Matija Pretnar
Faculty of Mathematics and Physics, University of Ljubljana
Jadranska 21,
SI-1000 Ljubljana
tel: +386 1 4766 668
mail: matija.pretnar@fmf.uni-lj.si
GitHub: matijapretnar
ORCID iD: 0000-0001-7755-2303
Bibliography:
COBISS
DBLP
Scholar
Scopus
Sicris
Research
I study formalization, implementation, and semantics of programming languages. My current research is focused on algebraic effects and their handlers.
- Eff: A functional programming language based on algebraic effect handlers
- Millet: An ML-like pure functional language that can be used as a template for creating your own language
- Æff: An interactive interpreter for asynchronous algebraic effects
Teaching
I work at the Faculty of Mathematics and Physics, where I mostly teach computer science courses.
- Introduction to programming (Uvod v programiranje): lecture notes (in Slovene)
- Programming 1: lecture notes (in Slovene)
- Theory of programming languages: lecture notes (in Slovene)
- Projekt Tomo: Web service for teaching programming
- Nadlogar: Web service for generating exercises
- Urnik: Web service for displaying and editing timetables
- LaTeX package for assembling exam papers
Activity
Titles of supervised theses are given in Slovenian, as registered.
-
2026
-
Talk
Mathematical Foundations for Symmetric Programming
- IFIP WG2.1 meeting #84
- 29 April 2026
- Vihula
Abstract
We propose abstractions for exploiting symmetries in programming and reasoning based on the mathematical proof principle “without-loss-of-generality” (wlog). We decompose such arguments into three components. The first component makes the symmetry explicit by defining appropriate groups and their action on the input/assumptions and output/conclusions. The second component explicates how to canonise the input, by choosing appropriate symmetries for each input. The third component is a core function/proof that transforms canonical inputs into outputs. The proposed wlog construct combines these components: given an input, calculate its canonising symmetry, use the symmetry to canonise the input, apply the core function to the canonical input, and apply the inverse symmetry to the output.
We illustrate the approach on running examples: sliding-tile merges in 2048, binary-tree insertion, and Schur’s inequality as a mathematical instance of WLOG. We extend the framework to algebraic datatypes using initial algebra semantics, showing how a G-symmetry strength on a functor lifts group actions to inductive types and that the unique fold into an equivariant algebra is itself equivariant, allowing us to avoid using general recursion to define a symmetric version of tree insertion. Finally, we develop the theory of equivariant canonisers and explore the cases when the WLOG construction is guaranteed to produce an equivariant function. Additionally, we recast the well-known Orbit-Stabiliser theorem in terms of an equivariant isomorphism.
Joint work with Ohad Kammar.
-
Talk
Uvod v kvantno računalništvo
- FMF seminar za učitelje matematike
- 23 January 2026
- Ljubljana
- Mathematica
-
Professional service
- Programme committee, OOPSLA
-
Talk
-
2025
-
Talk
Symmetric programming
- IFIP WG2.1 meeting #83
- 8 September 2025
- Viana do Castelo
Abstract
In computer science, symmetry in data structures such as binary search trees is often handled either by code replication or by clever tricks that unify symmetric cases. This talk explores a mathematical framework based on group actions, which captures such constructions directly and uniformly. It also provides a natural way to express proofs that rely on “without loss of generality” (wlog), a mathematical staple whose computational significance is increasingly important with the proliferation of proof assistants.
Joint work with Ohad Kammar.
-
Professional service
-
Vice-Dean for Informatics, UL FMF
- 2025–2027
- Programme committee, FoSSaCS
-
Vice-Dean for Informatics, UL FMF
-
Talk
-
2024
- Journal article
- Journal article
-
Talk
A case study in mathematically inspired language constructs
- IFIP WG2.1 meeting #81
- 5 April 2024
- Neustadt
Abstract
Even though the mathematical core of algebraic effect handlers has remained unchanged, they have evolved into a more useful programming construct since their introduction. In the talk, I will talk about steps (and one missed opportunity!) on the way to their discovery, initial considerations behind their design, and lessons learnt along the way.
