F. van Raamsdonk, P. Severi, M. H. S rensen, and H. Xi. Perpetual reductions in lambda calculus. Inf. and Comp., 149(2):173-225, 1999. 15  Home/Search Document Details and Download
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Continuous Normalization for the Lambda-Calculus and Gödel's T - Aehlig, Joachimski (Correct)
....( computes the normal form using the leftmost outermost strategy. This can be used to derive bounds for the length of reduction sequences that follow this strategy. Yet by only a minor tweak to the definition of ( it is possible to make the reduction strategy perpetual (in the sense of [vRSSX99]) so that the number of steps performed limits the height of the reduction tree altogether. To this end we slightly modify the grammar of #R (and its coinductive analogue) by adding a term as an index of the # constructor: # s r. The respective clause in the definition of ( is ....
....# n in subsection 3.3 to include reductions on the side term: r[s]#s # n t s #m s # 0 (#r)s#s # n m 1 t r[s]#s # n t 0 Herein, the free variables FV r are defined recursively as usual. The strategy # : # n is perpetual: it finds the longest possible reduction strategy (as reproved in [vRSSX99] with di#erent notations) 4.2. Types. Simple) Types #, #, # are generated from basic types # by # #. The level of # is given by lev # : 0 and lev (# #) max 1 lev #, lev # . The typed # calculi (in Church form) are obtained from the untyped ones by attaching types to # abstractions: ....
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Femke van Raamsdonk, Paula Severi, Morten Heine Srensen, and Hongwei Xi. Perpetual reductions in lambda-calculus. Information and Computation, 149(2):173--225, 1999.
On Zucker's isomorphism for LJ and its extension to Pure Type.. - Joachimski (2003) (Correct)
....= zt) xr)s) zt) r[x : s] t[z : r[x : s] ut 12 This result can be used to derive strong normalizability of terms in J from their strong normalizability as terms of . First, we recall a basic property of # , which has also been dubbed the fundamental lemma of perpetuality [vRSSX99]: Proposition 11. x 2 r = # ( xr)s) # (r[x : s] 1; x 62 r = # ( xr)s) # r # s 1: Lemma 12. r s = # r # s. Proof. Induction on . The inner reductions are all quite straightforward. The interesting case is that of a permutation In , the two ....
Femke van Raamsdonk, Paula Severi, Morten Heine S rensen, and Hongwei Xi. Perpetual reductions in lambda-calculus. Information and Computation, 149(2):173-225, 1999.
Continuous Normalization for the Lambda-Calculus and Gödel's T - Aehlig, Joachimski (Correct)
....( computes the normal form using the leftmost outermost strategy. This can be used to derive bounds for the length of reduction sequences that follow this strategy. Yet by only a minor tweak to the de nition of ( it is possible to make the reduction strategy perpetual (in the sense of [vRSSX99]) so that the number of steps performed limits the height of the reduction tree altogether. To this end we slightly modify the grammar of R (and its coinductive analogue) by adding a term as an index of the constructor: k j rs j r j Rr j s r: The respective clause in the de nition of ( ....
....3.3 to include reductions on the side term: r[s] s ; n t s ;m s 0 62 FV r ( r)s s ; n m 1 t r[s] s ; n t 0 2 FV r ( Herein, the free variables FV r are de ned recursively as usual. The strategy ; n ; n is perpetual: it nds the longest possible reduction strategy (as reproved in [vRSSX99] with di erent notations) 4.2. Types. Simple) Types ; are generated from basic types by . The level of is given by lev : 0 and lev ( maxf1 lev ; lev g. The typed calculi (in Church form) are obtained from the untyped ones by attaching types to abstractions: ....
[Article contains additional citation context not shown here]
Femke van Raamsdonk, Paula Severi, Morten Heine S rensen, and Hongwei Xi. Perpetual reductions in lambda-calculus. Information and Computation, 149(2):173-225, 1999.
Fixed Points of Type Constructors and Primitive Recursion - Abel, Matthes (Correct)
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F. van Raamsdonk, P. Severi, M. H. S rensen, and H. Xi. Perpetual reductions in lambda calculus. Inf. and Comp., 149(2):173-225, 1999. 15
Weak Normalization for the Simply-Typed Lambda-Calculus in Twelf.. - Abel (2004) (Correct)
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Femke van Raamsdonk, Paula Severi, Morten Heine S rensen, and Hongwei Xi. Perpetual reductions in lambda calculus. Information and Computation, 149(2):173-225, March 1999. 10
Strong normalisation of Herbelin's explicit substitution.. - Dyckhoff, Urban (Correct)
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F. van Raamsdonk, P. Severi, M. H. Sorensen and H. Xi. Perpetual Reductions in Lambda Calculus. Information and Computation 149, pages 173-225, 1999.
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