20-CS-4003-001 Organization of Programming Languages Fall 2018
Topological Sort

Lambda calculus, Type theory, Formal semantics, Program analysis

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Topological Sort - State Based

 ```(define take-helper (lambda (i lst acc) (if (<= i 0) acc (take-helper (- i 1) (cdr lst) (append acc (list (car lst))))))) ;; Returns a list of the first i members of the list lst (define take (lambda (i lst) (take-helper i lst '()))) ;; Returns a list of the last length(lst) - i members of lst (define drop (lambda (i lst) (if (<= i 0) lst (drop (- i 1) (cdr lst))))) ;; Returns '() if lst is '() or '(A), otherwise ;; returns a list containing the last member of lst (define tail (lambda (lst) (if (null? lst) '() (if (null? (cdr lst)) '() (if (null? (cddr lst)) (cdr lst) (tail (cdr lst))))))) ;; Returns the last member of lst (define last (lambda (lst) (if (null? lst) '() (car (tail lst))))) ;; Define state: ;; A list of m+2 lists ;; list 0: a vertex stack for DFS ;; lists 1-m: dependency lists for each vertex ;; last element of a dependency list is the ;; vertex itself ;; list m+1: solution list, in order from right ;; to left ;; Returns a new state from a current state according ;; to the following; ;; 1. if the vertex stack is empty - ;; return null ;; 2. if the dependency list of the top vertex in ;; the stack is null - ;; return same state except pop the stack ;; 3. if the dependency list of the top vertex in ;; the stack has one member (the vertex v) - ;; return a new state where the stack is popped, ;; vertex v is added to the solution list, ;; and vertex v is removed from its dep list ;; 4. otherwise ;; let w be the first member of the dependency ;; list of the vertex v at the top of the stack. ;; return the same state except that w is ;; removed from v's dependency list and w is ;; placed at the top of the stack. (define f (lambda (state) (if (null? (car state)) '() (let* ((v (caar state)) (lv (car (drop (+ v 1) state)))) (if (null? lv) (append (list (drop 1 (car state))) (drop 1 state)) (let* ((r (drop 1 lv)) (z (append (take (+ v 1) state) (list r) (drop (+ v 2) state)))) (if (null? (cdr lv)) (append (list (drop 1 (car state))) (drop 1 (take (- (length z) 1) z)) (list (cons v (last state)))) (append (list (append (take 1 (car (drop (+ v 1) state))) (car state))) (drop 1 z))))))))) ;; Given a state, with an assumed initial stack ;; containing just one member, apply f repeatedly ;; until the stack is empty (define h (lambda (state) (if (null? (car state)) state (h (f state))))) ;; Given a state and vertex v, change the stack so v ;; is the only member and return the modified state (define setInit (lambda (state v) (cons (list v) (cdr state)))) (define topo-helper (lambda (state i) (if (<= i 0) (h (setInit state 0)) (h (setInit (topo-helper state (- i 1)) i))))) ;; Find a topological sort for a given partial order (define topo (lambda (deps) (last (topo-helper (append '(()) deps '(())) (- (length deps) 1))))) ;; An example partial order (define ex '((2 3 4 0) (1) (1 2) (1 5 3) (3 5 4) (2 5) (1 7 6) (0 2 7))) ``` - Comments to be added