-
Talk
Effect handlers and mathematically inspired language constructs
- Structures de contrôle : de « goto » aux effets algébriques
- 7 March 2024
- Collège de France, Paris
Abstract
Effect handlers are a programming language construct able to express and combine diverse computational features such as backtracking, stream redirection, multiple scheduling strategies, or continuations. This flexibility comes as no surprise since handlers are based on even more versatile homomorphisms of algebraic theories. Even though the design of handlers witnessed multiple iterations and extensions, their mathematical core remained unchanged.
In this seminar, I will discuss the discovery of effect handlers and initial considerations behind their design, in particular steps required when translating a mathematical concept into a useful programming tool. We shall also take a look at subsequent research on handlers, for example various effect systems or an efficient transpiler to OCaml, comparing features guided by mathematics and those with a more practical motivation.
-
Professional service
- Programme committee, ESOP
- Programme committee, APLAS
-
2023
- Journal article
- Journal article
- Journal article
-
Talk
The state of Eff
- NII Shonan Meeting (No.203) – Effect Handlers and General-Purpose Languages
- 26 September 2023
- Shonan (remotely)
- PDF with presenter notes
Abstract
The talk describes the history and the current state of Eff, the first programming language with native support of algebraic effect handlers. The first version of Eff was developed by Andrej Bauer and myself and appeared in 2010. It was untyped and had a syntax similar to Python. In the next version in 2011, we introduced the more commonly known ML-like syntax and dynamic generation of effect instances that worked analogously to references in OCaml. After that, the versions are a bit harder to reconstruct, but the main improvement was a subtyping-based effect system.
Building on the effect system, the next goal for Eff was an optimizing compiler, on which I worked together with Tom Schrijvers and his students. The compiler would produce efficient code by inlining handlers as much as possible, and monadically embed the rest in OCaml. It soon became obvious that the effect system has to be more robust, which was achieved by using coercions as explicit witnesses of subtyping. Currently, Filip Koprivec, my PhD student, focuses on simplifying those witnesses in the polymorphic setting, as otherwise each coercion needs to be passed around as an additional parameter at runtime. In parallel to the optimizing compiler project, Žiga Lukšič developed EEff, a variant of Eff that tracks algebraic equations between operations that have to be respected by the handlers. Currently, EEff only prints out the obligations, though one could envision sending them to an SMT solver or producing specifications for a proof assistant.
Finally, the talk mentions Millet, a language one can use as a basis when developing a prototype language exploring an interesting novel idea. Millet implements all the boring and expected components of a programming language (parsing, algebraic datatypes, simple type-checking, interactive toplevel, compilation pipeline, …), and any fork just needs to extend all the components with the support for the additional features. Then, any later change to Millet (right now, a module system, a Wasm backend, and LSP support are in the works) should be orthogonal and can hopefully be merged into forks with not too much additional work.
-
Talk
Simplifying explicit subtyping
- IFIP WG2.1 meeting #80
- 18 July 2023
- Oxford
- Notes
Abstract
Our recent work (Karachalias et al., OOPSLA 2021) has shown that code written using the full flexibility of handlers can be transformed into a pure one that matches the performance of a conventional handcrafted one. However, to do so, the compiler tracks effect information through explicit subtyping coercions, and for polymorphic functions, these need to be passed around as additional parameters. Since subtyping coercions are inferred automatically, their number grows with the size of the program, which drastically reduces the performance. To avoid this, all polymorphic functions need to be annotated with particular types, or monomorphised by the compiler, neither of which is a satisfactory solution. In the talk, I will describe a simple algorithm that drastically, yet soundly, reduces (and often completely eliminates) redundant coercion parameters, leading to a performance comparable to monomorphic code.
-
Talk
Asynchronous Effects
- Scottish Programming Languages Seminar
- 7 June 2023
- University of the West of Scotland, Paisley
- SPLS
Abstract
In the standard algebraic approach to effects, once an operation is called, the evaluation of the continuation stalls until it gets a result (either from a built-in primitive effect or through a handler). But we often desire asynchronous behaviour, when the continuation may proceed with the evaluation and suitably incorporates the result once it arrives. I will describe a small calculus with primitives for sending such signals and receiving corresponding interrupts, and show a small prototype in which one can express promises, preemptive multi-threading and remote function calls.
Joint work with Danel Ahman.
