102 lines
3.2 KiB
Plaintext
102 lines
3.2 KiB
Plaintext
theory mathex
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imports "../../DOF/Isa_COL"
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begin
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(*<<*)
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text\<open>In our scenario, content has four different types of addressees:
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\<^item> the @{emph \<open>setter\<close>}, i.e. the author of the exam,
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\<^item> the @{emph \<open>student\<close>}, i.e. the addressee of the exam,
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\<^item> the @{emph \<open>checker\<close>}, i.e. a person that checks the exam for
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\<^item> the @{emph \<open>external\_examiner\<close>}, i.e. a person that checks the exam for
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feasibility and non-ambiguity.
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Note that the latter quality assurance mechanism is used in many universities,
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where for organizational reasons the execution of an exam takes place in facilities
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where the author of the exam is not expected to be physically present.
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\<close>
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datatype ContentClass =
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setter (* \<open>the 'author' of the exam\<close> *)
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| checker (* \<open>the 'proof-reader' of the exam\<close> *)
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| externalExaminer (* \<open>an external 'proof-reader' of the exam\<close> *)
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| student (* \<open>the victim ;-) ... \<close> *)
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doc_class Author =
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affiliation :: "string"
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email :: "string"
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datatype Subject =
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algebra | geometry | statistical | analysis
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datatype Level =
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oneStar | twoStars | threeStars
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datatype Grade =
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A1 | A2 | A3
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doc_class Exam_item =
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level :: "int option"
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concerns :: "ContentClass set"
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doc_class Header = Exam_item +
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examSubject :: "(Subject) list"
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date :: string
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timeAllowed :: int (* minutes *)
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type_synonym SubQuestion = string
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doc_class Answer_Formal_Step = Exam_item +
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justification :: string
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"term" :: "string"
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doc_class Answer_YesNo = Exam_item +
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step_label :: string
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yes_no :: bool (* \<open>for checkboxes\<close> *)
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datatype Question_Type =
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formal | informal | mixed
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doc_class Task = Exam_item +
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local_grade :: Level
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type :: Question_Type
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subitems :: "(SubQuestion * (Answer_Formal_Step list + Answer_YesNo)list) list"
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concerns :: "ContentClass set" <= "{setter,student,checker,externalExaminer}"
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mark :: int
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doc_class Exercise = Exam_item +
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content :: "(Task) list"
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concerns :: "ContentClass set" <= "{setter,student,checker,externalExaminer}"
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text\<open>In many institutions, it makes sense to have a rigorous process of validation
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for exam subjects : is the initial question correct ? Is a proof in the sense of the
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question possible ? We model the possibility that the @{term setter} validates a
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question by a sample proof validated by Isabelle. In our scenario this sample proofs
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are completely @{emph \<open>intern\<close>}, i.e. not exposed to the students but just additional
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material for the internal review process of the exam.\<close>
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doc_class Validation =
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tests :: "term list" <="[]"
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proofs :: "thm list" <="[]"
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doc_class Solution = Exam_item +
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content :: "Exercise list"
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valids :: "Validation list"
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concerns :: "ContentClass set" <= "{setter,checker,externalExaminer}"
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doc_class MathExam =
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content :: "(Header + Author + Exercise) list"
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global_grade :: Grade
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accepts "\<lbrace>Author\<rbrace>\<^sup>+ ~~ Header ~~ \<lbrace>Exercise ~~ Solution\<rbrace>\<^sup>+ "
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(*>>*)
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end
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