Partial inductive definitions
نویسندگان
چکیده
منابع مشابه
Inductive-Inductive Definitions
We present a principle for introducing new types in type theory which generalises strictly positive indexed inductive data types. In this new principle a set A is defined inductively simultaneously with an A-indexed set B, which is also defined inductively. Compared to indexed inductive definitions, the novelty is that the index set A is generated inductively simultaneously with B. In other wor...
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We describe how the calculus of partial inductive definitions is used to represent logics. This calculus includes the powerful principle of definitional reflection. We describe two conceptually different approaches to representing a logic, both making essential use of definitional reflection. In the deductive approach, the logic is defined by its inference rules. Only the succedent rules (in a ...
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In formal verification, inductive definitions of predicates are widely used when we define recursive notions and algorithms. In actual verification, we often introduce a new inductively defined predicate by modifying an existing inductive definition. In such a case, it is usual that there are some relationships between two predicates, and such relationship theorems make the properties on one pr...
متن کاملElaborating Inductive Definitions
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive types within type theory. By elaborating an inductive definition – a syntactic artefact – to its code – its semantics – we obtain an internalised account of inductives inside the type theory itself: we claim that reasoning about inductive...
متن کاملA finite axiomatisation of inductive-inductive definitions
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...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1991
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(06)80007-1