Evaluación procedimiento recursivos

letrec f(x,y) = if >(x,0) then +(y, (f -(x,1) y)) else y
in (f 2 3)

flowchart LR
    E["Empty-env"]
    A["envr0
    '(f)
    '((x,y))
    '(if..)"
    ]
    F1["envf1
    (x,y)
    (2,3)
    "]  
    F2["envf2
    (x,y)
    (1,3)
    "]
    F3["envf3
    (x,y)
    (0,3)
    "]      
    E --> A
    A --> F1
    A --> F2
    A --> F3

1. Envf1 if >(x,0) then +(y, (f -(x,1) y)) else y queda if >(2,0) then +(3, (f 1 3))
2. Enfv2 if >(x,0) then +(y, (f -(x,1) y)) queda if >(1,0) entonces +(3, (f 0 3))
3. Envf3 if >(x,0) then +(y, (f -(x,1) y)) else y entonces >(0,0) ejecuta else y, retorna 3

Observe la suma acumulada 1. +(3, (f 1 3)) 2. +(3, +(3, (f 0 3))) 3. +(3, +(3, 3)) = 9

let
    x = let x = 3 in +(x,3)
    y = 8
    z = proc(a,b) if >(a,b) then a else b
    in
        letrec
            f(x,y) = if >(x,0) then
                    +(y, (g -(x,2) +(y,1)))
                    else
                    let
                        t = (z (z x y) (z y x))
                        in +(t,1)
            g(m,n) = if >(m,0) then
                        *(n, (f -(m,1) -(n,1)))
                        else
                        n
            in
                (f x y)

Resultado es 809

flowchart LR
    E["Empty-env"]
    ENV0["env0
    (x,y,z)
    (6,8, closure(.. empty-env))"
    ]
    ENVX["envx0
    x
    3"
    ]   
    ENVR0["envr0
    '(f g)
    '((x,y)(m,n))
    '(if .. if ...)"
    ]

    ENVF1["
    envf1
    (x,y)
    (6,8)"
    ]
    ENVG1["
    envg1
    (m,n)
    (4,9)"
    ]   
    ENVF2["
    envf2
    (x,y)
    (3,8)"
    ]
    ENVG2["
    envg2
    (m,n)
    (1,9)"
    ]   
    ENVF3["
    envf3
    (x,y)
    (0,8)"
    ]
    ENVT["
    envt
    t
    8
    "
    ]
    ENVZ1["envz1
    (a,b)
    (0 8)   
    "
    ]
    ENVZ2["envz2
    (a,b)
    (8 0)   
    "
    ]
    ENVZ3["envz3
    (a,b)
    (8 8)   
    "
    ]
    E --> ENV0
    E --> ENVX
    ENV0 --> ENVR0
    ENVR0 --> ENVF1
    ENVR0 --> ENVG1
    ENVR0 --> ENVF2
    ENVR0 --> ENVG2
    ENVR0 --> ENVF3
    ENVF3 --> ENVT
    E --> ENVZ1
    E --> ENVZ2
    E --> ENVZ3

1. Envr0 (f x y) --> (f 6 8) f = closure((x,y) if .. envR0)
2. Envf1 if >(x,0) --> >(6,0) SI +(8, (g 4 9))
3. Envg1 if >(m,0) -> >(4,0) SI x(9, (f 3 8))
4. Envf2 if >(x,0) -> (3,0) SI +(8, (g 1 9))
5. Envg2 if >(m,0) -> (1,0) SI x(9, (f 0 8))
6. Envf3 if >(x,0) -> (0,0) ELSE t = (z (z 0 8) (z 8 0)) (z 8 (z 8 0)) -> (z 8 8) -> 8
   1. Envz1 if >(a,b) then a else b >(0,8) ELSE 8
   2. Envz2 if >(a,b) then a else b >(8,0)THEN a 8
   3. Envz3 if >(a,b) then a else b >(8,8) ELSE 8
   4. Envt Retorna 9

Evaluación total

1. +(8, (g 4 9))
2. +(8, x(9, (f 3 8)))
3. +(8, x(9, +(8, (g 1 9))))
4. +(8, x(9, +(8, x(9, (f 0 8)))))
5. +(8, x(9, +(8, x(9, 9)))) -> +(8, x(9, +(8, 81))) -> +(8, x(9, 89)) ->+(8, 801) -> 809