Quotient inductive-inductive types (QIITs) generalise inductive types in two ways: a QIIT can have more than one sort and the later sorts can be indexed over the previous ones. In addition, equality constructors are also allowed. We work in a setting with uniqueness of identity proofs, hence we use the term QIIT instead of higher inductive-inductive type. An example of a QIIT is the well-typed (intrinsic) syntax of type theory quotiented by conversion. In this paper first we specify finitary QIITs using a domain-specific type theory which we call the theory of signatures. The syntax of the theory of signatures is given by a QIIT as well. Then, using this syntax we show that all specified QIITs exist and they have a dependent elimination principle. We also show that algebras of a signature form a category with families (CwF) and use the internal language of this CwF to show that dependent elimination is equivalent to initiality.
Shading effect of external nets of different colours (white, green, yellow and red) on the yield of two “kapija†pepper (Capsicum anuum L.) cultivars was examined in walk-in plastic tunnels in Hungary under real cultivation circumstances. Shading nets decreased incoming radiation by 23-39% and reduced photosynthetically active radiation by 32-46%. The highest retention was obtained by yellow and green nets, in the range of 450-550 nm and 550-670 nm, respectively. Relation was reported between the degree of shading and the average air temperature of the tunnels, however, treatments did not decrease tunnel air temperature significantly, compared to that of unshaded and paint-shaded control tunnels. This can be explained by the applied proper ventilation and mist irrigation. A strong and negative relation was noted between the intensity of shading and the relative chlorophyll content (SPAD value) of leaves. Shading net treatments did not increase yields, yellow and green nets even decreased it. Instead of tunnel air temperature, yield was mainly affected by photosynthetically active radiation in the experiment. Strong positive linear relation was declared between the chlorophyll content of the leaves and the yield. Results of the current research led to the conclusions that under Hungarian climatic conditions the use of shading nets was less justified if proper cooling techniques (ventilation and mist irrigation) were applied; even under the relatively high incident radiation experienced during the trials. In greenhouses of less favourable climatic conditions, red or white shading nets are recommended instead of commonly used green ones in Hungary.
Shading effect of external nets of different colours (white, green, yellow and red) on the yield of two "kapija" pepper (Capsicum anuum L.) cultivars was examined in walk-in plastic tunnels in Hungary under real cultivation circumstances. Shading nets decreased incoming radiation by 23-39% and reduced photosynthetically active radiation by 32-46%. The highest retention was obtained by yellow and green nets, in the range of 450-550 nm and 550-670 nm, respectively. Relation was reported between the degree of shading and the average air temperature of the tunnels, however, treatments did not decrease tunnel air temperature significantly, compared to that of unshaded and paint-shaded control tunnels. This can be explained by the applied proper ventilation and mist irrigation. A strong and negative relation was noted between the intensity of shading and the relative chlorophyll content (SPAD value) of leaves. Shading net treatments did not increase yields, yellow and green nets even decreased it. Instead of tunnel air temperature, yield was mainly affected by photosynthetically active radiation in the experiment. Strong positive linear relation was declared between the chlorophyll content of the leaves and the yield. Results of the current research led to the conclusions that under Hungarian climatic conditions the use of shading nets was less justified if proper cooling techniques (ventilation and mist irrigation) were applied; even under the relatively high incident radiation experienced during the trials. In greenhouses of less favourable climatic conditions, red or white shading nets are recommended instead of commonly used green ones in Hungary.
Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors. QIITs are especially useful for algebraic descriptions of type theories and constructive definitions of real, ordinal and surreal numbers. We develop new metatheory for large QI-ITs, large elimination, recursive equations and infinitary constructors. As in prior work, we describe QIITs using a type theory where each context represents a QIIT signature. However, in our case the theory of signatures can also describe its own signature, modulo universe sizes. We bootstrap the model theory of signatures using self-description and a Church-coded notion of signature, without using complicated raw syntax or assuming an existing internal QIIT of signatures. We give semantics to described QI-ITs by modeling each signature as a finitely complete CwF (category with families) of algebras. Compared to the case of finitary QIITs, we additionally need to show invariance under algebra isomorphisms in the semantics. We do this by modeling signature types as isofibrations. Finally, we show by a term model construction that every QIIT is constructible from the syntax of the theory of signatures.
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