... ( Inductive Type Extensions ) 146 10.20 Theorem ( Inductive Type Extensions ) 146 10.21 Remark ( Inductive Types as Sets of Expressions ) 147 10.22 Inductive Type Theory Extension ( Boolean Values ) 148 10.23 Inductive Type Theory�...
... inductive type must live in a universe that already contains all the types going into its definition . Thus if in the definition of D , the ambiguous notation Prop means Propų , then we do not have D : U but only D : U ' for some larger�...
... inductive type are those that are given by a finite composition of its introduction forms. Consequently, if we specify the behavior of a function on each of the introduction forms of an inductive type, then its behavior is defined for�...
... inductive type of natural numbers has just two constructors : only the sec- ond is recursive , and only one argument of this constructor is in the inductive type itself . Other configurations are possible . For instance , we can�...
... inductive type of codes is defined simultaneously with the recursive function El . An example is the following definition of a small universe with bool and I. data U : Type bool : U pi : ( A : U ) → ( EI A → U ) → U EI : U Type El�...
... inductive type I , we want to declare a new inductive type I ' which corresponds to I plus one more constructor . For instance , let's say we have a syntax for lambda calculus : Inductive tm : Set : = tm . | var : nat → tm | lam : tm�...
... inductive type being defined and cis the constructor of this production rule . Aj and Br are the types of the arguments of c . Aj must be a type consisting of only non - inductive types and already defined inductive types . Bk contains�...
... inductive type ) . In this case we are mainly interested in the quotient type ( Z ) and we use the inductive type ( 2 ) to reason over the quotient type . Obtain a better computational behavior of a definable operation on an in- ductive�...
... inductive type we allow ourselves to pattern-match on objects of the abstract data type. For example, we may view built-in signed or unsigned integers as Peano numbers, and so on. We may also view a structured data type as some other�...
... inductive type . X is a bound variable in this type . This inductive type should be understood as ' the smallest set X that is closed under two constructors , one of type X and one of type X → X. More general Ind ( X : A ) { C1 || Cp }�...