-
Professional service
- Programme committee, OCaml Workshop
- Programme committee, ML Family Workshop
-
2022
- Supervision
-
Professional service
-
Organizing committee, OCaml Users and Developers Workshop
- 2022–2027
- Programme committee chair, OCaml Workshop
- Programme committee, ICFP
- Programme committee, TYPES
- Programme committee, ML Family Workshop
-
Organizing committee, OCaml Users and Developers Workshop
-
2021
-
Conference paper
(Higher-order) asynchronous effects
- Scalable handling of effects : Report from Dagstuhl Seminar 21292
- Journal article
- Journal article
-
Talk
Spletna storitev za generiranje nalog
- FMF seminar za učitelje matematike, Fakulteta za matematiko in fiziko
- 25 September 2021
- Ljubljana
-
Talk
Efficient compilation of algebraic effect handlers
- Dagstuhl Seminar 21292
- 21 July 2021
- Dagstuhl (remotely)
Abstract
The popularity of algebraic effect handlers as a programming language feature for user-defined computational effects is steadily growing. Yet, even though efficient runtime representations have already been studied, most handler-based programs are still much slower than hand-written code.
This paper shows that the performance gap can be drastically narrowed (in some cases even closed) by means of type-and-effect directed optimising compilation. Our approach consists of source-to-source transformations in two phases of the compilation pipeline. Firstly, elementary rewrites, aided by judicious function specialisation, exploit the explicit type and effect information of the compiler’s core language to aggressively reduce handler applications. Secondly, after erasing the effect information further rewrites in the backend of the compiler emit tight code.
This work comes with a practical implementation: an optimizing compiler from Eff, an ML style language with algebraic effect handlers, to OCaml. Experimental evaluation with this implementation demonstrates that in a number of benchmarks, our approach eliminates much of the overhead of handlers, outperforms capability-passing style compilation and yields competitive performance compared to hand-written OCaml code as well Multicore OCaml’s dedicated runtime support.
-
Talk
Introduction to Quantum Computing
Abstract
We often read in the media that quantum computers are fast because quantum superposition allows them to be in multiple states at once, enabling them to explore all the possible solutions in a single step.
As we shall see, things are not that simple because, in the end, we can observe only one randomly chosen result, which is likely not going to be the one we need. After all, with all the possible solutions out there, what’s the guarantee that the one we want is the one randomly chosen by the quantum computer? So we want to be able to increase the probability of getting the solution we want from among all the possible paths.
What can be done is to use interference to cancel out all the undesirable paths and unwanted solutions. Although we still end up with a randomly chosen path, it is a path chosen from among the ones we want.
- Supervision
-
Conference paper
-
2020
- Journal article
- Journal article
-
Talk
Kvantno računalništvo
- Gimnazija Bežigrad
- 23 January 2020
- Ljubljana
-
Talk
Asynchronous operations
- IFIP WG2.1 meeting #79
- 8 January 2020
- Otterlo
Abstract
In the standard algebraic approach to effects, once an operation is called, the evaluation of the continuation stalls until it gets a result (either from a built-in primitive effect or through a handler). But we often desire asynchronous behaviour, when the continuation may proceed with the evaluation and suitably incorporates the result once it arrives. I will describe a small calculus with primitives for sending and receiving such signals.
Joint work with Danel Ahman.
- Supervision
-
Professional service
-
Full member, IFIP Working Group 2.1 on Algorithmic Languages and Calculi
- 2020–
- Programme committee, LOLA
-
Full member, IFIP Working Group 2.1 on Algorithmic Languages and Calculi
-
2019
- Journal article
-
Talk
Bringing equations back to algebraic effect handlers
- LFCS seminar
- 2 July 2019
- Edinburgh
Abstract
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory, sacrificing both reasoning power and safety. I will present an alternative approach where the effect system tracks equations that are observed in subparts of the program, yielding a sound and flexible logic, and paving a way for practical optimizations and reasoning tools.
Joint work with Žiga Lukšič
-
Talk
Projekt Tomo
- Maps ∩ Configurations ∩ Polytopes ∩ Molecules ⊆ Graphs: The mathematics of Tomaž Pisanski on the occasion of his 70th birthday
- 23 May 2019
- Ljubljana
Abstract
Projekt Tomo is a web service for teaching programming that works by providing students immediate and low-overhead automated feedback on the correctness of the submitted solutions. In the talk, I will describe the basic principles of the service, its history and how its eponym helped shape it.
