# ========================================================================== # Easter — ARC-style # # This example computes the date of Easter Sunday in the Gregorian calendar. # For each year in a sample range, it applies the classic computus step by # step, explains the resulting month and day, and then checks independent # properties of the result: cycle bounds, remainder bounds, and the legal # Easter date window in March or April. # ========================================================================== @prefix : . @prefix math: . @prefix log: . @prefix string: . @prefix rdfs: . @prefix xsd: . <> rdfs:comment """This ARC-style version keeps the Gregorian computus from the original example and reports, for each sample year, an Answer, a Reason Why, and a set of independent Checks.""" . :y2026 a :Case; :year 2026 . :y2027 a :Case; :year 2027 . :y2028 a :Case; :year 2028 . :y2029 a :Case; :year 2029 . :y2030 a :Case; :year 2030 . :y2031 a :Case; :year 2031 . :y2032 a :Case; :year 2032 . :y2033 a :Case; :year 2033 . :y2034 a :Case; :year 2034 . :y2035 a :Case; :year 2035 . :goldenRemainder :value 0 . :goldenRemainder :value 1 . :goldenRemainder :value 2 . :goldenRemainder :value 3 . :goldenRemainder :value 4 . :goldenRemainder :value 5 . :goldenRemainder :value 6 . :goldenRemainder :value 7 . :goldenRemainder :value 8 . :goldenRemainder :value 9 . :goldenRemainder :value 10 . :goldenRemainder :value 11 . :goldenRemainder :value 12 . :goldenRemainder :value 13 . :goldenRemainder :value 14 . :goldenRemainder :value 15 . :goldenRemainder :value 16 . :goldenRemainder :value 17 . :goldenRemainder :value 18 . :epactRemainder :value 0 . :epactRemainder :value 1 . :epactRemainder :value 2 . :epactRemainder :value 3 . :epactRemainder :value 4 . :epactRemainder :value 5 . :epactRemainder :value 6 . :epactRemainder :value 7 . :epactRemainder :value 8 . :epactRemainder :value 9 . :epactRemainder :value 10 . :epactRemainder :value 11 . :epactRemainder :value 12 . :epactRemainder :value 13 . :epactRemainder :value 14 . :epactRemainder :value 15 . :epactRemainder :value 16 . :epactRemainder :value 17 . :epactRemainder :value 18 . :epactRemainder :value 19 . :epactRemainder :value 20 . :epactRemainder :value 21 . :epactRemainder :value 22 . :epactRemainder :value 23 . :epactRemainder :value 24 . :epactRemainder :value 25 . :epactRemainder :value 26 . :epactRemainder :value 27 . :epactRemainder :value 28 . :epactRemainder :value 29 . :weekdayRemainder :value 0 . :weekdayRemainder :value 1 . :weekdayRemainder :value 2 . :weekdayRemainder :value 3 . :weekdayRemainder :value 4 . :weekdayRemainder :value 5 . :weekdayRemainder :value 6 . :slot_m3_d22 :monthNum 3; :day 22 . :slot_m3_d23 :monthNum 3; :day 23 . :slot_m3_d24 :monthNum 3; :day 24 . :slot_m3_d25 :monthNum 3; :day 25 . :slot_m3_d26 :monthNum 3; :day 26 . :slot_m3_d27 :monthNum 3; :day 27 . :slot_m3_d28 :monthNum 3; :day 28 . :slot_m3_d29 :monthNum 3; :day 29 . :slot_m3_d30 :monthNum 3; :day 30 . :slot_m3_d31 :monthNum 3; :day 31 . :slot_m4_d1 :monthNum 4; :day 1 . :slot_m4_d2 :monthNum 4; :day 2 . :slot_m4_d3 :monthNum 4; :day 3 . :slot_m4_d4 :monthNum 4; :day 4 . :slot_m4_d5 :monthNum 4; :day 5 . :slot_m4_d6 :monthNum 4; :day 6 . :slot_m4_d7 :monthNum 4; :day 7 . :slot_m4_d8 :monthNum 4; :day 8 . :slot_m4_d9 :monthNum 4; :day 9 . :slot_m4_d10 :monthNum 4; :day 10 . :slot_m4_d11 :monthNum 4; :day 11 . :slot_m4_d12 :monthNum 4; :day 12 . :slot_m4_d13 :monthNum 4; :day 13 . :slot_m4_d14 :monthNum 4; :day 14 . :slot_m4_d15 :monthNum 4; :day 15 . :slot_m4_d16 :monthNum 4; :day 16 . :slot_m4_d17 :monthNum 4; :day 17 . :slot_m4_d18 :monthNum 4; :day 18 . :slot_m4_d19 :monthNum 4; :day 19 . :slot_m4_d20 :monthNum 4; :day 20 . :slot_m4_d21 :monthNum 4; :day 21 . :slot_m4_d22 :monthNum 4; :day 22 . :slot_m4_d23 :monthNum 4; :day 23 . :slot_m4_d24 :monthNum 4; :day 24 . :slot_m4_d25 :monthNum 4; :day 25 . # -------- # Computus # -------- { ?Case a :Case; :year ?Y. (?Y 19) math:remainder ?J. (?Y 100) math:integerQuotient ?K; math:remainder ?H. (?K 4) math:integerQuotient ?M; math:remainder ?N. ((?K 8)!math:sum 25) math:integerQuotient ?P. (((?K ?P)!math:difference 1)!math:sum 3) math:integerQuotient ?Q. ((((((19 ?J)!math:product ?K)!math:sum ?M)!math:difference ?Q)!math:difference 15)!math:sum 30) math:remainder ?R. (?H 4) math:integerQuotient ?S; math:remainder ?U. ((32 (2 ?N)!math:product (2 ?S)!math:product ?R!math:negation ?U!math:negation)!math:sum 7) math:remainder ?V. ((?J (11 ?R)!math:product (22 ?V)!math:product)!math:sum 451) math:integerQuotient ?W. ((?R ?V (7 ?W)!math:product!math:negation 114)!math:sum 31) math:integerQuotient ?X; math:remainder ?Z. (?Z 1) math:sum ?DAY. } => { ?Case :j ?J; :k ?K; :h ?H; :m ?M; :n ?N; :p ?P; :q ?Q; :r ?R; :s ?S; :u ?U; :v ?V; :w ?W; :monthNum ?X; :day ?DAY; :z ?Z. } . { ?Case :monthNum 3. } => { ?Case :monthName "March". } . { ?Case :monthNum 4. } => { ?Case :monthName "April". } . # ------------------ # Independent checks # ------------------ { ?Case :j ?J. :goldenRemainder :value ?J. } => { ?Case :check1 "C1 OK - the Golden Number remainder j is inside the 0–18 cycle.\n" . } . { ?Case :r ?R. :epactRemainder :value ?R. } => { ?Case :check2 "C2 OK - the epact-style remainder r is inside the 0–29 cycle.\n" . } . { ?Case :v ?V. :weekdayRemainder :value ?V. } => { ?Case :check3 "C3 OK - the weekday adjustment v is inside the 0–6 cycle.\n" . } . { ?Case :monthNum ?M; :monthName ?Name. } => { ?Case :check4 "C4 OK - the final month is a valid Easter month (March or April).\n" . } . { ?Case :monthNum ?M; :day ?D. ?Slot :monthNum ?M; :day ?D. } => { ?Case :check5 "C5 OK - the final date is inside the legal Gregorian Easter window.\n" . } . # ---------------- # ARC-style report # ---------------- { ?Case :year ?Y; :monthName ?Month; :day ?Day; :j ?J; :k ?K; :q ?Q; :r ?R; :v ?V; :monthNum ?X; :z ?Z; :check1 ?C1; :check2 ?C2; :check3 ?C3; :check4 ?C4; :check5 ?C5. ( "Easter — Gregorian computus\n\n" "=== " ?Y " ===\n" "Answer\n" "Easter Sunday falls on " ?Month " " ?Day ".\n\n" "Reason Why\n" "For year " ?Y ", the computus gives j=" ?J ", k=" ?K ", q=" ?Q ", r=" ?R ", v=" ?V ", and final month/day numbers x=" ?X ", z=" ?Z ". " "Because the day is z+1, the resulting Easter date is " ?Month " " ?Day ".\n\n" "Check\n" ?C1 ?C2 ?C3 ?C4 ?C5 ) string:concatenation ?Block. } => { :report log:outputString ?Block. } .