Monadic Presentations of Lambda Terms Using Generalized Inductive Types

Monadic Presentations of Lambda Terms Using Generalized Inductive Types (1999)

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by Thorsten Altenkirch , Bernhard Reus

Venue:	In Computer Science Logic
Citations:	68 - 14 self

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Datum	Value	Source
TITLE	Monadic Presentations of Lambda Terms Using Generalized Inductive Types	user correction - Legacy Corrections
AUTHOR NAME	Thorsten Altenkirch	SVM HeaderParse 0.1
AUTHOR ADDR	Ludwig-Maximilians-Universitat, Oettingenstr. 67, 80538 Munchen, Germany,	SVM HeaderParse 0.1
AUTHOR NAME	Bernhard Reus	SVM HeaderParse 0.1
AUTHOR ADDR	Ludwig-Maximilians-Universitat, Oettingenstr. 67, 80538 Munchen, Germany,	SVM HeaderParse 0.1
ABSTRACT	. We present a denition of untyped -terms using a heterogeneous datatype, i.e. an inductively dened operator. This operator can be extended to a Kleisli triple, which is a concise way to verify the substitution laws for -calculus. We also observe that repetitions in the denition of the monad as well as in the proofs can be avoided by using well-founded recursion and induction instead of structural induction. We extend the construction to the simply typed -calculus using dependent types, and show that this is an instance of a generalization of Kleisli triples. The proofs for the untyped case have been checked using the LEGO system. Keywords. Type Theory, inductive types, -calculus, category theory. 1 Introduction The metatheory of substitution for -calculi is interesting maybe because it seems intuitively obvious but becomes quite intricate if we take a closer look. [Hue92] states seven formal properties of substitution which are then used to prove a general substitution theor...	user correction - Legacy Corrections
YEAR	1999	INFERENCE
VENUE	In Computer Science Logic	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	453--468	INFERENCE
VOLUME	1683	INFERENCE
CITATIONS	24 found	ParsCit 1.0