Citation
Choo, Youngil (1987) Logic from Programming Language Semantics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd02282008111427
Abstract
Logic for reasoning about programs must proceed from the programming language semantics. It is our thesis that programs be considered as mathematical objects that can be reasoned about directly, rather than as linguistic expressions whose meanings are embedded in an intermediate formalism.
Since the semantics of many programming language features (including recursion, typefree application, infinite structures, selfreference, and reflection) require models that are constructed as limits of partial objects, a logic for dealing with partial objects is required.
Using the D_{∞} model of the λcalculus, a logic (called continuous logic) for reasoning about partial objects is presented. In continuous logic, the logical operations (negation, implication, and quantification) are defined for each of the finite levels and then extended to the limit, giving us a model of typefree logic.
The triples of Hoare Logic are interpreted as partial assertions over the domain of partial states, and contradictions arising from rules for function definitions are analyzed. Recursive procedures and recursive functions are both proved using mathematical induction.
A domain of infinite lists is constructed as a model for languages with lazy evaluation and it is compared to an ordinalheirarchic construction. A model of objects and multiple inheritance is constructed where objects are selfreferential states and multiple inheritance is defined using the notion of product of classes. The reflective processor for a language with environment and continuation reflection is constructed as the projective limit of partial reflective processors of finite height.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Computer Science 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Computer Science 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  21 May 1987 
Record Number:  CaltechETD:etd02282008111427 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd02282008111427 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  811 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  12 Mar 2008 
Last Modified:  13 Jun 2019 21:33 
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