6
6
and symmetric monoidal closed categories, and enrichment, as covered
7
7
by Kelly~\cite{kelly:basic-concepts-of-enriched-category-theory}.
9
\nocats{}The ``cat-free'' parts of this thesis assume only basic
10
categorical notions, which are common knowledge in the semantics and
11
functional programming communities. In particular, we assume
9
\nocats{}The ``cat-free'' parts assume only basic
10
categorical notions, previously used in the semantics and
11
functional programming communities. We assume
12
12
familiarity with functors, monads, natural transformations, and monad
13
morphisms. These parts of the thesis are designed to be understood if
14
read sequentially, skipping over the sections marked with ``beware
15
cats''. Of course, while the statements are formulated in these
13
morphisms. These parts may be
14
read sequentially, skipping over ``beware
15
cats'' sections. While the statements are formulated in these
16
16
more accessible terms, their proofs may rely on categorically involved
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17
accounts. The scope of these two modifiers extends to the end of the literary
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18
unit they are introduced in, such as Chapter, Section, or Proof.
20
We revisit some definitions and examples in the course of the
21
development. In cases where the revisited unit bears close resemblance
22
to its original, we \DELTA{shade the parts} that changed.
23
Definitions, theorems, and examples that are recast in terms of
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\emph{generic effects} are marked with an asterisk, such as
25
\definitionref+{generic-model}. An $\omega$ reflects that the
26
revisited unit is a domain-theoretic specialisation, such as
27
\definitionref+{recursion-signature}. Reformulation in set-theoretic
28
terms of categorically involved definitions is marked with a
29
(revisited) suffix, such as
30
\definitionref+{set-type-assignment}. Algebraic reformulation in terms
31
of theories and/or presentations is marked with a suffixed plus, such
32
as \definitionref+{presentation-model}. These modifiers to numbering
20
We revisit definitions, examples, and theorems during the development.
22
\DELTA{Shading} indicates the difference from the original unit.
24
An asterisk, e.g., \definitionref+{generic-model}, indicates the
25
revisited unit is recast in terms of generic effects.
27
An $\omega$, e.g., \definitionref+{recursion-signature}, indicates the
28
revisited unit is a domain-theoretic specialisation.
30
A (revisited) mark, e.g., \definitionref+{set-type-assignment},
31
indicates the revisited unit is a set-theoretic reformulation of a
32
categorically involved unit.
34
A plus,e.g. \definitionref+{presentation-model}, indicates the
35
revisited unit is an algebraic reformulation in terms of theories
38
These modifiers combine, e.g.,
34
39
Definition~\algebraicrevisit{definition}{generic-model}{set-generic-model},
35
40
meaning an algebraic reforumaltion of the set-theoretic instance of
36
41
the generic effects alternative to \definitionref{categorical-model}.
38
Electronic versions of this document should include hyper-reference to
39
ease cross-references. The following appendices provide indices for
42
\chapter{Table of definitions and results}
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\chapter{Table of examples}
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Electronic versions of this document use hyper-references to
44
ease cross-references.