A lambda-calculus schema is an expression of the lambda calculus augmented by uninterpreted constant and operator symbols. It is an abstraction of programming languages such as LISP which permit functions to be passed to and returned from other functions. When given an interpretation for its constant and operator symbols, certain schemata, called lambda abstractions, naturally define partial functions over the domain of interpretation. Two implementation strategies are considered: the retention strategy in which all variable bindings are retained until no longer needed (implying the use of some sort of garbage-collected store) and the deletion strategy, modeled after the usual stack implementation of ALGOL 60, in which variable bindings are destroyed when control leaves the procedure (or block) in which they were created. Not all lambda abstractions evaluate correctly under the deletion strategy. Nevertheless, both strategies are equally powerful in the sense that any lambda abstraction can be mechanically translated into another that evaluates correctly under the deletion strategy and defines the same partial function over the domain of interpretation as the original. Proof is by translation into continuation-passing style.

Denotational semantics is now used widely for the formal definition of programming languages but there is a lack of appropriate tools to support language development. General purpose language implementation systems are oriented to syntax with poor support for semantics. Specialised denotational semantics based systems correspond closely to the formalism but are rendered inflexible for language experimentation by their monolithic multiple stages Exploratory language development with formal definitions is better served by a unitary notation, encompassing syntax and semantics, which is close to but simpler than denotational semantics. Interactive implementation of the notation then facilitates language investigation through the direct execution of a formal definition as an interpreter for the defined language. This thesis presents Navel, a run-time typed, applicative order, pure functional programming language with integrated context free grammar rules. Navel has been used to develop prot...

Linguistic mechanisms which can be used to protect one subprogram from another's malfunctioning are described. Function-producing functions and various type-tagging schemes are considered. An attempt is made to distinguish between access limitation and authentication. Key Words and Phrases: protection, types, environments, trademarks, seals, access keys, access