********** source program ********** fn f (0 = Int: x) -> Int { if ((x == 0)) return x; else return f(0 = (x - 1)); } fn main () -> Int { return f(0 = 2); } ********** type checking ********** --- step exp Int ---> --- step exp Int ---> --- step exp Int ---> --- step exp Int ---> --- step exp Int ---> --- step exp Int ---> ********** type checking complete ********** fn f (0 = Int: x) -> Int { if ((x == 0)) return x; else return f(0 = (x - 1)); } fn main () -> Int { return f(0 = 2); } ********** starting execution ********** ********** initializing globals ********** --- step exp (0 = Int: x) ---> --- step exp Int: x ---> --- step exp Int ---> --- handle value Int with Int: x<1>(Int,) ---> --- handle value Int: x with (0 = Int: x)<1>(Int: x,) ---> --- step exp () ---> ********** calling main function ********** { stack: top{main()<-1>} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp main() ---> { stack: top{main<-1> :: main()<0>} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp main ---> { stack: top{fun
<-1> :: main()<0>} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- handle value fun
with main()<1>(fun
,) ---> { stack: top{()<-1> :: main()<1>(fun
,)} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp () ---> { stack: top{()<-1> :: main()<1>(fun
,)} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- handle value () with main()<2>(fun
,(),) ---> pattern_match((), ()) { stack: main{return f(0 = 2);<-1>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step stmt return f(0 = 2); ---> { stack: main{f(0 = 2)<-1> :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp f(0 = 2) ---> { stack: main{f<-1> :: f(0 = 2)<0> :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp f ---> { stack: main{fun<-1> :: f(0 = 2)<0> :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- handle value fun with f(0 = 2)<1>(fun,) ---> { stack: main{(0 = 2)<-1> :: f(0 = 2)<1>(fun,) :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp (0 = 2) ---> { stack: main{2<-1> :: (0 = 2)<0> :: f(0 = 2)<1>(fun,) :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- step exp 2 ---> { stack: main{2<-1> :: (0 = 2)<0> :: f(0 = 2)<1>(fun,) :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, env: main: fun
, f: fun, } --- handle value 2 with (0 = 2)<1>(2,) ---> { stack: main{(0 = 2@3)<-1> :: f(0 = 2)<1>(fun,) :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, env: main: fun
, f: fun, } --- handle value (0 = 2@3) with f(0 = 2)<2>(fun,(0 = 2@3),) ---> pattern_match((0 = Int: x@0), (0 = 2@3)) pattern_match(Int: x, 2) { stack: f{if ((x == 0)) ... else ... <-1>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step stmt if ((x == 0)) ... else ... ---> { stack: f{(x == 0)<-1> :: if ((x == 0)) ... else ... <0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp (x == 0) ---> { stack: f{x<-1> :: (x == 0)<0> :: if ((x == 0)) ... else ... <0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp x ---> { stack: f{2<-1> :: (x == 0)<0> :: if ((x == 0)) ... else ... <0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value 2 with (x == 0)<1>(2,) ---> { stack: f{0<-1> :: (x == 0)<1>(2,) :: if ((x == 0)) ... else ... <0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp 0 ---> { stack: f{0<-1> :: (x == 0)<1>(2,) :: if ((x == 0)) ... else ... <0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value 0 with (x == 0)<2>(2,0,) ---> { stack: f{false<-1> :: if ((x == 0)) ... else ... <0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value false with if ((x == 0)) ... else ... <1>(false,) ---> { stack: f{return f(0 = (x - 1));<-1>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step stmt return f(0 = (x - 1)); ---> { stack: f{f(0 = (x - 1))<-1> :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp f(0 = (x - 1)) ---> { stack: f{f<-1> :: f(0 = (x - 1))<0> :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp f ---> { stack: f{fun<-1> :: f(0 = (x - 1))<0> :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value fun with f(0 = (x - 1))<1>(fun,) ---> { stack: f{(0 = (x - 1))<-1> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp (0 = (x - 1)) ---> { stack: f{(x - 1)<-1> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp (x - 1) ---> { stack: f{x<-1> :: (x - 1)<0> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp x ---> { stack: f{2<-1> :: (x - 1)<0> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value 2 with (x - 1)<1>(2,) ---> { stack: f{1<-1> :: (x - 1)<1>(2,) :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- step exp 1 ---> { stack: f{1<-1> :: (x - 1)<1>(2,) :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value 1 with (x - 1)<2>(2,1,) ---> { stack: f{1<-1> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, env: x: 2, main: fun
