Type-checking injective pure type systems

The Semi-Full Closure of Pure Type Systems

We show that every functional Pure Type System may be extended to a semi-full Pure Type System. Moreover, the extension is conservative and preserves weak normalization. Based on these results, we give a new, conceptually simple type-checking algorithm for functional Pure Type Systems.

Checking Algorithms for Pure Type Systems

On the Role of Type Decorations in the Calculus of Inductive Constructions

In proof systems like Coq [15], proof-checking involves comparing types modulo β-conversion, which is potentially a time-consuming task. Significant speed-ups are achieved by compiling proof terms, see [8]. Since compilation erases some type information, we have to show that convertibility is preserved by type erasure. This article shows the equivalence of the Calculus of Inductive Construction...

On Injective Embeddings of Tree Patterns

We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational properties vary (from P to NP-complete). We present a thorough study of the complexity of the model checking problem, i.e., is there an embedding of a given t...

$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity

In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.