Both of these problems arise in connection with the Scott-Strachey approach to programming language semantics.

Doctor of Philosophy Abstract Multi-stage programming MSP is a style of writing program generatorsprograms which generate programssupported by special annotations that direct construction, combination, and execution of object programs.

Various researchers have shown MSP to be effective in writing efficient programs without sacrificing genericity. However, correctness proofs of such programs have so far received limited attention, and approaches and challenges for that task have been largely unexplored.

In this thesis, I establish formal equational properties of the multi-stage lambda calculus and related proof techniques, as well as results that delineate the intricacies of multi-stage languages that one must be aware of. In particular, I settle three basic questions that naturally arise when verifying multi-stage functional programs.

Firstly, can adding staging MSP to a language compromise the interchangeability of terms that held in the original language? Unfortunately it can, and more care is needed to reason about terms with free variables.

I give termination conditions that characterize when this guarantee holds. Finally, do multi-stage languages satisfy extensional facts, for example that functions agreeing on all arguments are equivalent?

I develop a sound and complete notion of applicative bisimulation, which can establish not only extensionality but, in principle, any other valid program equivalence as well.

These results improve our general understanding of staging and enable us to prove the correctness of complicated multi-stage programs.3 The equivalence between ∀∃ =x ux u() and ∀∃ =uxx u() concept of the nature of an entity had to be introduced and an extensional mereology to be applied: The nature of an entity is a property, which that entity possesses and Let us disregard thesis (3) and return to the common conception of prop-.

THE SEPARATED EXTENSIONAL CHU CATEGORY MICHAEL BARR Transmitted by ABSTRACT. thesis of P.-H. Chu that described what seemed at the time a too-simple-to-be-interesting a contravariant equivalence, so that Chu(A;?) is a self-dual category.

Less obvious, but. type as partial equivalence relations ("pers") over terms - thereby building a variety [a,b] to define the model inductively In his thesis Allen compares his models to those of Aczel [], Beeson, and Smith [].

The modeling techniques Notice equality on pers is extensional.

Synthetic Cohomology in Homotopy Type Theory Evan Cavallo December 16, Contents Introduction iii In extensional Martin-L of type theory [18], such types have at This thesis is an exploration of basic ideas in cohomology, which is a central tool from homotopy.

A Dilemma for the Weak Deflationist about Truth Glen Hoffmann.

1 Introduction. The deflationist about truth is committed to a triviality or transparency thesis: the content of the truth predicate is exhausted by its involvement in some version of the truth-schema [P] is true iff P (where `[P]' stands for any declarative propositional object and `P' stands for `[P]'s object-level equivalent).

Abstract. Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis.

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