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**1 - 7**of**7**### A Flexible Semantic Framework for Effects

"... Effects are a powerful and convenient component of programming. They enable programmers to interact with the user, take advantage of efficient stateful memory, throw exceptions, and nondeterministically execute programs in parallel. However, they also complicate every aspect of reasoning about a pro ..."

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Effects are a powerful and convenient component of programming. They enable programmers to interact with the user, take advantage of efficient stateful memory, throw exceptions, and nondeterministically execute programs in parallel. However, they also complicate every aspect of reasoning about a program or language, and as a result it is crucially important to have a good understanding of what effects are and how they work. In this paper we present a new framework for formalizing the semantics of effects that is more general and thorough than previous techniques while clarifying many of the important concepts. By returning to the categorytheoretic roots of monads, our framework is rich enough to describe the semantics of effects for a large class of languages including common imperative and functional languages. It is also capable of capturing more expressive, precise, and practical effect systems than previous approaches. Finally, our framework enables one to reason about effects in a language-independent manner, and so can be applied to many stages of language design and implementation in order to create more broadly applicable tools for programming languages. 1.

### unknown title

, 2007

"... This paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∧ B) ∨ (C ∧ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connect ..."

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This paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∧ B) ∨ (C ∧ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connection with n-fold loop spaces, and for which a related, but different, coherence result was obtained previously by Balteanu, Fiedorowicz, Schwänzl and Vogt. The results of the present paper strengthen up to a point this previous result, and show that two-fold loop spaces arise in the manner envisaged by these authors out of categories of a more general kind, which are not two-fold monoidal in their sense. In particular, some categories with finite products and coproducts are such. Coherence in Mac Lane’s “all diagrams commute ” sense is proved here first for categories where for ∧ and ∨ one assumes only intermutation, and next for categories where one also assumes natural associativity isomorphisms.

### unknown title

, 2008

"... This paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∧ B) ∨ (C ∧ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connect ..."

Abstract
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This paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∧ B) ∨ (C ∧ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connection with n-fold loop spaces, and for which a related, but different, coherence result was obtained previously by Balteanu, Fiedorowicz, Schwänzl and Vogt. The results of the present paper strengthen up to a point this previous result, and show that two-fold loop spaces arise in the manner envisaged by these authors out of categories of a more general kind, which are not two-fold monoidal in their sense. In particular, some categories with finite products and coproducts are such. Coherence in Mac Lane’s “all diagrams commute ” sense is proved here first for categories where for ∧ and ∨ one assumes only intermutation, and next for categories where one also assumes natural associativity isomorphisms.

### unknown title

, 2008

"... This paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∧ B) ∨ (C ∧ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connect ..."

Abstract
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This paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∧ B) ∨ (C ∧ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connection with n-fold loop spaces, and for which a related, but different, coherence result was obtained previously by Balteanu, Fiedorowicz, Schwänzl and Vogt. The results of the present paper strengthen up to a point this previous result, and show that two-fold loop spaces arise in the manner envisaged by these authors out of categories of a more general kind, which are not two-fold monoidal in their sense. In particular, some categories with finite products and coproducts are such. Coherence in Mac Lane’s “all diagrams commute ” sense is proved here first for categories where for ∧ and ∨ one assumes only intermutation, and next for categories where one also assumes natural associativity isomorphisms.

### unknown title

, 2007

### unknown title

, 2007

### Symmetric bimonoidal intermuting categories and ω × ω reduced bar constructions

, 906

"... A new, self-contained, proof of a coherence result for categories equipped with two symmetric monoidal structures bridged by a natural transformation is given. It is shown that this coherence result is sufficient for ω × ω-indexed family of iterated reduced bar constructions based on such a category ..."

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A new, self-contained, proof of a coherence result for categories equipped with two symmetric monoidal structures bridged by a natural transformation is given. It is shown that this coherence result is sufficient for ω × ω-indexed family of iterated reduced bar constructions based on such a category.