Results

**1 - 2**of**2**### THEME Programs, Verification and Proofs

"... 3. Scientific Foundations.....................................................................2 3.1. Proof theory and the Curry-Howard correspondence 2 3.1.1. Proofs as programs 2 3.1.2. Towards the calculus of constructions 2 3.1.3. The Calculus of Inductive Constructions 3 3.2. The development of ..."

Abstract
- Add to MetaCart

3. Scientific Foundations.....................................................................2 3.1. Proof theory and the Curry-Howard correspondence 2 3.1.1. Proofs as programs 2 3.1.2. Towards the calculus of constructions 2 3.1.3. The Calculus of Inductive Constructions 3 3.2. The development of Coq 3 3.2.1. The underlying logic and the verification kernel 3 3.2.2. Programming and specification languages 4

### Journal of Automated Reasoning manuscript No. (will be inserted by the editor) A Two-Valued Logic for Properties of Strict Functional Programs allowing Partial Functions

"... Abstract A typed program logic LMF for recursive specification and veri-fication is presented. It comprises a strict functional programming language with polymorphic and recursively defined partial functions and polymorphic data types. The logic is two-valued with the equality symbol as only predica ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract A typed program logic LMF for recursive specification and veri-fication is presented. It comprises a strict functional programming language with polymorphic and recursively defined partial functions and polymorphic data types. The logic is two-valued with the equality symbol as only predicate. Quantifiers range over the values, which permits inductive proofs of properties. The semantics is based on a contextual (observational) semantics, which gives a consistent presentation of higher-order functions. Our analysis also sheds new light on the the role of partial functions and loose specifications. It is also an analysis of influence of extensions of programs on the tautologies. The main result is that universally quantified equations are conservative, which is also the base for several other conservative classes of formulas.