These notes provide a brief introduction to structural induction for proving properties of ML programs. We assume that the reader is already familiar with ML and the notes on evaluation and natural number induction for pure ML programs. We write e k =⇒ e′ for a computation of k steps, e =⇒ e′ for a computation of any number of steps (including 0), e ↪→ v for a complete computation of e to a val...

Douven (in press) observes that Schurz's meta-inductive justification of induction cannot explain the great empirical success induction, and offers an explanation based on computer simulations social evolutionary development our inductive practices. In this paper, I argue Douven's account does not address explanatory question argument leaves open, assumption environment's induction-friendliness...

Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary [Formula: see text]-modules. In the 1980s, Guillemin Sternberg established parallel property Hamiltonian text]-spaces, which (as we show) unfortunately fails mirror situation where more than one text]-module “quantizes” given text]-space. This paper offers evidence is...

context : cumin ( cuminum cyminum l.) as a member of the apiaceae family is one of the most important medicinal plants in the world. objective : an experiment was conducted for evaluation of callus induction optimization in cumin accessions (shahdad, koohbanan, badrood and afghanistan). materials and methods : factorial experiment based on completely randomized design (crd) with three replicati...