Related papers: Initial Semantics for Reduction Rules
We give an algebraic characterization of the syntax and semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as…
In this thesis we give an algebraic characterization of the syntax and semantics of simply-typed languages. More precisely, we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the…
Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…
We present a probabilistic version of PCF, a well-known simply typed universal functional language. The type hierarchy is based on a single ground type of natural numbers. Even if the language is globally call-by-name, we allow a…
Initial semantics aims to capture inductive structures and their properties as initial objects in suitable categories. We focus on the initial semantics aiming to model the syntax and substitution structure of programming languages with…
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
In this paper, we introduce a novel approach for semantic description of object features based on the prototypicality effects of the Prototype Theory. Our prototype-based description model encodes and stores the semantic meaning of an…
Dependently typed lambda calculi such as the Edinburgh Logical Framework (LF) are a popular means for encoding rule-based specifications concerning formal syntactic objects. In these frameworks, relations over terms representing formal…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as…