Ejercicio

,

let
    x = let x = let x = 3 in +(x,3)
                         in +(x,3)
    y = 5
    h = proc(m,n) if >(m,n) 
                    then +(m,n) 
                    else -(m,n)
    in
        letrec
            f(x,y) = if >(x,0) then
                        +(y, (f -(x,1) +(y,2)))
                    else
                        let k = (h 2 3) in
                            let s = (h 2 4)
                                in +(k,s)
        in
            (f x y)

Da 114

flowchart LR
    E["empty env"]
    ENV0["
    env0
    (x,y,h)
    (9,5,closure(..,empty-env))
    "]

    ENVX0["
    envx0
    x
    6
    "]
    ENVX1["
    envx1
    x
    3
    "]  
    ENVR0["
    envr0
    (f)
    ((x,y))
    (...)"
    ]
    ENVF1["
    envf1
    (x,y)
    (9,5)
    "]
    ENVF2["
    envf2
    (x,y)
    (8,7)
    "]
    ENVF3["
    envf3
    (x,y)
    (7,9)
    "]
    ENVF4["
    envf4
    (x,y)
    (6,11)
    "]
    ENVF5["
    envf5
    (x,y)
    (5,13)
    "]
    ENVF6["
    envf6
    (x,y)
    (4,15)
    "]
    ENVF7["
    envf7
    (x,y)
    (3,17)
    "]
    ENVF8["
    envf8
    (x,y)
    (2,19)
    "]
    ENVF9["
    envf9
    (x,y)
    (1,21)
    "]
    ENVF10["
    envf10
    (x,y)
    (0,23)
    "]

    ENVH1["
    envh1
    m,n
    2,3"
    ]

    ENVH2["
    envh2
    m,n
    2,4"
    ]

    ENVK["envk
    k
    -1  
    "]

    ENVS["envs
    s
    -2
    "]

    E --> ENV0
    E --> ENVX0
    E --> ENVX1
    ENV0 --> ENVR0
    ENVR0 --> ENVF1
    ENVR0 --> ENVF2
    ENVR0 --> ENVF3
    ENVR0 --> ENVF4
    ENVR0 --> ENVF5
    ENVR0 --> ENVF6
    ENVR0 --> ENVF7
    ENVR0 --> ENVF8
    ENVR0 --> ENVF9
    ENVR0 --> ENVF10

    ENVF10 --> ENVK
    ENVK --> ENVS
    E --> ENVH1
    E --> ENVH2

1. Envr0 (f x y) (f 9 5)
2. Al evaluar (f 9 5) genera una clausura que hereda de envr0
3. envf1 >(9,0) THEN +(5, (f 8 7))
4. envf2 >(8,0) THEN +(7, (f 7 9))
5. enf3,4,5,6,7,8,10 +(5,+(7, +(9, +
6. (11, +(13, +(15, +(17,+(19, +(21 (f 0 23)))))))))
7. envf10 x = 0 y = 23 >(x,0) NO

                           let k = (h 2 3) in
                               let s = (h 2 4)
                                   in +(k,s)
   

   El cuerpo de h es

        if >(m,n) 
                       then +(m,n) 
                       else -(m,n)
   

8. -(2,3) = -1

9. (2,4) --> -(2,4) = -2

10. envs --> +(k,s) -->+(-1,-2) = -3
11. +(5, +(7, +(9, (11, +(13, +(15, +(17,+(19, +(21 -3)))))))
    1. +(5, +(7, +(9, (11, +(13, +(15, +(17,+(19, 18))))))
    2. +(5, +(7, +(9, (11, +(13, +(15, +(17,37)))))
    3. +(5, +(7, +(9, (11, +(13, +(15, 54))))
    4. +(5, +(7, +(9, (11, +(13, 69)))
    5. (11, 82))
    6. +(5, +(7, +(9, 93)))
    7. +(5, +(7, 102))
    8. +(5, 109)
    9. 114