-
Talk
Local algebraic effect theories
- Meet The Jury!
- 23 January 2019
- Leuven
Abstract
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory, sacrificing both reasoning power and safety.
We present an alternative approach where the type system tracks equations thar are observed in subparts of the program, yielding a sound and flexible logic, and paving a way for practical optimizations and reasoning tools.
Joint work with Žiga Lukšič.
- Supervision
-
Professional service
-
Head of the programming club, UL FMF
- 2019–
-
Head of the programming club, UL FMF
-
2018
- Conference paper
- Conference paper
-
Talk
Putting reason back into handlers
- IFIP WG2.1 meeting #77
- 3 July 2018
- Brandenburg
Abstract
The main premise of algebraic effects is that effects can be described with an equational theory consisting of a set of operations and equations between them. However, many computationally interesting algebraic effect handlers do not respect these equations, which most approaches nowadays reconcile by assuming a trivial equational theory. I will present an approach in which the expected equations may be encoded in computation types.
Joint work with Žiga Lukšič.
- Supervision
-
Professional service
- Co-organizer, Dagstuhl Seminar 18172 (Algebraic Effect Handlers go Mainstream)
-
Coordinator, BSc and MSc programmes in Computer Science and Mathematics, UL FMF
- 2018–2025
-
2017
-
Conference paper
Modelling the spread of bluetongue in Slovenia.
- ModAH, Nantes, 14 - 16. June 2017
- Journal article
- Journal article
-
Talk
Explicit effects subtyping
- IFIP WG2.1 meeting #76
- 18 October 2017
- Lesbos
- HTML
Abstract
To inform the programmer about the effects of a given program, a bottom up inference algorithm that Eff provides is sufficient. However, for an optimizing compiler, we need access to effects of all subterms. It turned out that adapting the current algorithm is overly error-prone as the core language is implicitly typed and subtyping-based.
In hope of remedying the situation, we present an explicitly-typed polymorphic core calculus, which reifies appeals to subtyping in explicit casts with coercions that witness the subtyping proof. We provide a constraint-based inference algorithm that turns an implicitly-typed term into our calculus, and effect erasure, which allows us to targets an ML-like language with or without support for algebraic effects.
The talk will include a brief introduction to algebraic effect handlers.
Joint work with Amr Hany Saleh, George Karachalias and Tom Schrijvers.
- Supervision
-
Professional service
- Organizer, MFPS and CALCO (joint conferences)
- Programme committee co-chair, LOLA
- Programme committee, HOPE
-
Conference paper
-
2016
-
Conference paper
Capturing algebraic equations in an effect system.
- From theory to practice of algebraic effects and handlers : Report from Dagstuhl Seminar 16112
-
Conference paper
Compiling Eff to OCaml.
- From theory to practice of algebraic effects and handlers : Report from Dagstuhl Seminar 16112
-
Conference paper
No value restriction is needed for algebraic effects and handlers.
- From theory to practice of algebraic effects and handlers : Report from Dagstuhl Seminar 16112
- DBLP
-
Conference paper
Towards an effect system for OCaml.
- From theory to practice of algebraic effects and handlers : Report from Dagstuhl Seminar 16112
-
Conference paper
A tutorial on algebraic effects and handlers.
- From theory to practice of algebraic effects and handlers : Report from Dagstuhl Seminar 16112
-
Conference paper
Executive summary.
- From theory to practice of algebraic effects and handlers : Report from Dagstuhl Seminar 16112
-
Conference paper
Design and implementation of the Andromeda proof assistant
- TYPES 2016 : book of abstracts
- DBLP
-
Conference paper
No value restriction is needed for algebraic effects and handlers
- TYPES 2016 : book of abstracts
- DBLP
-
Talk
Hekerski pristop k statistiki
- FMF seminar za učitelje matematike
- 1 October 2016
- Ljubljana
-
Conference paper
Modeliranje širjenja kužnih bolezni: primer bolezni modrikastega jezika v Sloveniji
- 6. Slovenski veterinarski kongres 2016
-
Supervision
Student supervision
-
Valerija Kac:
Razvoj podatkovne baze za veterinarsko ambulanto
- BSc thesis
- COBISS
-
Valerija Kac:
Razvoj podatkovne baze za veterinarsko ambulanto
-
Professional service
- Co-organizer, Dagstuhl Seminar 16112 (From Theory to Practice of Algebraic Effects and Handlers)
-
Timetable system for UL FMF, set up and developed
- 2016–2021
- AFlabs later built the university-wide timetable solution on top of this service.
