Induction-induction is a principle for mutually defining data types A ∶ Set and B ∶ A→ Set. Both A and B are defined inductively, and the constructors for A can refer to B and vice versa. In addition, the constructor for B can refer to the constructor for A. Induction-induction occurs in a natural way when formalising dependent type theory in type theory. We give some examples of inductive-indu...

Higher inductive-inductive types (HIITs) generalise inductive types of dependent type theories in two directions. On the one hand they allow the simultaneous definition of multiple sorts that can be indexed over each other. On the other hand they support equality constructors, thus generalising higher inductive types of homotopy type theory. Examples that make use of both features are the Cauch...

statement of problem: the guided bone regeneration (gbr) technique does not always produce consistent results. bone filling within the space provided by the membrane can be incomplete. purpose: the aim of this study was to evaluate the effect of a collagen membrane (bio-gide) in combination with or without deproteinezed bovine bone mineral (bio-oss) on the healing of calvarial defects in rabbit...

Inductive programming—the use of inductive reasoning methods for programming, algorithm design, and software development—is a currently emerging research field. A major subfield is inductive program synthesis, the (semi-)automatic construction of programs from exemplary behavior. Inductive program synthesis is not a unified research field until today but scattered over several different establi...

Abstract. Inductive constellations are one-sided analogues of inductive categories which correspond to left restriction semigroups in a manner analogous to the correspondence between inverse semigroups and inductive groupoids. In this paper, we define the notions of the action and partial action of an inductive constellation on a set, before introducing the Szendrei expansion of an inductive co...

Induction-induction is a principle for defining data types in Martin-Löf Type Theory. An inductive-inductive definition consists of a set A, together with an A-indexed family B : AÑ Set, where both A and B are inductively defined in such a way that the constructors for A can refer to B and vice versa. In addition, the constructors for B can refer to the constructors for A. We extend the usual i...

Traditional inductive logging uses sources whose focussing input waveform does not change with borehole position. While this arrangement facilitates hardware design, the resolution which it provides varies from formation to formation, and is only accidentally optimal for any given sound position. Optimization theory provides a method for designing a distributed inductive borehole source array ,...

this study investigated the relative effects of deductive and inductive form-focused instruction (ffi) on the acquisition of 4 non-generic definite article uses(cultural, situational, structural, and textual) as assessed by explicit and implicit outcome measures. the tests utilized to assess efl learners' acquisition of definite article uses were timed and untimed grammaticality judgment t...