Completeness for typed lazy inequalities

Familiar βη-equational reasoning on λ-terms is unsound for proving observational congruences when termination of the standard lazy interpreter is taken into account. A complete logic, based on sequents, for proving termination-observational congruences between simply-typed terms without constants is developed. It is shown that the theory, like that of βη-reasoning in the ordinary types λ-calculus, is decidable. The authors examined the termination behavior of the functional language PCF under the standard interpreters