Table Of Links Taboolaanshaha ABSTRACT Haku 1 INTRODUCTION 1 Qalabka 2 DEPENDENTLY-TYPED OBJECT-ORIENTED PROGRAMMING 2 Qalabka dhismaha dhismaha dhismaha 3 CASE STUDY 3 Qalabka 4 DESIGN CONSTRAINTS AND SOLUTIONS 4 Qalabka iyo Solution Design 5 FORMALIZATION 5 Qalabka 6 DE/REFUNCTIONALIZATION 6 De / Refunctionalization 7 FUTURE WORK 7 Qiimeeyaasha 8 RELATED WORK 8 Qalabka Qalabka 9   CONCLUSION AND REFERENCES 9 Tusaale iyo References Shuruudaha Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Ma rabtaa in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay. 2.1 Method Call Syntax and Self Parameters Waayo, waxaa laga yaabaa in ay ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah Sida loo yaabaa, waxaan ka heli karo Agda ka mid ah Figure 4 ah, booleans waxaa la aasaasay sida daawada data, negation waxaa la aasaasay sida function non-dependent ka booleans, iyo neg_- inverse waxaa la aasaasay sida function dependent ka mid ah boolean x ka aasaasay sida x waa neg(neg x). In our nidaamka, waxaan u baahan tahay in la xiriyaan sida neg iyo neg_inverse oo aan la isticmaalo function non-dependent ama dependent. Def Bool.neg: Bool { True => False, False => True } Marka aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Waayo, waxaa laga yaabaa in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Shuruudaha ugu horeysay ee codata-ka dhismaha waaweyn ee codata-ka dhismaha: auto-parameters in destructors. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Waayo, waxaa laga yaabaa in codata iyo codata, waxaa loo isticmaali karaa in la isticmaali karaa interfaces iyo class. 2.2 Verified Interfaces and Classes Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Waxa uu isticmaali karaa mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Waxaad u aragto, sida loo isticmaali karo (co)pattern caadiga ah, ka mid ah macluumaad pattern caadiga ah waxaa loo yaqaan 'absurd'. Waxaad ku yaalaa in la isticmaali karaa interfaces buffer for the empty buffer, waxaan u baahan yahay in la isticmaali karaa methode read sida waxaa la isticmaali karaa in la isticmaali karaa. Waxaan sidoo kale soojiyo si ay u aragto extrinsic, oo aad u aragto in ay u aragto objectadaadaada. Jacobs [1995] waxay ku dhigi karaa dhismaha ugu horeysay ee sida loo yaabaa in aad u aragto. Waxay ku sugeeyaan nidaamka dhismaha coalgebraic oo loo isticmaali karaa si ay u aragto dhismaha object-oriented. Si kastaba ha ahaatee, Figuur 5a wuxuu ku yaalaa dhismaha coalgebraic for a one-element buffer that exhibits persistent read (PR) behavior: Ka dib markii a element waa ku salaysan, waa in ay ku yaalaa loo isticmaali karaa nidaamka store. Markaas, waxa uu u baahan tahay in ay ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid 2.3 Dependent Functions Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Waayo, waxaa laga yaabaa in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Waayo, sidoo kale waxaa loo yaabaa in ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad (Goetz et al. 2014; Setzer 2003) ee Java 8. Sida loo isticmaali karaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah 2.4 Weak and Strong Dependent Pairs Sida loo yaqaan 'P-type', waxaan u baahan tahay in ay ku yaalaa codata type4, laakiin sida loo yaqaan 'S-type', waxaan sidoo kale ka heli karaa in ay ku saabsan codata-type ama data-type. Taasi waa in loo yaqaan 'S-type' iyo 'S-type' (Howard 1980): 'S-type' waxay ku yaalaa codata-type oo ka mid ah two-projections, oo ku saabsan codata-type waxaa ka mid ah codata-type iyo codata-type. Waxaad ka soo xigtay in la soo xigtay oo ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Markaas ah, Agda waxay ku yaalaa Σ-types ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah, laakiin waxaa ka mid ah wax soo saarka: Agda waxay ku yaalaa in ay ka mid ah codata-types, iyo codata-types waxay ku yaalaa in ay ka mid ah codata-types, oo ku yaalaa mid ka mid ah codata-types waa mid ka mid ah. Si kastaba ha ahaatee, dhismaha oo ka mid ah codata-type waa mid ah ee Agda, sidaas ka mid ka mid ah codata-type iyo codata-type-type-type. Markaas ka mid ah in ay u baahan tahay in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah. 2.5 Codata Encodings of Natural Numbers Ka dib markii loo yaqaan lambda calculus, warshadaha waxaa ka mid ah coding functional of data types such as booleans, daawada dabiiciga iyo lists. Qalabka klassical ee coding functional waa coding Church, Scott iyo Parigot of data types (cf. Geuvers [2014]; Koopman et al. [2014]). Functions waa ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah coding codata, sidaas waxaan u mid ah mid ka mid ah mid ka mid ah coding codata ka mid ah coding functional. Inta badan codata coding of data types can be obtained by refunctionalizing a data type with an appropriate observation. That the Church coding can be obtained from refunctionalizing a program with Peano numbers and an iter function has already been observed by Ostermann and Jabs [2018]; we rebat this example in Figure 6. Waxaad ku yaalaa in codata nooca in Figure 6b, oo ku yaalaa coding Church of natural numbers, waxaa laga yaabaa in coding coding coding. This corresponds to the well-known theorem that Church coding can be typed in pure system F. If we apply the same method to obtain the Scott or Parigot coding of natural numbers, then we can observe that the resulting codata type is recursive. This corresponds to the other well-known theorem that these coding cannot be typed in pure System F and require recursive types. We can even go one step further. Geuvers [2001] ayaa soo bandhigay in ay ka mid ah codsado ka horay induction ama elimination-dependent. One way to obtain typed functional encodings that can express induction is to add a form of self types to the system; this kind of encoding was introduced by Fu and Stump [2014]. Haddii waa in ay ku yaalaa adeegga caadiga ah, waxaan ahaysaa in la mid ah dhismaha codsado ee Fu iyo Stump waa in la soo bandhigay in our system in Figure 7 and Figure 8. Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid Waxa uu ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa. 
 
 
 Haku: 
 
 
 
 
 David Binder Haku Group Tim Süberkrüb Klaus Ostermann Authors: 
 
 
 
 
 David Qalabka Haku Group Qalabka Qalabka Marka: Klaus Ostermann 
 
 Waxaa laga yaabaa in arkiv ee CC 4.0 license. Waxaa laga yaabaa in arkiv ee CC 4.0 license. xoolaha

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