AssessmentType
plain-language theorem explainer
This inductive definition enumerates five canonical assessment types in education as an inductive type with constructors for diagnostic, formative, summative, criterion-referenced, and portfolio cases. Education researchers modeling assessment cycles inside Recognition Science would cite it when fixing configDim to 5. The declaration is a direct inductive construction that derives Fintype to enable immediate cardinality results.
Claim. Let $A$ be the inductive type whose five constructors are diagnostic, formative, summative, criterion-referenced, and portfolio, equipped with decidable equality, representation, boolean equality, and finite-type structure.
background
The module introduces five canonical educational assessment types tied to configDim equal to 5. These span the practical assessment cycle: baseline evaluation, ongoing feedback, certification, standard matching, and longitudinal artifacts. The local setting is an application of Recognition Science to education depth with zero sorry or axiom statements. No upstream lemmas are required since the declaration stands as a foundational enumeration.
proof idea
The declaration is a direct inductive definition that lists the five constructors and derives the type classes DecidableEq, Repr, BEq, and Fintype in a single step.
why it matters
This supplies the type required by the downstream cardinality theorem establishing exactly five elements and by the certification structure that records the same cardinality fact. It realizes the education module's claim that configDim equals 5 for assessment types, placing the enumeration inside the broader Recognition Science treatment of dimensions.
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