145 lines
2.9 KiB
Plaintext
145 lines
2.9 KiB
Plaintext
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1 -> (s (0));
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neg (neg ?x) -> ?x;
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neg (0) -> 0;
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add (s ?x) (s ?y) -> s (add ?x (s ?y));
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add (0) (s ?x) -> s ?x;
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add (s ?x) (0) -> s ?x;
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add (0) (0) -> 0;
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?x + ?y + ?z -> (?x + ?y) + ?z;
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?x + ?y -> add ?x ?y;
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sub (s ?x) (s ?y) -> sub ?x ?y;
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sub (s ?x) (0) -> s ?x;
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sub (0) (s ?x) -> neg (s ?x);
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sub (0) (0) -> 0;
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?x - ?y -> sub ?x ?y;
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mul (s ?x) (s ?y) -> (s ?x) + (mul (s ?x) ((s ?y) - 1));
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mul (s ?x) (s (0)) -> s ?x;
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mul (s ?x) (0) -> 0;
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mul (0) (s ?x) -> 0;
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?x * ?y -> mul ?x ?y;
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Ensures that a list or a number has been reduced to its normal form. ;
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reduced (0) -> true;
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reduced (nil) -> true;
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reduced (s ?x) -> reduced ?x;
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reduced (?h : ?t) -> reduced ?t;
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reduced ?x -> false;
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Because there may be conflicts with expressions that
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are currently being reduced, we need to fold over reduced
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lists, i.e ones that have already been fully generated. ;
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fold (?f) ?i ?l -> fold reduced ?l (?f) ?i ?l;
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fold true (?f) ?i (nil) -> ?i;
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fold true (?f) ?i (?h : (nil)) -> ?f ?i ?h;
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fold true (?f) ?i (?h : ?t) -> ?f ?i (fold (?f) ?h ?t);
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fold false (?f) ?i ?l -> fold (?f) ?i ?l;
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factorial (s (0)) -> s (0);
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factorial (s ?x) -> (s ?x) * (factorial ((s ?x) - 1));
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sum (?h : ?t) -> fold (add) (0) (?h : ?t);
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range ?x (s (0)) -> ?x : (nil);
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range ?x (s ?y) -> ?x : (range (?x + 1) ((s ?y) - 1));
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Disgusting (yet valid) hack for currying.
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We need lambdas. ;
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unpack (?h : nil) -> ?h;
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unpack (?h : ?t) -> ?h unpack ?t;
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unpack (?x) -> ?x;
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unpack (?x . -> ?x unpack (;
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:: (?f) ?a -> ?f unpack ?a;
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mapp (?f) ?a (nil) -> nil;
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mapp (?f) ?a (?h : (nil)) -> (?f unpack ?a ?h) : (nil);
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mapp (?f) ?a (?h : ?t) -> (?f unpack ?a ?h) : (mapp (?f) ?a ?t);
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map (?f) (nil) -> nil;
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map (?f) (?h : nil) -> (?f ?h) : (nil);
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map (?f) (?h : ?t) -> (?f ?h) : (map (?f) ?t);
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product ?x -> fold (mul) 1 ?x;
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factorial2 ?x -> product (range 1 ?x);
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contains ?x (nil) -> false;
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contains ?x (?x : ?t) -> true;
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contains ?x (?h : ?t) -> contains ?x ?t;
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unique (nil) -> nil;
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unique false (?h : ?t) -> ?h : (unique ?t);
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unique true (?h : ?t) -> unique ?t;
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unique (?h : ?t) -> unique contains ?h ?t (?h : ?t);
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length (nil) -> 0;
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length (?h : ?t) -> s (length ?t);
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zipWith (?f) (nil) (nil) -> nil;
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zipWith (?f) (?h : ?t) (nil) -> nil;
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zipWith (?f) (nil) (?h : ?t) -> nil;
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zipWith (?f) (?h1 : ?t1) (?h2 : ?t2) -> (?f ?h1 ?h2) : (zipWith (?f) ?t1 ?t2);
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evens ?x -> zipWith (add) (range (0) ?x) (range (0) ?x);
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not (not ?x) -> ?x;
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not true -> false;
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not false -> true;
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any ?x -> contains true ?x;
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all ?x -> not contains false ?x;
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none ?x -> not any ?x;
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add1 ?x -> add ?x 1;
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square ?x -> ?x * ?x;
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reduce (s ?x) -> s (reduce ?x);
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reduce (0) -> (0);
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reduce (?h : ?t) -> ?h : (reduce ?t);
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reduce (nil) -> nil;
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