AssessmentType
AssessmentType enumerates the five canonical assessment modes aligned with configDim equal to 5 in the Recognition Science education model. Education researchers formalizing assessment cycles would cite this enumeration to anchor the baseline-to-longitudinal progression. The declaration is a direct inductive construction that derives Fintype to support immediate cardinality computation.
claimLet $A$ be the inductive type whose constructors are diagnostic, formative, summative, criterion-referenced, and portfolio; $A$ carries decidable equality and finite type structure.
background
The module Assessment Types from configDim establishes five canonical educational assessment types for configDim D = 5. These span the practical assessment cycle: baseline, feedback, certification, standard-match, and longitudinal artifact. The setting supplies a direct inductive foundation with zero sorry or axiom.
proof idea
The declaration proceeds by direct inductive enumeration of the five constructors followed by derivation of DecidableEq, Repr, BEq, and Fintype instances.
why it matters in Recognition Science
This definition supplies the base enumeration for the education component, directly feeding the theorem that Fintype.card AssessmentType equals 5 and the certification structure asserting five types. It instantiates the configDim = 5 requirement for E5 Education Depth within the Recognition framework.
scope and limits
- Does not define ordering or relations among the five types.
- Does not prove any properties beyond the enumeration and derived instances.
- Does not link to physical constants or forcing-chain steps.
- Does not address implementation in specific curricula.
formal statement (Lean)
18inductive AssessmentType where
19 | diagnostic
20 | formative
21 | summative
22 | criterionReferenced
23 | portfolio
24 deriving DecidableEq, Repr, BEq, Fintype
25