Extensional normalisation and type-directed partial evaluation for typed lambda calculus with sums

Balat, Vincent; Cosmo, Roberto Di; Fiore, Marcelo

doi:10.1145/964001.964007

Cited by 48 publications

(48 citation statements)

References 21 publications

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“…There is a general consensus that normalization by evaluation is an art because one must invent a non-standard, extensional evaluation function and its left inverse [1,6,7,10,12,14,16,26,32,35,37,44].…”

Section: Resultsmentioning

confidence: 99%

“…Normalization by evaluation therefore requires one to extensionally define a reduction-free normalization function, which is non-trivial [6,7]. Nevertheless, it is our contention that the computational content of a reduction-based normalization function-i.e., a function intensionally defined as the transitive closure of one-step reduction-can pave the way to constructing a reductionfree normalization function:…”

Section: Introductionmentioning

confidence: 95%

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From Reduction-based to Reduction-free Normalization

Danvy

2005

Electronic Notes in Theoretical Computer Science

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We present a systematic construction of a reduction-free normalization function. Starting from a reduction-based normalization function, i.e., the transitive closure of a one-step reduction function, we successively subject it to refocusing (i.e., deforestation of the intermediate reduced terms), simplification (i.e., fusing auxiliary functions), refunctionalization (i.e., Church encoding), and direct-style transformation (i.e., the converse of the CPS transformation). We consider two simple examples and treat them in detail: for the first one, arithmetic expressions, we construct an evaluation function; for the second one, terms in the free monoid, we construct an accumulatorbased flatten function. The resulting two functions are traditional reduction-free normalization functions. The construction builds on previous work on refocusing and on a functional correspondence between evaluators and abstract machines. It is also reversible.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

From Reduction-based to Reduction-free Normalization

Danvy

2005

Electronic Notes in Theoretical Computer Science

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“…In the following sections, we will make use of the notational equivalence of expressions such as x1 :: x2 :: xs (x1 :: x2 :: nil) @ xs [x1, x2] @ xs where :: denotes infix list construction and @ denotes infix list concatenation. In an environment where x1 denotes 1, x2 denotes 2, and xs denotes [3,4,5], each of the three expressions above evaluates to [1,2,3,4,5].…”

Section: Overviewmentioning

confidence: 99%

“…Given two trees of integers, one wants to know whether they have the same sequence of leaves when read from left to right. For example, the two trees NODE (NODE (LEAF 1, LEAF 2), LEAF 3) and NODE (LEAF 1, NODE (LEAF 2, LEAF 3)) have the same fringe [1,2,3] (representing it as a list) even though they are shaped differently: …”

Section: The Samefringe Problemmentioning

confidence: 99%

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On the static and dynamic extents of delimited continuations

Biernacki

Danvy

Shan

2006

Science of Computer Programming

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We show that breadth-first traversal exploits the difference between the static delimited-control operator shift (alias S) and the dynamic delimited-control operator control (alias F). For the last 15 years, this difference has been repeatedly mentioned in the literature but it has only been illustrated with one-line toy examples. Breadth-first traversal fills this vacuum.We also point out where static delimited continuations naturally give rise to the notion of control stack whereas dynamic delimited continuations can be made to account for a notion of 'control queue'.

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Relative Full Completeness for Bicategorical Cartesian Closed Structure

Fiore

Saville

2020

Lecture Notes in Computer Science

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The glueing construction, defined as a certain comma category, is an important tool for reasoning about type theories, logics, and programming languages. Here we extend the construction to accommodate '2-dimensional theories' of types, terms between types, and rewrites between terms. Taking bicategories as the semantic framework for such systems, we define the glueing bicategory and establish a bicategorical version of the well-known construction of cartesian closed structure on a glueing category. As an application, we show that free finite-product bicategories are fully complete relative to free cartesian closed bicategories, thereby establishing that the higher-order equational theory of rewriting in the simply-typed lambda calculus is a conservative extension of the algebraic equational theory of rewriting in the fragment with finite products only.

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Extensional normalisation and type-directed partial evaluation for typed lambda calculus with sums

Cited by 48 publications

References 21 publications

From Reduction-based to Reduction-free Normalization

From Reduction-based to Reduction-free Normalization

On the static and dynamic extents of delimited continuations

Relative Full Completeness for Bicategorical Cartesian Closed Structure

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