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Abstract Modularity
[chapter]

2005
*
Lecture Notes in Computer Science
*

We now show that strong

doi:10.1007/978-3-540-32033-3_5
fatcat:4q2eamf54retlnlmk2azxuorn4
*normalisation*is*monadic*. ... Now observe that the free lifting M ∅ of the*monad*M is strongly*normalising*because the only rewrites in M ∅ are variable rewrites. ...##
###
Monadic translation of classical sequent calculus

2013
*
Mathematical Structures in Computer Science
*

*normalisation*. ... Through strict simulation, the strong

*normalisation*of simply typed λ-calculus is inherited by

*monadic*λµ, and then by cbn and cbv λµμ, thus reproving strong

*normalisation*in an elementary syntactical ... Since the optimised cbn CPS translation also preserves typability, we can infer the strong

*normalisation*of λµμ n from the strong

*normalisation*of λ[β v ]. A.3.2. Cbv case. ...

##
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Monads and modular term rewriting
[chapter]

1997
*
Lecture Notes in Computer Science
*

This paper provides further support for

doi:10.1007/bfb0026982
fatcat:h44atucbzfg6loz7hocujyb5su
*monadic*semantics of rewriting by giving a categorical proof of the most general theorem concerning the modularity of strong*normalisation*. ...*Monads*can be used to model term rewriting systems by generalising the well-known equivalence between universal algebra and*monads*on the category Set. ... Firstly,*monads*can be used to model more general notions of term rewriting for which current modularity results are less than satisfactory. ...##
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Monad Comprehensions: A Versatile Representation for Queries
[chapter]

2004
*
The Functional Approach to Data Management
*

The

doi:10.1007/978-3-662-05372-0_12
fatcat:atrdgwaj5beedkapgmzata7crq
*monad*comprehension*normalisation*rules provide an elegant proof of this transformation: select distinct f x from xs as x where p x z = {f x | x ← xs,p x z} = {f x | x ← xs,or [ |p x v | v ← z| ]} ... = {f x | x ← xs,v ← z,p x v} = {f x | x ← xs,v ←{ |g x y | y ← ys,q x y } |,p x v} = {f x | x ← xs,y ← ys,q x y,p x (g x y)} More Unnesting*Monad*comprehension*normalisation*readily unnests queries of ...##
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The marriage of effects and monads

1999
*
SIGPLAN notices
*

Here we marry effects to

doi:10.1145/291251.289429
fatcat:xnty2prj5ndv3cjrf3qyh2yyue
*monads*, uniting two previously separate lines of research. ... The same technique should allow one to transpose any effect system into a corresponding*monad*system. ... (τ, κ) whereω is a sequence of type, region, or effect variables; the scheme is*normalised*if τ is*normalised*. ...##
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The marriage of effects and monads

2003
*
ACM Transactions on Computational Logic
*

Here we marry effects to

doi:10.1145/601775.601776
fatcat:mommvu6runc7zcp7ifiudwu37a
*monads*, uniting two previously separate lines of research. ... The same technique should allow one to transpose any effect system into a corresponding*monad*system. ... (τ, κ) whereω is a sequence of type, region, or effect variables; the scheme is*normalised*if τ is*normalised*. ...##
###
The marriage of effects and monads

1998
*
Proceedings of the third ACM SIGPLAN international conference on Functional programming - ICFP '98
*

Here we marry effects to

doi:10.1145/289423.289429
dblp:conf/icfp/Wadler98
fatcat:hcyld6qx6rapxcwqh3cu7gvdfy
*monads*, uniting two previously separate lines of research. ... The same technique should allow one to transpose any effect system into a corresponding*monad*system. ... (τ, κ) whereω is a sequence of type, region, or effect variables; the scheme is*normalised*if τ is*normalised*. ...##
###
Computational types from a logical perspective

1998
*
Journal of functional programming
*

We give natural deduction, sequent calculus and Hilbert-style presentations of this logic and prove strong

doi:10.1017/s0956796898002998
fatcat:bz7weznvwjehfkdqnseaacmj5a
*normalisation*and con uence results. ... Moggi's computational lambda calculus is a metalanguage for denotational semantics which arose from the observation that many di erent notions of computation have the categorical structure of a strong*monad*... c into a precongruence and these all follow trivially from the compositional nature of the translation.Corollary 10 (Strong*Normalisation*)*monad*over a category C with nite products is a*monad*(T; ; ...##
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Algebras of Higher Operads as Enriched Categories

