Showing papers in "Lecture Notes in Computer Science in 1982"

Algebraic specifications for parametrized data types with minimal parameter and target algebras

Abstract: We conceive a parametrized data type as a partial functor φ: ALG (∑) --> ALG (Δ), where Δ is a signature extending ∑ and ALG (∑) is the class of minimal ∑-algebras which serve as parameters. We focus attention on one particular method of algebraically specifying parametrized data types: finite specifications with conditional equations using auxiliary sorts and functions provided with initial algebra semantics. We introduce the concept of an effective parametrized data type. A satisfactory adequacy result is then obtained: each effective parametrized data type possesses a finite algebraic specification under initial semantics.

A formalized proof system for total correctness of while programs

Abstract: We introduce datatype specifications based on schemes, a slight generalization of first order specifications. For a schematic specification (Σ, \(\mathbb{E}\)), Hoare's Logic HL (Σ, \(\mathbb{E}\)) for partial correctness is defined as usual and on top of it a proof system (Σ, \(\mathbb{E}\)) ⊢ p → S ↓ for termination assertions is defined. The system is first order in nature, but we prove it sound and complete w.r.t. a second order semantics. We provide a translation of a standard proof system HLT(A) for total correctness on a structure A into our format.