scholarly journals Structural Induction Principles for Functional Programmers

2013 ◽  
Vol 136 ◽  
pp. 16-26 ◽  
Author(s):  
James Caldwell
Keyword(s):  
Structural Induction

Synthesis of cubic boron nitride by structural induction effect

2004 ◽  
Vol 270 (1-2) ◽  
pp. 192-196 ◽  
Author(s):  
Xiaopeng Hao ◽  
Jie Zhan ◽  
Wei Fang ◽  
Deliang Cui ◽  
Xiangang Xu ◽  
...  
Keyword(s):  
Boron Nitride ◽  
Cubic Boron Nitride ◽  
Induction Effect ◽  
Structural Induction

scholarly journals Structural Induction and Coinduction in a Fibrational Setting

1998 ◽  
Vol 145 (2) ◽  
pp. 107-152 ◽  
Author(s):  
Claudio Hermida ◽  
Bart Jacobs
Keyword(s):  
Structural Induction

scholarly journals Structural induction in institutions

2011 ◽  
Vol 209 (9) ◽  
pp. 1197-1222 ◽  
Author(s):  
Răzvan Diaconescu
Keyword(s):  
Structural Induction

The equational part of proofs by structural induction

1993 ◽  
Vol 33 (4) ◽  
pp. 596-618
Author(s):  
Olav Lysne
Keyword(s):  
Structural Induction

Proving Properties of Programs by Structural Induction

1969 ◽  
Vol 12 (1) ◽  
pp. 41-48 ◽  
Author(s):  
R. M. Burstall
Keyword(s):  
Structural Induction

scholarly journals A Simple Correctness Proof of the Direct-Style Transformation

2002 ◽  
Vol 9 (2) ◽  
Author(s):  
Lasse R. Nielsen
Keyword(s):  
Program Transformation ◽  
Higher Order ◽  
Correctness Proof ◽  
First Order ◽  
Structural Induction ◽  
Higher Order Functions

We build on Danvy and Nielsen's first-order program transformation into continuation-passing style (CPS) to present a new correctness proof of the converse transformation, i.e., a one-pass transformation from CPS back to direct style. Previously published proofs were based on, e.g., a one-pass higher-order CPS transformation, and were complicated by having to reason about higher-order functions. In contrast, this work is based on a one-pass CPS transformation that is both compositional and first-order, and therefore the proof simply proceeds by structural induction on syntax.

scholarly journals Structural induction: towards automatic ontology elicitation

2008 ◽  
Author(s):  
Adrian Silvescu
Keyword(s):  
Structural Induction

scholarly journals A First-Order One-Pass CPS Transformation

2001 ◽  
Vol 8 (49) ◽  
Author(s):  
Olivier Danvy ◽  
Lasse R. Nielsen
Keyword(s):  
Control Flow ◽  
Logical Relation ◽  
Correctness Proof ◽  
First Order ◽  
Structural Induction ◽  
Flow Information

We present a new transformation of call-by-value lambda-terms into continuation-passing style (CPS). This transformation operates in one pass and is both compositional and first-order. Because it operates in one pass, it directly yields compact CPS programs that are comparable to what one would write by hand. Because it is compositional, it allows proofs by structural induction. Because it is first-order, reasoning about it does not require the use of a logical relation.<br /> <br />This new CPS transformation connects two separate lines of research. It has already been used to state a new and simpler correctness proof of a direct-style transformation, and to develop a new and simpler CPS transformation of control-flow information.

scholarly journals Deep Induction: Induction Rules for (Truly) Nested Types

2020 ◽  
pp. 339-358
Author(s):  
Patricia Johann ◽  
Andrew Polonsky
Keyword(s):  
Fixed Points ◽  
Programming Languages ◽  
Case Studies ◽  
Level Structure ◽  
Structured Data ◽  
Proof Assistants ◽  
Data Types ◽  
Structural Induction ◽  
Locally Presentable Categories ◽  
Standing Problem

AbstractThis paper introduces deep induction, and shows that it is the notion of induction most appropriate to nested types and other data types defined over, or mutually recursively with, (other) such types. Standard induction rules induct over only the top-level structure of data, leaving any data internal to the top-level structure untouched. By contrast, deep induction rules induct over all of the structured data present. We give a grammar generating a robust class of nested types (and thus ADTs), and develop a fundamental theory of deep induction for them using their recently defined semantics as fixed points of accessible functors on locally presentable categories. We then use our theory to derive deep induction rules for some common ADTs and nested types, and show how these rules specialize to give the standard structural induction rules for these types. We also show how deep induction specializes to solve the long-standing problem of deriving principled and practically useful structural induction rules for bushes and other truly nested types. Overall, deep induction opens the way to making induction principles appropriate to richly structured data types available in programming languages and proof assistants. Agda implementations of our development and examples, including two extended case studies, are available.

Baseline conditions in structural induction: Comment on Pitt, Smith, and Klein (1998).

1999 ◽  
Vol 25 (5) ◽  
pp. 1472-1475
Author(s):  
Athanassios Protopapas ◽  
Steven A. Finney ◽  
Peter D. Eimas
Keyword(s):  
Structural Induction ◽  
Baseline Conditions
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