Interpreter za parcijalno rekurzivne funkcije

master's thesis

• Title (english): Interpreter for partially recursive functions
• Author: Marko Eterović
• Mentor: Vedran Čačić (mentor)
• Committee member: Vedran Čačić (predsjednik povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Matej Mihelčić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-11-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu proučavamo parcijalno rekurzivne funkcije te izrađujemo interpreter za njih. U prvom poglavlju definiramo inicijalne funkcije i tri osnovne operacije (kompoziciju, primitivnu rekurziju i minimizaciju) na funkcijama i relacijama. Dokazujemo da je skup Python-izračunljivih funkcija zatvoren na te tri operacije. Definiramo neke dodatne funkcije, operacije i logičke operatore te dokazujemo njihovu primitivnu rekurzivnost. U drugom poglavlju koristimo framework vepar kako bismo u Pythonu izradili interpreter koji podržava sve funkcije i operacije na funkcijama definirane u prvom poglavlju. Kroz poglavlje postupno dodajemo nove funkcionalnosti u interpreter i opisujemo razne mogućnosti vepra.

Abstract (english)

In this paper we study partial recursive functions and develop an intepreter for them. In the first chapter we define initial functions and three primary operations (composition, primitive recursion and minimisation) on functions and relations. We prove that the set of all Python-computable functions is closed under those three operations. We define some other functions, operations and logical operators and prove they are primitive recursive (or that they preserve primitive recursivity). In the second chapter we use a framework called vepar to develop an interpreter in Python which supports all functions and operations on functions defined in the first chapter. Throughout the chapter we incrementally add new functionalities to the interpreter and describe various capabilities of vepar.

• Keywords: skup Python-izračunljivih funkcija; framework vepar
• Keywords (english): Python-computable functions; framework called vepar
• Language: croatian
• URN:NBN: urn:nbn:hr:217:641266
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar računarstva i matematike (sveučilišni magistar računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-12 10:52:22