Related papers: Matrix Code
The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Current language models tailored for code tasks often adopt the pre-training-then-fine-tuning paradigm from natural language processing, modeling source code as plain text. This approach, however, overlooks the unambiguous structures…
We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and…
Being declarative means that we do computer programming on higher levels of abstraction. This vague definition identifies declarativeness with the act of ignoring details, but it is a special case of abstraction. The unspecified part is…
The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
Results in interpretability suggest that large vision and language models learn implicit linear encodings when models are biased by in-context prompting. However, the existence of similar linear representations in more general adaptation…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the…
An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Requirements and code, in conventional software engineering wisdom, belong to entirely different worlds. Is it possible to unify these two worlds? A unified framework could help make software easier to change and reuse. To explore the…
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Implicit Computational Complexity makes two aspects implicit, by manipulating programming languages rather than models of com-putation, and by internalizing the bounds rather than using external measure. We survey how automata theory…
The Huffman coding algorithm is interpreted in the lattice of partitions of the source alphabet. Maximal chains in the partition lattice correspond to linear extensions of tree orders, and those among the chains that exhibit a simple greedy…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
Assisting LLMs with code generation improved their performance on mathematical reasoning tasks. However, the evaluation of code-assisted LLMs is generally restricted to execution correctness, lacking a rigorous evaluation of their generated…