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Improve answer to exercises
The identity function is not used in the answers. Sort list, prn, hash-map by increasing difficulty. Fix indentation consistency in concat. Avoid using the same identifier twice. In do3, make explicit that acc is not used. In _quasiquote_iter, call the tested quasiquote2 instead of the original quasiquote. In the quoting section, add foldr_pairs to hide recursions. The compose function is not used in the answers.
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@ -37,7 +37,7 @@ make REGRESS=1 TEST_OPTS='--hard --pre-eval=\(load-file\ \"../answer.mal\"\)' te
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- Implement `>`, `<=` and `>=` with `<`.
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- Implement `hash-map`, `list`, `prn` and `swap!` as non-recursive
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- Implement `list`, `prn`, `hash-map` and `swap!` as non-recursive
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functions.
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- Implement `count`, `nth`, `map`, `concat` and `conj` with the empty
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@ -1,8 +1,7 @@
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;; These are the answers to the questions in ../docs/exercise.md.
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;; In order to avoid unexpected circular dependencies among solutions,
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;; this files attempts to be self-contained.
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(def! identity (fn* [x] x))
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;; this answer file attempts to be self-contained.
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(def! reduce (fn* (f init xs)
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(if (empty? xs) init (reduce f (f init (first xs)) (rest xs)))))
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(def! foldr (fn* [f init xs]
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@ -23,9 +22,9 @@
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(def! <= (fn* [a b] (not (< b a))))
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(def! >= (fn* [a b] (not (< a b))))
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(def! hash-map (fn* [& xs] (apply assoc {} xs)))
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(def! list (fn* [& xs] xs))
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(def! prn (fn* [& xs] (println (apply pr-str xs))))
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(def! hash-map (fn* [& xs] (apply assoc {} xs)))
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(def! swap! (fn* [a f & xs] (reset! a (apply f (deref a) xs))))
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(def! count
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@ -45,25 +44,26 @@
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(foldr (fn* [x acc] (cons (f x) acc)) () xs)))
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(def! concat
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(fn* [& xs]
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(foldr (fn* [xs ys] (foldr cons ys xs)) () xs)))
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(foldr (fn* [x acc] (foldr cons acc x)) () xs)))
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(def! conj
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(fn* [xs & ys]
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(if (vector? xs)
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(apply vector (concat xs ys))
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(reduce (fn* [xs x] (cons x xs)) xs ys))))
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(reduce (fn* [acc x] (cons x acc)) xs ys))))
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(def! do2 (fn* [& xs] (nth xs (- (count xs) 1))))
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(def! do3 (fn* [& xs] (reduce (fn* [acc x] x) nil xs)))
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(def! do3 (fn* [& xs] (reduce (fn* [_ x] x) nil xs)))
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;; do2 will probably be more efficient when lists are implemented as
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;; arrays with direct indexing, but when they are implemented as
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;; linked lists, do3 may win because it only does one traversal.
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(defmacro! quote (fn* [ast] (list (fn* [] ast))))
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(defmacro! quote2 (fn* [ast]
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(list (fn* [] ast))))
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(def! _quasiquote_iter (fn* [x acc]
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(if (if (list? x) (= (first x) 'splice-unquote)) ; logical and
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(list 'concat (first (rest x)) acc)
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(list 'cons (list 'quasiquote x) acc))))
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(defmacro! quasiquote (fn* [ast]
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(list 'cons (list 'quasiquote2 x) acc))))
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(defmacro! quasiquote2 (fn* [ast]
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(if (list? ast)
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(if (= (first ast) 'unquote)
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(first (rest ast))
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@ -73,36 +73,36 @@
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(list 'apply 'list (foldr _quasiquote_iter () ast))
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(list 'quote ast)))))
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(def! _letA_keys (fn* [binds]
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(if (empty? binds)
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()
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(cons (first binds) (_letA_keys (rest (rest binds)))))))
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(def! _letA_values (fn* [binds]
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(if (empty? binds)
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()
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(_letA_keys (rest binds)))))
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(def! _letA (fn* [binds form]
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(cons (list 'fn* (_letA_keys binds) form) (_letA_values binds))))
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;; Interpret kvs as [k1 v1 k2 v2 ... kn vn] and returns
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;; (f k1 v1 (f k2 v2 (f ... (f kn vn)))).
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(def! _foldr_pairs (fn* [f init kvs]
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(if (empty? kvs)
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init
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(let* [key (first kvs)
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rst (rest kvs)
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val (first rst)
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acc (_foldr_pairs f init (rest rst))]
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(f key val acc)))))
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(defmacro! let*A (fn* [binds form]
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(let* [formal (_foldr_pairs (fn* [key val acc] (cons key acc)) () binds)
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actual (_foldr_pairs (fn* [key val acc] (cons val acc)) () binds)]
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`((fn* ~formal ~form) ~@actual))))
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;; Fails for (let* [a 1 b (+ 1 a)] b)
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(def! _letB (fn* [binds form]
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(if (empty? binds)
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form
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(list (list 'fn* [(first binds)] (_letB (rest (rest binds)) form))
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(first (rest binds))))))
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(defmacro! let*B (fn* [binds form]
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(let* [f (fn* [key val acc]
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`((fn* [~key] ~acc) ~val))]
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(_foldr_pairs f form binds))))
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;; Fails for (let* (cst (fn* (n) (if (= n 0) nil (cst (- n 1))))) (cst 1))
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(def! _c_combinator (fn* [x] (x x)))
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(def! _d_combinator (fn* [f] (fn* [x] (f (fn* [v] ((x x) v))))))
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(def! _Y_combinator (fn* [x] (_c_combinator (_d_combinator x))))
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(def! _letC
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(fn* [binds form]
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(if (empty? binds)
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form
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(list (list 'fn* [(first binds)] (_letC (rest (rest binds)) form))
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(list '_Y_combinator (list 'fn* [(first binds)] (first (rest binds))))))))
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(defmacro! let*C (fn* [binds form]
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(let* [f (fn* [key val acc]
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`((fn* [~key] ~acc) (_Y_combinator (fn* [~key] ~val))))]
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(_foldr_pairs f form binds))))
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;; Fails for mutual recursion.
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;; See http://okmij.org/ftp/Computation/fixed-point-combinators.html
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;; if you are motivated to implement solution D.
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(defmacro! let* _letC)
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(def! apply
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;; Replace (f a b [c d]) with ('f 'a 'b 'c 'd) then evaluate the
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@ -156,10 +156,8 @@
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(fn* [xs]
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(reduce update_max 0 xs))))
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(def! compose
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(let* [compose2 (fn* [f acc] (fn* [x] (f (acc x))))]
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(fn* [& fs]
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(foldr compose2 identity fs))))
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;; ((compose f1 f2) x) is equivalent to (f1 (f2 x))
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;; This is the mathematical composition. For practical purposes, `->`
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;; and `->>` defined in `core.mal` are more efficient and general.
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;; (fn* [& fs] (foldr (fn* [f acc] (fn* [x] (f (acc x)))) identity fs))
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;; computes the composition of an arbitrary number of functions.
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;; The first anonymous function is the mathematical composition.
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;; For practical purposes, `->` and `->>` in `core.mal` are more
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;; efficient and general.
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