scalia") "Scalia, C."))
(constraint (= (f "Jeff" "Quashie") "Quashie, J."))
(constraint (= (f "Vena" "Babiarz") "Babiarz, V."))
(constraint (= (f "Karrie" "Lain") "Lain, K."))
(constraint (= (f "Tobias" "Dermody") "Dermody, T."))
(constraint (= (f "Celsa" "Hopkins") "Hopkins, C."))
(constraint (= (f "Kimberley" "Halpern") "Halpern, K."))
(constraint (= (f "Phillip" "Rowden") "Rowden, P."))
(constraint (= (f "Elias" "Neil") "Neil, E."))
(constraint (= (f "Lashanda" "Cortes") "Cortes, L."))
(constraint (= (f "Mackenzie" "Spell") "Spell, M."))
(constraint (= (f "Kathlyn" "Eccleston") "Eccleston, K."))
(constraint (= (f "Georgina" "Brescia") "Brescia, G."))
(constraint (= (f "Beata" "Miah") "Miah, B."))
(constraint (= (f "Desiree" "Seamons") "Seamons, D."))
(constraint (= (f "Jeanice" "Soderstrom") "Soderstrom, J."))
(constraint (= (f "Mariel" "Jurgens") "Jurgens, M."))
(constraint (= (f "Alida" "Bogle") "Bogle, A."))
(constraint (= (f "Jacqualine" "Olague") "Olague, J."))
(constraint (= (f "Joaquin" "Clasen") "Clasen, J."))
(constraint (= (f "Samuel" "Richert") "Richert, S."))
(constraint (= (f "Malissa" "Marcus") "Marcus, M."))
(constraint (= (f "Alaina" "Partida") "Partida, A."))
(constraint (= (f "Trinidad" "Mulloy") "Mulloy, T."))
(constraint (= (f "Carlene" "Garrard") "Garrard, C."))
(constraint (= (f "Melodi" "Chism") "Chism, M."))
(constraint (= (f "Bess" "Chilcott") "Chilcott, B."))
(constraint (= (f "Chong" "Aylward") "Aylward, C."))
(constraint (= (f "Jani" "Ramthun") "Ramthun, J."))
(constraint (= (f "Jacquiline" "Heintz") "Heintz, J."))
(constraint (= (f "Hayley" "Marquess") "Marquess, H."))
(constraint (= (f "Andria" "Spagnoli") "Spagnoli, A."))
(constraint (= (f "Irwin" "Covelli") "Covelli, I."))
(constraint (= (f "Gertude" "Montiel") "Montiel, G."))
(constraint (= (f "Stefany" "Reily") "Reily, S."))
(constraint (= (f "Rae" "Mcgaughey") "Mcgaughey, R."))
(constraint (= (f "Cruz" "Latimore") "Latimore, C."))
(constraint (= (f "Maryann" "Casler") "Casler, M."))
(constraint (= (f "Annalisa" "Gregori") "Gregori, A."))
(constraint (= (f "Jenee" "Pannell") "Pannell, J."))

(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.substr ntString ntInt ntInt)))
    (ntInt Int (0 1 2 (+ ntInt ntInt) (- 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") "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:


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.substr" " " ntString " " ntInt " " ntInt ")"
ntInt ::= "0" | "1" | "2" | "(" "+" " " ntInt " " ntInt ")" | "(" "-" " " ntInt " " ntInt ")" | "(" "str.len" " " ntString ")" | "(" "str.indexof" " " ntString " " ntString " " ntInt ")"
ntBool ::= "true" | "false" | "(" "str.prefixof" " " ntString " " ntString ")" | "(" "str.suffixof" " " ntString " " ntString ")"