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 ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." "Dr." (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 "Nancy FreeHafer") "Dr. Nancy"))
(constraint (= (f "Andrew Cencici") "Dr. Andrew"))
(constraint (= (f "Jan Kotas") "Dr. Jan"))
(constraint (= (f "Mariya Sergienko") "Dr. Mariya"))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.++ (str.++ "Dr." " ") (str.substr name 0 (str.indexof name " " 0))))

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." "Dr." (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 name String)
(constraint (= (f "Nancy FreeHafer") "Dr. Nancy"))
(constraint (= (f "Andrew Cencici") "Dr. Andrew"))
(constraint (= (f "Jan Kotas") "Dr. Jan"))
(constraint (= (f "Mariya Sergienko") "Dr. Mariya"))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.++ (str.++ "Dr." " ") (str.substr name 0 (str.indexof name " " 0))))

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." "Dr." "D" "r" (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") "Dr. Launa"))
(constraint (= (f "Lakenya Edison") "Dr. Lakenya"))
(constraint (= (f "Brendan Hage") "Dr. Brendan"))
(constraint (= (f "Bradford Lango") "Dr. Bradford"))
(constraint (= (f "Rudolf Akiyama") "Dr. Rudolf"))
(constraint (= (f "Lara Constable") "Dr. Lara"))
(constraint (= (f "Madelaine Ghoston") "Dr. Madelaine"))
(constraint (= (f "Salley Hornak") "Dr. Salley"))
(constraint (= (f "Micha Junkin") "Dr. Micha"))
(constraint (= (f "Teddy Bobo") "Dr. Teddy"))
(constraint (= (f "Coralee Scalia") "Dr. Coralee"))
(constraint (= (f "Jeff Quashie") "Dr. Jeff"))
(constraint (= (f "Vena Babiarz") "Dr. Vena"))
(constraint (= (f "Karrie Lain") "Dr. Karrie"))
(constraint (= (f "Tobias Dermody") "Dr. Tobias"))
(constraint (= (f "Celsa Hopkins") "Dr. Celsa"))
(constraint (= (f "Kimberley Halpern") "Dr. Kimberley"))
(constraint (= (f "Phillip Rowden") "Dr. Phillip"))
(constraint (= (f "Elias Neil") "Dr. Elias"))
(constraint (= (f "Lashanda Cortes") "Dr. Lashanda"))
(constraint (= (f "Mackenzie Spell") "Dr. Mackenzie"))
(constraint (= (f "Kathlyn Eccleston") "Dr. Kathlyn"))
(constraint (= (f "Georgina Brescia") "Dr. Georgina"))
(constraint (= (f "Beata Miah") "Dr. Beata"))
(constraint (= (f "Desiree Seamons") "Dr. Desiree"))
(constraint (= (f "Jeanice Soderstrom") "Dr. Jeanice"))
(constraint (= (f "Mariel Jurgens") "Dr. Mariel"))
(constraint (= (f "Alida Bogle") "Dr. Alida"))
(constraint (= (f "Jacqualine Olague") "Dr. Jacqualine"))
(constraint (= (f "Joaquin Clasen") "Dr. Joaquin"))
(constraint (= (f "Samuel Richert") "Dr. Samuel"))
(constraint (= (f "Malissa Marcus") "Dr. Malissa"))
(constraint (= (f "Alaina Partida") "Dr. Alaina"))
(constraint (= (f "Trinidad Mulloy") "Dr. Trinidad"))
(constraint (= (f "Carlene Garrard") "Dr. Carlene"))
(constraint (= (f "Melodi Chism") "Dr. Melodi"))
(constraint (= (f "Bess Chilcott") "Dr. Bess"))
(constraint (= (f "Chong Aylward") "Dr. Chong"))
(constraint (= (f "Jani Ramthun") "Dr. Jani"))
(constraint (= (f "Jacquiline Heintz") "Dr. Jacquiline"))
(constraint (= (f "Hayley Marquess") "Dr. Hayley"))
(constraint (= (f "Andria Spagnoli") "Dr. Andria"))
(constraint (= (f "Irwin Covelli") "Dr. Irwin"))
(constraint (= (f "Gertude Montiel") "Dr. Gertude"))
(constraint (= (f "Stefany Reily") "Dr. Stefany"))
(constraint (= (f "Rae Mcgaughey") "Dr. Rae"))
(constraint (= (f "Cruz Latimore") "Dr. Cruz"))
(constraint (= (f "Maryann Casler") "Dr. Maryann"))
(constraint (= (f "Annalisa Gregori") "Dr. Annalisa"))
(constraint (= (f "Jenee Pannell") "Dr. Jenee"))

(check-synth)
Solution:
(define-fun f ((name String)) String (str.++ (str.++ "Dr." " ") (str.substr name 0 (str.indexof name " " 0))))

Question:
(set-logic SLIA)

(synth-fun f ((name String)) String
    ((Start String) (ntString String) (ntInt Int) (ntBool Bool))
    ((Start String (ntString))
    (ntString String (name " " "." "Dr." (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 "Nancy FreeHafer") "Dr. Nancy"))
(constraint (= (f "Andrew Cencici") "Dr. Andrew"))
(constraint (= (f "Jan Kotas") "Dr. Jan"))
(constraint (= (f "Mariya Sergienko") "Dr. Mariya"))

(check-synth)
Solution:


Output grammar:
root ::= "(define-fun f ((name String)) String " Start ")"
Start ::= ntString
ntString ::= "name" | "\" \"" | "\".\"" | "\"Dr.\"" | "(" "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 ")"