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@pchampin
Created September 22, 2020 12:38
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N3 axiomatization of builtin predicate `list:memberAt`
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.
@prefix math: <http://www.w3.org/2000/10/swap/math#>.
@prefix : <#>.
{ (?lst 1) :memberAt ?elt } <= { ?lst rdf:first ?elt. }.
{ (?lst ?i) :memberAt ?elt } <= { ?lst rdf:first ?elt. ?i math:equalTo 1. }.
{ (?lst ?i) :memberAt ?elt } <= { ?lst rdf:rest ?rest. (?rest ?j) :memberAt ?elt. (?j 1) math:sum ?i. }.
{ ((41) 1) :memberAt 41 } => { :TEST :PASS 1 }.
{ ((41) 1.0) :memberAt 41 } => { :TEST :PASS 2 }.
{ ((41) 1) :memberAt ?x } => { :TEST :PASS (3 ?x) }.
{ ((41) ?i) :memberAt 41 } => { :TEST :PASS (4 ?i) }.
{ ((41 42 43) 1) :memberAt 41 } => { :TEST :PASS 5 }.
{ ((41 42 43) 2) :memberAt 42 } => { :TEST :PASS 6 }.
{ ((41 42 43) 3) :memberAt 43 } => { :TEST :PASS 7 }.
{ ((41 42 43) 2.0) :memberAt 42 } => { :TEST :PASS 8 }.
{ ((41 42 41) ?i) :memberAt 41 } => { :TEST :PASS (9 ?i) }.
{ ((41 42 43) 2) :memberAt ?x } => { :TEST :PASS (10 ?x) }.
{ ((41) 0) :memberAt 41 } => { :TEST :SHOULDNT_PASS 1 }.
{ ((41) 1) :memberAt 42 } => { :TEST :SHOULDNT_PASS 2 }.
{ ((41) 2) :memberAt 41 } => { :TEST :SHOULDNT_PASS 3 }.
{ ((41 42 43) 0) :memberAt 41 } => { :TEST :SHOULDNT_PASS 4 }.
{ ((41 42 43) 1) :memberAt 42 } => { :TEST :SHOULDNT_PASS 5 }.
{ ((41 42 43) 2) :memberAt 41 } => { :TEST :SHOULDNT_PASS 6 }.
{ ((41 42 43) 2) :memberAt 43 } => { :TEST :SHOULDNT_PASS 7 }.
{ ((41 42 43) 4) :memberAt 44 } => { :TEST :SHOULDNT_PASS 8 }.
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