- Programme committee, IFL
-
Conference paper
-
2015
-
Talk
A low overhead automated service for teaching programming
- Koli Calling 2015
- 20 November 2015
- Koli
Abstract
Programming is a skill that often demands that students engage in a significantly high amount of individual practice and experimentation in order to acquire basic competence. Teachers are required to both encourage students by exposing them to numerous problems and supervise the students’ attempts to solve them.
To support this teaching approach we developed a web service called Projekt Tomo, presented in the article. The service is designed in such a way that it requires little or no additional work from students and teachers, enabling them to focus on the content. Furthermore, the service can be used in almost all teaching environments, as it can be adapted to most programming languages and has minor technical requirements.
Joint work with Matija Lokar.
-
Conference paper
A low overhead automated service for teaching programming.
- 15th Koli Calling Conference on Computing Education Research, November 19-22, 2015
- DOI
-
Conference paper
An introduction to algebraic effects and handlers. Invited tutorial paper.
- The 31st Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXI)
- DOI
-
Talk
An Introduction to Algebraic Effects and Handlers
- MFPS XXXI
- 22 June 2015
- Nijmegen
-
Conference paper
Preparing programming exercises with efficient automated validation tests.
- International Conference on Informatics in Schools - ISSEP 2015
- Journal article
-
Conference paper
A web service for teaching programming.
- International Conference on Informatics in Schools - ISSEP 2015, September 28- October 1, Ljubljana, Slovenia
-
Conference paper
YASAAPE - Yet Another System for Automatic Assessment of Programming Exercises.
- International Conference on Informatics in Schools - ISSEP 2015, September 28- October 1, Ljubljana, Slovenia
- Supervision
-
Professional service
-
Boter, administrative records system for UL FMF, set up and developed
- 2015–2020
-
Boter, administrative records system for UL FMF, set up and developed
-
Talk
-
2014
- Journal article
- Journal article
-
Journal article
Osnove kvantnega računalništva, 2. del
- Obzornik za matematiko in fiziko
-
Conference paper
Spletna storitev za poučevanje programiranja.
- Vzgoja in izobraževanje v informacijski družbi - VIVID 2014
-
2013
- Conference paper
- Journal article
-
Journal article
Osnove kvantnega računalništva, 1. del.
- Obzornik za matematiko in fiziko
- Supervision
-
2012
-
Supervision
Student supervision
-
Supervision
-
2011
-
Talk
The f-calculus
- Domains X
- 5 September 2011
- Swansea
Abstract
To see how useful Plotkin and Power’s algebraic effects are in programming, Andrej Bauer and I have developed a language called eff, based on such an approach. As it turns out, eff is very suitable for writing programs that use nondeterminism, rollback, delimited continuations, scheduling, and many other effects. In the talk, I will present the f-calculus, which formalizes eff’s core, its type system, and its semantics.
-
Professional service
- Co-organizer, European Workshop on Computational Effects
-
Talk
-
2010
-
Thesis
The logic and handling of algebraic effects
- University of Edinburgh
- COBISS
-
Professional service
-
Secretary, Slovenian branch of the ACM
- 2010–2012
-
Secretary, Slovenian branch of the ACM
-
Thesis
-
2009
-
Conference paper
Handlers of algebraic effects.
- 18th European Symposium on Programming, ESOP 2009
- ETAPS 2022 Test of Time Award
- DOI
-
Professional service
- Co-organizer, 6th International Conference on Computability and Complexity in Analysis (CCA)
-
Moodle administrator, UL FMF
- 2009–
-
Conference paper
-
2008
-
Conference paper
A logic for algebraic effects.
- Twenty-third Annual IEEE Symposium on Logic in Computer Science, LICS 2008
- DOI
-
Conference paper
-
2005
-
Thesis
Sintetična topologija
- University of Ljubljana
- Faculty Prešeren Award
-
Thesis