;; 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))))))