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Update LambdaCalculus.md

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Krasimir Angelov
2021-11-04 17:26:47 +01:00
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doc/hackers-guide/LambdaCalculus.md
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@@ -151,12 +151,20 @@ x.s2+x.s2 where x = {s1="s"; s2="b"}
```
we branch only after encountering the variant in the `s2` field.
The implementation for variants requires the introduction of a nondeterministic monad in the evaluator. See this [paper](https://gup.ub.gu.se/file/207634):
The implementation for variants requires the introduction of a nondeterministic monad with a support for logical variables. See this [paper](https://gup.ub.gu.se/file/207634):
Claessen, Koen & Ljunglöf, Peter. (2000). Typed Logical Variables in Haskell. Electr. Notes Theor. Comput. Sci.. 41. 37. 10.1016/S1571-0661(05)80544-4.
Claessen, Koen & Ljunglöf, Peter. (2000). Typed Logical Variables in Haskell. Electronic Notes Theoretical Computer Science. 41. 37. 10.1016/S1571-0661(05)80544-4.
The monad (let's call it `EvalM`) must provide the primitives:
for possible implementations. Our concrete implemention is built on top of the `ST` monad in Haskell and provides the primitives:
```Haskell
newThunk :: Env s -> Term -> EvalM s (Thunk s)
newEvaluatedThunk :: Value s -> EvalM s (Thunk s)
force :: Thunk s -> EvalM s (Value s)
msum :: [EvalM s a] -> EvalM s a
```
Here, a `Thunk` is either an unevaluated term or an already computed value. Internally, it is implement as an `STRef`. If the thunk is unevaluated, it can be forced to an evaluated state by calling `force`. In addition, `msum` makes it possible to nondeterministically branch into a list of possible actions.
The terms and the values in the extended language are similar with two exceptions. We add the constructor `FV` for encoding variants in the terms, and the constructors for values now take lists of thunks instead of values:
```Haskell
data Term
= Vr Ident -- i.e. variables: x,y,z ...
@@ -170,7 +178,9 @@ data Value s
= VApp Ident [Thunk s] -- i.e. constructor application
| VClosure (Env s) Term -- i.e. a closure contains an environment and the term for a lambda abstraction
| VGen Int [Thunk s] -- i.e. an internal representation for free variables
```
```Haskell
eval env (Vr x) args = do tnk <- lookup x env
v <- force tnk
apply v args