Well-founded semantics for dependent, recursive record types with type complement

Bc. Jozef Mikušinec

Master's thesis

Abstract:

Táto práca definuje dobre založenú sémantiku pre vysoko expresívny typový systém, ktorý zahrňuje záznamové typy, typové zjednotenie, prienik a doplnok, a kvantifikátory. Na rozdiel od predošlých prístupov, ktoré skúmajú typový doplnok, my nekladieme syntaktické reštrikcie na typové definície – dobre založená sémantika dáva význam na všetky z nich, vrátane tých, ktoré sú sporné v klasickom zmysle (ako T = nie T), pomocou práce v troj-stavovom prostredí, kde každý prvok buď určite patrí do typu, určite nepatrí, alebo je v dodatočnom špeciálnom stave, "nedeterminovaný". Naviac, my skúmame tri (zväčša) syntaktické podmienky (konkrétne, lokálna a globálna stratifikácia, a kontraktivita), ktoré každá garantujú, že typové definície ich spĺňajúce sú klasické (dvoj-stavové), a dokážeme tento fakt.

Abstract:

This thesis defines a well-founded semantics for a highly expressive type system that includes record types, type union, intersection and complement, and quantifiers. Unlike previous approaches that investigate type complement, we place no syntactic restrictions on type definitions – well-founded semantics gives meaning to all of them, including those that are contradictory in the classical sense (like T = not T), by working in a three-valued setting where every element either definitely belongs to a type, definitely does not, or is in an additional special state, "undetermined". In addition, we study three (mostly) syntactic conditions (namely, local and global stratifiability, and contractiveness), which each guarantee that the type definitions satisfying them are classical (two-valued), and prove this fact.

Keywords

well-founded semantics, type complement, set-theoretic types, recursive types, quantified types, WFRQ, stratifiability

Language used: English

Date on which the thesis was submitted / produced: 17. 5. 2022

Thesis defence

• Date of defence: 21. 6. 2022
• Supervisor: doc. Mgr. Jan Obdržálek, PhD.
• Reader: Dr. rer. nat. Achim Blumensath

Masaryk University

Faculty of Informatics

Master programme / field:
Theoretical computer science / Principles of programming languages