{"id":{"repo_id":"lethbridge","oai_identifier":"oai:opus.uleth.ca:10133/1296"},"canonical_url":"https://search.dev.ndltd.org/etd/lethbridge/oai:opus.uleth.ca:10133/1296","repository":{"repo_id":"lethbridge","name":"University of Lethbridge","base_url":"https://opus.uleth.ca/server/oai/request"},"display":{"title":"A new program for combinatory reduction and abstraction","abstract":"Even though lambda calculus (λ-calculus) and combinatory logic (CL) appear to be equivalent, they are not. As yet we do not have a reduction in CL which corresponds to β-reduction in λ-calculus. There are three proposals but they all have few problems one of which is the lack of a complete characterization of CL-terms corresponding to λ-terms in β-normal form. Finding such a characterization for any of the three proposals appears to require a lot of examples which are tedious and time consuming to develop by hand. For this reason, a computer program to do reductions and abstractions of CL-terms would be useful. This thesis is about an attempt to write such a program. The program that we have does not yet work for the three proposals but it works for βη-strong reduction. Coding this program turned out to be much harder than anticipated. Dr. Robin Cockett developed a semantic translation which helped in coding the program but his semantic translation needs to be extended to all three proposals to obtain the program originally desired and that needs a lot of research.","abstract_html":"Even though lambda calculus (λ-calculus) and combinatory logic (CL) appear to be equivalent, they are not. As yet we do not have a reduction in CL which corresponds to β-reduction in λ-calculus. There are three proposals but they all have few problems one of which is the lack of a complete characterization of CL-terms corresponding to λ-terms in β-normal form. Finding such a characterization for any of the three proposals appears to require a lot of examples which are tedious and time consuming to develop by hand. For this reason, a computer program to do reductions and abstractions of CL-terms would be useful. This thesis is about an attempt to write such a program. The program that we have does not yet work for the three proposals but it works for βη-strong reduction. Coding this program turned out to be much harder than anticipated. Dr. Robin Cockett developed a semantic translation which helped in coding the program but his semantic translation needs to be extended to all three proposals to obtain the program originally desired and that needs a lot of research.","abstract_has_math":false,"creators":["Deshpande, Sushant","University of Lethbridge. Faculty of Arts and Science"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-27T20:02:11Z","subjects":["Combinatory logic","Lambda calculus","Dissertations, Academic"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/1296"],"render_values":[{"text":"hdl:10133/1296","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Combinatory logic","Lambda calculus","Dissertations, Academic"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/1296"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["Even though lambda calculus (λ-calculus) and combinatory logic (CL) appear to be equivalent, they are not. As yet we do not have a reduction in CL which corresponds to β-reduction in λ-calculus. There are three proposals but they all have few problems one of which is the lack of a complete characterization of CL-terms corresponding to λ-terms in β-normal form. Finding such a characterization for any of the three proposals appears to require a lot of examples which are tedious and time consuming to develop by hand. For this reason, a computer program to do reductions and abstractions of CL-terms would be useful. This thesis is about an attempt to write such a program. The program that we have does not yet work for the three proposals but it works for βη-strong reduction. Coding this program turned out to be much harder than anticipated. Dr. Robin Cockett developed a semantic translation which helped in coding the program but his semantic translation needs to be extended to all three proposals to obtain the program originally desired and that needs a lot of research."]},{"key":"dc:title","label":"Title","values":["A new program for combinatory reduction and abstraction"]}]}],"canonical_facts":{"dc:date.issued":["2009"],"dc:description.other":["Even though lambda calculus (λ-calculus) and combinatory logic (CL) appear to be equivalent, they are not. As yet we do not have a reduction in CL which corresponds to β-reduction in λ-calculus. There are three proposals but they all have few problems one of which is the lack of a complete characterization of CL-terms corresponding to λ-terms in β-normal form. Finding such a characterization for any of the three proposals appears to require a lot of examples which are tedious and time consuming to develop by hand. For this reason, a computer program to do reductions and abstractions of CL-terms would be useful. This thesis is about an attempt to write such a program. The program that we have does not yet work for the three proposals but it works for βη-strong reduction. Coding this program turned out to be much harder than anticipated. Dr. Robin Cockett developed a semantic translation which helped in coding the program but his semantic translation needs to be extended to all three proposals to obtain the program originally desired and that needs a lot of research."],"dc:identifier":["hdl:10133/1296"],"dc:subject":["Combinatory logic","Lambda calculus","Dissertations, Academic"],"dc:title":["A new program for combinatory reduction and abstraction"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:02:11Z"}