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Elementary Affine Logic (EAL) is a variant of Linear Logic characterizing the computational power of the elementary bounded Turing machines. The EAL Type Inference problem is the problem of automatically assigning to terms of λ-calculus EAL formulas as types. This problem, restricted to the...
The question whether a given functional of some full type structure (FTS for short) is λ-definable by a closed λ-term, known as the Definability Problem, was proved to be undecidable by R. Loader in 1993 (cf (Loa01a)). Later on, R. Loader refined his first result by establishing that the...
In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by...
The λμ-calculus features both variables and names together with their binding mechanisms. This means that constructions on open terms are necessarily parameterized in two different ways for both variables and names. Semantically, such a construction must be modeled by a biparameterized family...
Quasi-interpretations are a tool to bound the size of the values computed by a first-order functional program (or a term rewriting system) and thus a mean to extract bounds on its computational complexity. We study the synthesis of quasi-interpretations selected in the space of polynomials over...
This paper and our conference paper (Abbott, Altenkirch, Ghani, and McBride, 2003b) explain and analyse the notion of the derivative of a data structure as the type of its one-hole contexts based on the central observation made by McBride (2001). To make the idea precise we need a generic notion...
We study a notion of bounded stable biorder, showing that the monotone and stable functions on such biorders are sequential. We construct bounded biorder models of a range of sequential, higher-order functional calculi, including unary PCF, (typed and untyped) call-by-value and lazy λ-calculi,...
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