47,056 research outputs found
New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized
The definitional equality of an intensional type theory is its test of type
compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws
Combining typing and size constraints for checking the termination of higher-order conditional rewrite systems
In a previous work, the first author extended to higher-order rewriting and
dependent types the use of size annotations in types, a termination proof
technique called type or size based termination and initially developed for
ML-like programs. Here, we go one step further by considering conditional
rewriting and explicit quantifications and constraints on size annotations.
This allows to describe more precisely how the size of the output of a function
depends on the size of its inputs. Hence, we can check the termination of more
functions. We first give a general type-checking algorithm based on constraint
solving. Then, we give a termination criterion with constraints in Presburger
arithmetic. To our knowledge, this is the first termination criterion for
higher-order conditional rewriting taking into account the conditions in
termination
Theory of size-dependent resonance Raman intensities in InP nanocrystals
The resonance Raman spectrum of InP nanocrystals is characterized by features ascribable to both longitudinal (LO) and transverse (TO) optical modes. The intensity ratio of these modes exhibits a strong size dependence. To calculate the size dependence of the LO and TO Raman cross sections, we combine existing models of Raman scattering, the size dependence of electronic and vibrational structure, and electron vibration coupling in solids. For nanocrystals with a radius >10 Å, both the LO and TO coupling strengths increase with increasing radius. This, together with an experimentally observed increase in the electronic dephasing rate with decreasing size, allows us to account for the observed ratio of LO/TO Raman intensities
- …