, f: fun, } --- handle value 1 with (0 = (x - 1))<1>(1,) ---> { stack: f{(0 = 1@5)<-1> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, env: x: 2, main: fun
, f: fun, } --- handle value (0 = 1@5) with f(0 = (x - 1))<2>(fun,(0 = 1@5),) ---> pattern_match((0 = Int: x@0), (0 = 1@5)) pattern_match(Int: x, 1) { stack: f{if ((x == 0)) ... else ... <-1>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step stmt if ((x == 0)) ... else ... ---> { stack: f{(x == 0)<-1> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp (x == 0) ---> { stack: f{x<-1> :: (x == 0)<0> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp x ---> { stack: f{1<-1> :: (x == 0)<0> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value 1 with (x == 0)<1>(1,) ---> { stack: f{0<-1> :: (x == 0)<1>(1,) :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp 0 ---> { stack: f{0<-1> :: (x == 0)<1>(1,) :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value 0 with (x == 0)<2>(1,0,) ---> { stack: f{false<-1> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value false with if ((x == 0)) ... else ... <1>(false,) ---> { stack: f{return f(0 = (x - 1));<-1>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step stmt return f(0 = (x - 1)); ---> { stack: f{f(0 = (x - 1))<-1> :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp f(0 = (x - 1)) ---> { stack: f{f<-1> :: f(0 = (x - 1))<0> :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp f ---> { stack: f{fun<-1> :: f(0 = (x - 1))<0> :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value fun with f(0 = (x - 1))<1>(fun,) ---> { stack: f{(0 = (x - 1))<-1> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp (0 = (x - 1)) ---> { stack: f{(x - 1)<-1> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp (x - 1) ---> { stack: f{x<-1> :: (x - 1)<0> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp x ---> { stack: f{1<-1> :: (x - 1)<0> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value 1 with (x - 1)<1>(1,) ---> { stack: f{1<-1> :: (x - 1)<1>(1,) :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- step exp 1 ---> { stack: f{1<-1> :: (x - 1)<1>(1,) :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value 1 with (x - 1)<2>(1,1,) ---> { stack: f{0<-1> :: (0 = (x - 1))<0> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, env: x: 1, main: fun
, f: fun, } --- handle value 0 with (0 = (x - 1))<1>(0,) ---> { stack: f{(0 = 0@7)<-1> :: f(0 = (x - 1))<1>(fun,) :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, env: x: 1, main: fun
, f: fun, } --- handle value (0 = 0@7) with f(0 = (x - 1))<2>(fun,(0 = 0@7),) ---> pattern_match((0 = Int: x@0), (0 = 0@7)) pattern_match(Int: x, 0) { stack: f{if ((x == 0)) ... else ... <-1>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- step stmt if ((x == 0)) ... else ... ---> { stack: f{(x == 0)<-1> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- step exp (x == 0) ---> { stack: f{x<-1> :: (x == 0)<0> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- step exp x ---> { stack: f{0<-1> :: (x == 0)<0> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- handle value 0 with (x == 0)<1>(0,) ---> { stack: f{0<-1> :: (x == 0)<1>(0,) :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- step exp 0 ---> { stack: f{0<-1> :: (x == 0)<1>(0,) :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- handle value 0 with (x == 0)<2>(0,0,) ---> { stack: f{true<-1> :: if ((x == 0)) ... else ... <0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- handle value true with if ((x == 0)) ... else ... <1>(true,) ---> { stack: f{return x;<-1>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- step stmt return x; ---> { stack: f{x<-1> :: return x;<0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- step exp x ---> { stack: f{0<-1> :: return x;<0>} :: f{return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, 0, env: x: 0, main: fun
, f: fun, } --- handle value 0 with return x;<1>(0,) ---> { stack: f{0<-1> :: return f(0 = (x - 1));<0>} :: f{return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, 1, 0, !!0, env: x: 1, main: fun
, f: fun, } --- handle value 0 with return f(0 = (x - 1));<1>(0,) ---> { stack: f{0<-1> :: return f(0 = (x - 1));<0>} :: main{return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, 2, 1, !!1, 0, !!0, env: x: 2, main: fun
, f: fun, } --- handle value 0 with return f(0 = (x - 1));<1>(0,) ---> { stack: main{0<-1> :: return f(0 = 2);<0>} :: top{} heap: Int: x, fun, fun
, 2, !!2, 1, !!1, 0, !!0, env: main: fun
, f: fun, } --- handle value 0 with return f(0 = 2);<1>(0,) ---> { stack: top{0<-1>} heap: Int: x, fun, fun
, 2, !!2, 1, !!1, 0, !!0, env: main: fun
, f: fun, } result: 0