A new approach to abstract syntax with variable binding

MJ Gabbay, AM Pitts - Formal aspects of computing, 2002 - Springer
The permutation model of set theory with atoms (FM-sets), devised by Fraenkel and
Mostowski in the 1930s, supports notions of 'name-abstraction'and 'fresh name'that provide …

Notions of computation determine monads

G Plotkin, J Power - International Conference on Foundations of Software …, 2002 - Springer
We model notions of computation using algebraic operations and equations. We show that
these generate several of the monads of primary interest that have been used to model …

A new approach to abstract syntax involving binders

M Gabbay, A Pitts - Proceedings. 14th Symposium on Logic in …, 1999 - ieeexplore.ieee.org
The Fraenkel-Mostowski permutation model of set theory with atoms (FM-sets) can serve as
the semantic basis of meta-logics for specifying and reasoning about formal systems …

[PDF][PDF] Intuitionistic reasoning about shared mutable data structure

JC Reynolds - Millennial perspectives in computer science, 2000 - Citeseer
Drawing upon early work by Burstall, we extend Hoare's approach to proving the
correctness of imperative programs, to deal with programs that perform destructive updates …

FreshML: Programming with binders made simple

MR Shinwell, AM Pitts, MJ Gabbay - Proceedings of the eighth ACM …, 2003 - dl.acm.org
FreshML extends ML with elegant and practical constructs for declaring and manipulating
syntactical data involving statically scoped binding operations. User-declared FreshML …

Monads and effects

N Benton, J Hughes, E Moggi - International Summer School on Applied …, 2000 - Springer
A tension in language design has been between simple semantics on the one hand, and
rich possibilities for side-effects, exception handling and so on on the other. The introduction …

An effect system for algebraic effects and handlers

A Bauer, M Pretnar - Logical methods in computer science, 2014 - lmcs.episciences.org
We present an effect system for core Eff, a simplified variant of Eff, which is an ML-style
programming language with first-class algebraic effects and handlers. We define an …

Dilations and information flow axioms in categorical probability

T Fritz, T Gonda, NG Houghton-Larsen… - … Structures in Computer …, 2023 - cambridge.org
We study the positivity and causality axioms for Markov categories as properties of dilations
and information flow and also develop variations thereof for arbitrary semicartesian …

Structural foundations for probabilistic programming languages

DM Stein - 2021 - ora.ox.ac.uk
Probability theory and statistics are fundamental disciplines in a data-driven world. Synthetic
probability theory is a general, axiomatic formalism to describe their underlying structures …

Step-indexed Kripke models over recursive worlds

L Birkedal, B Reus, J Schwinghammer… - ACM SIGPLAN …, 2011 - dl.acm.org
Over the last decade, there has been extensive research on modelling challenging features
in programming languages and program logics, such as higher-order store and storable …