Fibrations, Logical Predicates and Indeterminates

Breaking the Loop: Recursive Proofs for Coinductive Predicates in Fibrations

The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of up-to techniques. This approach lifts the burden to guess invariants, like bisimulation relations, beforehand. Rather, they allow one to start with the soug...

Logical Predicates for Intuitionistic Linear Type Theories

LFP – A Logical Framework with External Predicates

The LFP Framework is an extension of the Harper-HonsellPlotkin’s Edinburgh Logical Framework LF with external predicates. This is accomplished by defining lock type constructors, which are a sort of -modality constructors, releasing their argument under the condition that a possibly external predicate is satisfied on an appropriate typed judgement. Lock types are defined using the standard patt...

A Logical Framework for Graded Predicates

Categorical Glueing and Logical Predicates for Models of Linear Logic

We give a series of glueing constructions for categorical models of fragments of linear logic. Specifically, we consider the glueing of (i) symmetric monoidal closed categories (models of Multiplicative Intuitionistic Linear Logic), (ii) symmetric monoidal adjunctions (for interpreting the modality !) and (iii) -autonomous categories (models of Multiplicative Linear Logic); the glueing construc...