Steven Schaefer Daniel Calco Max S. New https://stevenschaefer.net/home/ home /home/ About Me false Steven Schaefer I am a PhD candidate at the University of Michigan advised by Max New. I am interested in the mathematical study of programming languages. In particular, I study the application of logic and category theory to the design and implementation of provably correct software. Steven Schaefer 2024 8 6 https://stevenschaefer.net/sss-000F/ sss-000F /sss-000F/ Research Interests Correct-by-Construction Parsing Mechanized category theory in Agda Steven Schaefer https://stevenschaefer.net/publications/ publications /publications/ Publications Steven Schaefer https://stevenschaefer.net/conferences/ conferences /conferences/ Conferences Steven Schaefer Max S. New Pedro H. Azevedo de Amorim Nathan Varner 2025 https://stevenschaefer.net/sss-000I/ sss-000I /sss-000I/ Intrinsic Verification of Parsers and Formal Grammar Theory in Dependent Lambek Calculus Reference wide 10.1145/3729281 https://arxiv.org/abs/2504.03995 /bafkrmigntbark2vfgpsseipqmwyvctoupwkj3kiq7vg4hhynk7isd7jvgu.pdf DOI: https://dl.acm.org/doi/10.1145/3729281 Extended Version: https://arxiv.org/abs/2504.03995 Repository: https://github.com/maxsnew/grammars-and-semantic-actions We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In Dependent Lambek Calculus, linear types are used as a syntax for formal grammars, and parsers can be written as linear terms. The linear typing restriction provides a form of intrinsic verification that a parser yields only valid parse trees for the input string. We demonstrate the expressivity of this system by showing that the combination of inductive linear types and dependency on non-linear data can be used to encode commonly used grammar formalisms such as regular and context-free grammars as well as traces of various types of automata. Using these encodings, we define parsers for regular expressions using deterministic automata, as well as examples of verified parsers of context-free grammars. We present a denotational semantics of our type theory that interprets the types as a mathematical notion of formal grammars. Based on this denotational semantics, we have made a prototype implementation of Dependent Lambek Calculus using a shallow embedding in the Agda proof assistant. All of our examples parsers have been implemented in this prototype implementation. https://stevenschaefer.net/talks/ talks /talks/ Talks false Steven Schaefer Johnson He Max S. New 2026 6 1 https://stevenschaefer.net/sss-00DK/ sss-00DK /sss-00DK/ Lessons from Mechanizing Categorical Logic in Cubical Agda Talk /sss-00D2/ Ontario Programming Languages Seminar We present cubical-categorical-logic, a library of formalized category theory in Cubical Agda. The library's core idea is to treat syntax as a free categorical structure whose dependent eliminator is stated via (displayed) universal properties. From the same reusable components we have proven canonicity and conservativity results across several type theories, as well as the coherence theorem for monoidal categories. In this talk, we discuss these applications and reflect on Cubical Agda as a host for mechanized metatheory, where it is sometimes a boon and sometimes a bane. The slides for this talk were made using Forester and reveal.js. They are found within this forest at Lessons from Mechanizing Categorical Logic in Cubical Agda! Steven Schaefer Max S. New Pedro H. Azevedo de Amorim Nathan Varner 2025 6 19 https://stevenschaefer.net/sss-002R/ sss-002R /sss-002R/ Intrinsic Verification of Parsers and Formal Grammar Theory in Dependent Lambek Calculus Talk /bafkrmigg3ciyi6dkiy3djg6jxxyh6a5berwwdzbzbvay6akltbyyi67p5e.pdf PLDI https://www.youtube.com/watch?v=O1eXYHv2VU8 We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In Dependent Lambek Calculus, linear types are used as a syntax for formal grammars, and parsers can be written as linear terms. The linear typing restriction provides a form of intrinsic verification that a parser yields only valid parse trees for the input string. We demonstrate the expressivity of this system by showing that the combination of inductive linear types and dependency on non-linear data can be used to encode commonly used grammar formalisms such as regular and context-free grammars as well as traces of various types of automata. Using these encodings, we define parsers for regular expressions using deterministic automata, as well as examples of verified parsers of context-free grammars. We present a denotational semantics of our type theory that interprets the types as a mathematical notion of formal grammars. Based on this denotational semantics, we have made a prototype implementation of Dependent Lambek Calculus using a shallow embedding in the Agda proof assistant. All of our examples parsers have been implemented in this prototype implementation. Steven Schaefer Max S. New Pedro H. Azevedo de Amorim Nathan Varner 2024 11 22 https://stevenschaefer.net/sss-001B/ sss-001B /sss-001B/ Intrinsic Verification of Parsers and Formal Grammar Theory in Dependent Lambek Calculus Talk /bafkrmiaespdfbomemqbdtv57qoddjzhuf2uekrwfljkswigyd5ueh6ac4y.pdf Midwest Programming Languages Summit We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In Dependent Lambek Calculus, linear types are used as a syntax for formal grammars, and parsers can be written as linear terms. The linear typing restriction provides a form of intrinsic verification that a parser yields only valid parse trees for the input string. We demonstrate the expressivity of this system by showing that the combination of inductive linear types and dependency on non-linear data can be used to encode commonly used grammar formalisms such as regular and context-free grammars as well as traces of various types of automata. Using these encodings, we define parsers for regular expressions using deterministic automata, as well as examples of verified parsers of context-free grammars. We present a denotational semantics of our type theory that interprets the types as a mathematical notion of formal grammars. Based on this denotational semantics, we have made a prototype implementation of Dependent Lambek Calculus using a shallow embedding in the Agda proof assistant. All of our examples parsers have been implemented in this prototype implementation. Steven Schaefer 2020 12 4 https://stevenschaefer.net/sss-000L/ sss-000L /sss-000L/ LLL Algorithm Talk https://www.youtube.com/watch?v=U8MI2a_BHHo Lenstra-Lenstra-Lovasz (LLL) Lattice Basis Reduction Algorithm. A very useful algorithm for computational number theory. Final project for M602 Algebraic Number Theory at Indiana University. Special thanks to Grant Sanderson for creating the manim library, and to Jeff Suzuki for illuminating videos on the algorithm! Steven Schaefer Daniel Calco Max S. New https://stevenschaefer.net/teaching/ teaching /teaching/ Teaching Max S. New Steven Schaefer Daniel Calco https://stevenschaefer.net/sss-000G/ sss-000G /sss-000G/ Compiler Construction Course https://maxsnew.com/teaching/eecs-483-fa23/ Graduate student instructor for EECS 483 Compiler Construction in Fall 2023. Steven Schaefer 2024 8 6 https://stevenschaefer.net/sss-000E/ sss-000E /sss-000E/ About This Website I built this website using Forester. You may search through this site using Ctrl-k. References Context Backlinks Related Contributions