delete upcoming topics, tweak index/new_stuff

[lambda.git] / cps.mdwn

diff --git a/cps.mdwn b/cps.mdwn
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-;; call-by-value CPS
-; see Dancy and Filinski, "Representing control: a study of the CPS transformation" (1992)
-; and Sabry, "Note on axiomatizing the semantics of control operators" (1996)
-
-; [x] = var x
-let var = \x (\k. k x) in
-; [\x. body] = lam (\x. [body])
-let lam = \x_body (\k. k (\x. x_body x)) in
-; [M N] = app [M] [N]
-let app = \m n. (\k. m (\m. n (\n. m n k))) in
-
-; helpers
-let app3 = \a b c. app (app a b) c in
-let app4 = \a b c d. app (app (app a b) c) d in
-; [succ] = op1 succ
-let op1 = \op. \u. u (\a k. k (op a)) in
-; [plus] = op2 plus
-let op2 = \op. \u. u (\a v. v (\b k. k (op a b))) in
-let op3 = \op. \u. u (\a v. v (\b w. w (\c k. k (op a b c)))) in
-
-;; continuation operators
-; [let/cc k M] = letcc (\k. [M])
-let callcc = \k. k (\f u. (\j. f j u) (\y w. u y)) in
-let letcc = \x_body. app callcc (lam x_body) in
-let letcc = \k_body. \k. (\j. (k_body j) k) (\y w. k y) in
-
-; [abort M] = abort [M]
-let abort = \body. \k. body (\m m) in
-; [prompt M] = prompt [M]
-let prompt = \body. \k. k (body (\m m)) in
-; [shift k M] = shift (\k. [M])
-let shift = \k_body. \k. (\j. (k_body j) (\m m)) (\y w. w (k y)) in
-
-;; examples
-; (+ 100 (let/cc k (+ 10 1))) ~~> 111
-; app3 (op2 plus) (var hundred) (letcc (\k. app3 (op2 plus) (var ten) (var one)))
-
-; (+ 100 (let/cc k (+ 10 (k 1)))) ~~> 101
-; app3 (op2 plus) (var hundred) (letcc (\k. app3 (op2 plus) (var ten) (app (var k) (var one))))
-
-; (+ 100 (+ 10 (abort 1))) ~~> 1
-; app3 (op2 plus) (var hundred) (app3 (op2 plus) (var ten) (abort (var one)))
-
-; (+ 100 (prompt (+ 10 (abort 1)))) ~~> 101
-; app3 (op2 plus) (var hundred) (prompt (app3 (op2 plus) (var ten) (abort (var one))))
-
-; (+ 1000 (prompt (+ 100 (shift k (+ 10 1))))) ~~> 1011
-; app3 (op2 plus) (var thousand) (prompt (app3 (op2 plus) (var hundred) (shift (\k. ((op2 plus) (var ten) (var one))))))
-
-; (+ 1000 (prompt (+ 100 (shift k (k (+ 10 1)))))) ~~> 1111
-; app3 (op2 plus) (var thousand) (prompt (app3 (op2 plus) (var hundred) (shift (\k. (app (var k) ((op2 plus) (var ten) (var one)))))))
-
-; (+ 1000 (prompt (+ 100 (shift k (+ 10 (k 1)))))) ~~> 1111 but added differently
-; app3 (op2 plus) (var thousand) (prompt (app3 (op2 plus) (var hundred) (shift (\k. ((op2 plus) (var ten) (app (var k) (var one)))))))
-
-; (+ 100 ((prompt (+ 10 (shift k k))) 1)) ~~> 111
-; app3 (op2 plus) (var hundred) (app (prompt (app3 (op2 plus) (var ten) (shift (\k. (var k))))) (var one))
-
-; (+ 100 (prompt (+ 10 (shift k (k (k 1)))))) ~~> 121
-; app3 (op2 plus) (var hundred) (prompt (app3 (op2 plus) (var ten) (shift (\k. app (var k) (app (var k) (var one))))))
-