Galois connections and computer science applications

Melton, Austin; Schmidt, David A.; Strecker, G. E.

doi:10.1007/3-540-17162-2_130

Cited by 59 publications

(38 citation statements)

References 8 publications

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“…In this section we recall some concepts (mainly from [16]) about reduction relations, especially notions used to relate one calculus to another. Definition 1 (Simulation) Let R be a total function from a set A to a set B, respectively equipped with the reduction relations →A and →B.…”

Section: Preliminary Notionsmentioning

confidence: 99%

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Call-by-Value -calculus and LJQ

Dyckhoff

Lengrand

2007

Journal of Logic and Computation

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LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premiss of the usual left introduction rule for implication. In a previous paper we discussed its history (going back to about 1950, or beyond) and presented its basic theory and some applications; here we discuss in detail its relation to call-by-value reduction in lambda calculus, establishing a connection between LJQ and the CBV calculus λ C of Moggi. In particular, we present an equational correspondence between these two calculi forming a bijection between the two sets of normal terms, and allowing reductions in each to be simulated by reductions in the other.

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Section: Preliminary Notionsmentioning

confidence: 99%

“…We now define some more elaborate notions based on simulation, such as equational correspondence [24], Galois connection and reflection [16]. A useful account of these notions, with intuitive explanations, can be found for instance in [25].…”

Section: Preliminary Notionsmentioning

confidence: 99%

Call-by-Value -calculus and LJQ

Dyckhoff

Lengrand

2007

Journal of Logic and Computation

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“…Given several versions of the same program with varied nesting, lambda-lifting maps them into the same set of mutually recursive equations. We thus conjecture the following two properties, which are reminiscent of a Galois connection [31]:…”

Section: Correctness Issuesmentioning

confidence: 91%

Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure

Danvy¹,

Schultz²

1999

BRICS

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Lambda-lifting a block-structured program transforms it into a set of recursive equations. We present the symmetric transformation: lambdadropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.For lack of block structure and lexical scope, recursive equations must carry around all the parameters that any of their callees might possibly need. Both lambda-lifting and lambda-dropping thus require one to compute Def/Use paths:• for lambda-lifting: each of the functions occurring in the path of a free variable is passed this variable as a parameter;• for lambda-dropping: parameters which are used in the same scope as their definition do not need to be passed along in their path.A program whose blocks have no free variables is scope-insensitive. Its blocks are then free to float (for lambda-lifting) or to sink (for lambdadropping) along the vertices of the scope tree. *

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“…[21]) is a pair of mappings f ♭ : B → A and f ♯ : A → B between posets (A, ≤ A ) and (B, ≤ B ) such that, for all a ∈ A and b ∈ B,…”

Section: Galois Connectionsmentioning

confidence: 99%

Algebraic Notions of Termination

Struth¹,

Moeller²,

Desharnais³

2011

Logical Methods in Computer Science

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Abstract. Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, Löb's formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To model infinite behaviours, idempotent semirings are extended to divergence semirings, divergence Kleene algebras and omega algebras. The resulting notions and techniques are used in calculational proofs of classical theorems of rewriting theory. These applications show that modal semirings are powerful tools for reasoning algebraically about the finite and infinite dynamics of programs and transition systems.

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Galois connections and computer science applications

Cited by 59 publications

References 8 publications

Call-by-Value -calculus and LJQ

Call-by-Value -calculus and LJQ

Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure

Algebraic Notions of Termination

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