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Guillaume Allais

Publications and source records attributed to Guillaume Allais.

9 recordsLinked to original sources

Co-Lecturing With the DED: Explaining Circuit Design via the Draw Encode Display Loop

When representing digital circuits, 2 dimensional hand drawings free us from the linear structure of hardware description languages, enabling intuitive reasoning and making structure explicit. However these drawings are imprecise and inert: they do not enforce that the circuits are well defined and cannot be tested. We want both intuitive visual representations and well defined testable ones but students can struggle to link one to the other. To bridge this gap we present the Draw Encode Display Loop (DED), a Co-Lecturing dynamic which equips students with a systematic method to tackle natural language specifications: 1. Draw: visually informative intermediate representations (truth tables, characteristic tables) to generate a structured circuit diagram. 2. Encode: the diagram by labelling inputs, outputs and intermediate values which can be directly converted to code. 3. Display: the code using an in-house diagrammatic renderer. This is supported by Syrup, an education-focused hardware description language which allows students to define, experiment with and display their own circuits. We support these approaches with survey data gathered from two cohorts of students.

cs.HC

Frex: dependently-typed algebraic simplification

We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's dependently typed interface guarantees that both built-in and user-defined simplification modules are terminating, sound, and complete with respect to a well-specified class of equations. We have implemented the design in the Idris 2 and Agda dependently typed programming languages and shown that it supports modular extension to new theories, proof extraction and certification, goal extraction via reflection, and interactive development.

cs.PL

Seamless, Correct, and Generic Programming over Serialised Data

In typed functional languages, one can typically only manipulate data in a type-safe manner if it first has been deserialised into an in-memory tree represented as a graph of nodes-as-structs and subterms-as-pointers. We demonstrate how we can use QTT as implemented in \idris{} to define a small universe of serialised datatypes, and provide generic programs allowing users to process values stored contiguously in buffers. Our approach allows implementors to prove the full functional correctness by construction of the IO functions processing the data stored in the buffer.

cs.PL

Scoped and Typed Staging by Evaluation

Using a dependently typed host language, we give a well scoped-and-typed by construction presentation of a minimal two level simply typed calculus with a static and a dynamic stage. The staging function partially evaluating the part of a term that are static is obtained by a model construction inspired by normalisation by evaluation. We then go on to demonstrate how this minimal language can be extended to provide additional metaprogramming capabilities, and to define a higher order functional language evaluating to digital circuit descriptions.

cs.PL

Type Theory as a Language Workbench

Language Workbenches offer language designers an expressive environment in which to create their DSLs. Similarly, research into mechanised meta-theory has shown how dependently typed languages provide expressive environments to formalise and study DSLs and their meta-theoretical properties. But can we claim that dependently typed languages qualify as language workbenches? We argue yes! We have developed an exemplar DSL called Velo that showcases not only dependently typed techniques to realise and manipulate IRs, but that dependently typed languages make fine language workbenches. Velo is a simple verified language with well-typed holes and comes with a complete compiler pipeline: parser, elaborator, REPL, evaluator, and compiler passes. Specifically, we describe our design choices for well-typed IRs design that includes support for well-typed holes, how CSE is achieved in a well-typed setting, and how the mechanised type-soundness proof for Velo is the source of the evaluator.

cs.PL

Builtin Types viewed as Inductive Families

State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the data, even though more efficient representations could be available. Using Quantitative Type Theory, we demonstrate how to define an invariant-rich, typechecking time data structure packing an efficient runtime representation together with runtime irrelevant invariants. The compiler can then aggressively erase all such invariants during compilation. Unlike other approaches, the complexity of the resulting representation is entirely predictable, we do not require both representations to have the same structure, and yet we are able to seamlessly program as if we were using the high-level structure.

cs.PL

A Type and Scope Safe Universe of Syntaxes with Binding: Their Semantics and Proofs

Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of $α$-equivalence, capture-avoiding substitution, typing contexts, runtime environments, and so on. In the past, implementing and reasoning about programming languages required careful handling to maintain the correct behaviour of bound variables. Modern programming languages include features that enable constraints like scope safety to be expressed in types. Nevertheless, the programmer is still forced to write the same boilerplate over again for each new implementation of a scope safe operation (e.g., renaming, substitution, desugaring, printing, etc.), and then again for correctness proofs. We present an expressive universe of syntaxes with binding and demonstrate how to (1) implement scope safe traversals once and for all by generic programming; and (2) how to derive properties of these traversals by generic proving. Our universe description, generic traversals and proofs, and our examples have all been formalised in Agda and are available in the accompanying material available online at https://github.com/gallais/generic-syntax.

cs.PL

Generic Level Polymorphic N-ary Functions

Agda's standard library struggles in various places with n-ary functions and relations. It introduces congruence and substitution operators for functions of arities one and two, and provides users with convenient combinators for manipulating indexed families of arity exactly one. After a careful analysis of the kinds of problems the unifier can easily solve, we design a unifier-friendly representation of n-ary functions. This allows us to write generic programs acting on n-ary functions which automatically reconstruct the representation of their inputs' types by unification. In particular, we can define fully level polymorphic n-ary versions of congruence, substitution and the combinators for indexed families, all requiring minimal user input.

cs.PL

New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized

The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation fails to identify two `obviously' equal terms. If only the machine could decide a richer theory! We propose a way to decide theories which supplement evaluation with `$ν$-rules', rearranging the neutral parts of normal forms, and report a successful initial experiment. We study a simple -calculus with primitive fold, map and append operations on lists and develop in Agda a sound and complete decision procedure for an equational theory enriched with monoid, functor and fusion laws.

cs.PL