In the untyped-calculus some terms have an infinite reduction path. The simplest example is the
|
414
|
Termination of rewriting
– Dershowitz
- 1987
|
|
168
|
Ordering by divisibility in abstract algebras
– Higman
- 1952
|
|
152
|
R.Feys: Combinatory logic
– Curry
- 1958
|
|
113
|
The Lambda Calculus: Its Syntax and Semantics. North-Holland, revised edition
– Barendregt
- 1984
|
|
85
|
the Tree Theorem, and Vazsonyi's conjecture
– Well-quasi-ordering
- 1960
|
|
45
|
On well-quasi-ordering finite trees
– Nash-Williams
- 1963
|
|
36
|
What’s so Special about Kruskal’s Theorem and the Ordinal Γ0
– Gallier
- 1991
|
|
30
|
An analysis of loop checking mechanisms for logic programs
– Bol, Krzysztof, et al.
- 1991
|
|
21
|
The longest perpetual reductions in orthogonal expression reduction systems
– Khasidashvili
- 1994
|
|
16
|
The Undecidability of Self-Embedding for Term Rewriting Systems
– Plaisted
- 1985
|
|
13
|
Degrees, reductions and representability in the lambda calculus
– Barendregt, Bergstra, et al.
- 1976
|
|
11
|
Perpetuality and strong normalization in orthogonal term rewriting systems
– Khasidashvili
- 1994
|
|
9
|
terms as total or partial functions on normal forms
– Bohm, Dezani-Ciancaglini
- 1975
|
|
7
|
Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Baume
– Simpson
- 1985
|
|
6
|
BCK-Algebras and Lambda Calculus
– Komori
- 1987
|
|
6
|
Effective longest and infinite reduction paths in untyped -calculus
– Srensen
- 1996
|
|
4
|
Semantics of lambda-I and of other substructure calculi
– Jacobs
- 1993
|
|
3
|
Infinitary Normalization
– Klop, Vrijer
- 2005
|
|
3
|
A loop-detecting interpreter for lazy programs
– Holst, Hughes
- 1992
|
|
3
|
Lambda-calculus terms that reduce to themselves. Notre Dame
– Lercher
- 1976
|
|
2
|
Termination tests inside -calculus
– Bohm, Coppo, et al.
- 1975
|
|
2
|
Naive Set Theory. Springer-Verlag. Undergraduate texts in mathematics
– Halmos
- 1960
|
|
1
|
BCK-Combinators and Linear -Terms have Types. Theoretical Computer Science 64:97--105
– Hindley
- 1989
|
|
1
|
Centre de Recherche en Informatique de Nancy
– INRIA-Lorraine
- 1995
|
|
1
|
Combinatory Reduction Systems. Doctoral dissertation
– Klop
- 1980
|