2008
*
Applied Categorical Structures
*

We decribe the correspondence between

doi:10.1007/s10485-008-9179-7
fatcat:wx7wskqgsre4pc7w36f7bglsc4
*normalised*ω-operads in the sense of [1] and certain lax monoidal structures on the category of globular sets. ... Within the aforementioned correspondence, we provide also an equivalence between the algebras of a given*normalised*ωoperad, and categories enriched in globular sets for the induced lax monoidal structure ... A is*normalised*as a*monad*or endofunctor. ...##
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Algebras of higher operads as enriched categories
[article]

2008
*
arXiv
*
pre-print

We decribe the correspondence between

arXiv:0803.3594v1
fatcat:azzsreetprg4hoe2w5n2adgo3y
*normalised*$\omega$-operads and certain lax monoidal structures on the category of globular sets. ... Within the aforementioned correspondence, we provide also an equivalence between the algebras of a given*normalised*$\omega$-operad, and categories enriched in globular sets for the induced lax monoidal ... A is*normalised*as a*monad*or endofunctor. ...##
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Interactive Programs in Dependent Type Theory
[chapter]

2000
*
Lecture Notes in Computer Science
*

The inspiration is the 'I/O-

doi:10.1007/3-540-44622-2_21
fatcat:rpbpqq4sond2ngof2wjp3kfapu
*monad*' of Haskell. ... We present I/O-trees in two forms that we call 'non-*normalising*' and '*normalising*'. ... A special case of a*monad*is the I/O-*monad*. When referring to the I/O-*monad*we write (IO A) instead of (M A). The interpretation of IO is as follows. ...##
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Reducibility and ⊤ ⊤-Lifting for Computation Types
[chapter]

2005
*
Lecture Notes in Computer Science
*

We propose -lifting as a technique for extending operational predicates to Moggi's

doi:10.1007/11417170_20
fatcat:yyq2cyfucvdojl2wbzapquncta
*monadic*computation types, independent of the choice of*monad*. ... The method appears robust: we apply it to show strong*normalisation*for the computational metalanguage extended with sums, and with exceptions. ... simulate all definable*monads*[12] . ...##
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Monadic Translation of Intuitionistic Sequent Calculus
[chapter]

2009
*
Lecture Notes in Computer Science
*

Indeed, strong

doi:10.1007/978-3-642-02444-3_7
fatcat:2mgnq6ckerftdlw7oakm4ezsha
*normalisation*follows immediately from strict simulation, since the target system is itself strongly*normalising*. ... Section 4 defines and proves the properties of the*monadic*translation and its optimized variant, and strong*normalisation*for λJ mse is obtained. ... Strong*normalisation*of λ[β, assoc, perm] will be needed below in Section 5.1 for translation F . ...##
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Backtracking with cut via a distributive law and left-zero monoids

2017
*
Journal of functional programming
*

We give two descriptions of the resulting

doi:10.1017/s0956796817000077
fatcat:ziro3piclvg6hgwrc5xvmxx6pq
*monad*: as the*monad*of free left-zero monoids, and as a composition via a distributive law of the list*monad*and the 'unary idempotent operation'*monad*. ... We employ the framework of algebraic effects to augment the list*monad*with the pruning cut operator known from Prolog. ... If R is confluent and*normalising*, then for all Σ T -terms t and s, it is the case that t ≈ T s if and only if nf(t) = nf(s). ...##
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A Lean Tactic for Normalising Ring Expressions with Exponents (Short Paper)
[chapter]

2020
*
Lecture Notes in Computer Science
*

This paper describes the design of the

doi:10.1007/978-3-030-51054-1_2
fatcat:xx42pfvq3vhazojqowowiudwea
*normalising*tactic ring exp for the Lean prover. This tactic improves on existing tactics by extending commutative rings with a binary exponent operator. ... The ring exp m*monad*contains a state*monad*transformer to keep track of which atoms are definitionally equal. ... The calculations of the eval function are thus done in an extension of the tactic*monad*, called the ring exp m*monad*. ...
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