I wonder whether it is that they neglect it or that I consider too much. Those implementations do not force eval opd.
I raised this question because many example implementations I have seen seem not to take this into account. Make sure that call-by-value is implemented faithfully in Haskell. But I do not wanna bother it for the moment. I am aware that the evaluation order dependence between the object and meta- level can be avoid by CPS transformation. On the line with comment, should I force the evaluation of eval opd by using fun $! eval opd instead? We find that the interpreter does implement the expected result.When implementing call-by-value lambda-calculus in Haskell, should I force the evaluation of the arguments to a function in the object language (i.e., the call-by-value lambda-calculus) to get around the call-by-need evaluation order of the meta-language (i.e., Haskell)?Ĭoncretely, for the following implementation using higher-order abstract syntax: data ExpĪbs fun -> eval (fun $ eval opd) - argument evaluation Now let us see what our interpreter actually implements.ĮvalCBN (EApp (EAbs (Id "x") (EAbs (Id "x") (EVar (Id "x")))) (EVar (Id "a"))) = - line 6ĮvalCBN(subst (Id "x") (EVar (Id "a")) (EAbs (Id "x") (EVar (Id "x")))) = - line 22ĮvalCBN(EAbs (Id "y") (subst (Id "x") (EVar (Id "a")) (EVar (Id "y")))) = - line 16ĮvalCBN(EAbs (Id "y") (EVar (Id "y"))) = - line 8 **Activity:** Discuss which of the two possible choices is taken in the programming languages you know. This makes a difference, because in the first case $(\lambda x.\lambda x. $$(\lambda \color$ is bound by the red or by the blue one. Our next example is $(\lambda x.\lambda x. We will continue this on Thursday, but try to do similar examples yourself before.
Then, for the pattern matching my eyes only need to be able to identify what the "variable", the "argument" and the "body" are in the term at hand. For example, the equation of `line 6` I remember as "substitute the variable by the argument in the body". **Tip:** It is easier to apply an equation if one has an English phrase for it. x) a$$ Following the steps specified in the interpreter, we compute (line numbers refer to ()):ĮvalCBN (EApp (EAbs (Id "x") (EVar (Id "x"))) (EVar (Id "a"))) = - line 6ĮvalCBN (subst (Id "x") (EVar (Id "a")) (EVar (Id "x"))) = - line 15 We do some computations by hand to convince ourselves that the substitution function `subst` is doing its job. In the following we will execute the interpreter pen-and-paper, both using concrete syntax and abstract syntax. This semantics has been implemented by (). Mathematically, the semantics of $\lambda$-calculus is given by the $\beta$-rule, which is to say, by capture avoiding substitution.
Haskell lambda calculus interpreter how to#
If you know the order of operations and how to translate concrete syntax to ASTs, you don't need to make a detour via CSTs. If you want to design your own grammar, you need to understand CSTs in order to get the order of operation right. Why do I need to understand what a CST is? The parser creates first a CST and then turns it into an AST. What are they for then?ĬSTs are an intermediate representation used by the parser. But I remember there was also sth like concrete syntax trees. The AST is used by the interpreter to evaluate (=run=execute) the program. The parser is needed to turn a program into its AST. The grammar is needed to generate the parser. For readability, in the following, it is tempting to abbreviate these trees as inīut it is safer to do this only after we gained some practice. TestLambdaNat` gives us the linearized AST Parsing this program via `echo "(\ x.x)a" |. The $\lambda$-caclulus term $(\lambda x.x) a$ is written in our programming language LambdaNat as `(\x.x)a`. We review one example to remind us of the relevant notation. how our Haskell implementation of the interpreter for $\lambda$-calculus works. to execute by hand $\lambda$-calculus programs according to its operatial semantics the formal definition of capture avoiding substitution
Haskell lambda calculus interpreter full#
Refer back to the earlier parts of these lecture notes for full detail. Quite some material has accumulated, so I here summarize some salient points and then discuss the interpreter in more detail. # Interpreting Lambda Calculus Pen-and-Paper
0 kommentar(er)
