Initial and Final Algebra Semantics for Data Type Specifications: Two Characterization Theorems

J. A. Bergstra, J. V. Tucker
1983 SIAM journal on computing (Print)  
We prove that those data types which may be defined by conditional equation specifications and final algebra semantics are exactly the cosemicomputable data typesthose data types which are effectively computable, but whose inequality relations are recursively enumerable. And we characterize the computable data types as those data types which may be specified by conditional equation specifications using both initial algebra semantics and final algebra semantics. Numerical bounds for the number
more » ... auxiliary functions and conditional equations required are included in both theorems.
doi:10.1137/0212024 fatcat:kmous3qll5epblieg57c4savga