Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`Parser`Languages`Lambda`
LambdaAST  |
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LambdaAST
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The surface syntax is namebody (or the unicode namebody) for abstraction, juxtaposition for application (left associative), and parentheses for grouping. is sugar for . In a Wolfram string a backslash doubles, so the term is written .
\
.
λ
.
\xy.b
\x.\y.b
\x.x
"\\x.x"
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runs the same grammar over instead, compiling each abstraction to a native and letting the kernel beta-reduce. The grammar is written once; only the algebra differs.
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Application binds tighter than abstraction, so reads as , not .
\x.xy
\x.(xy)
(\x.x)y
Examples
(4)
Basic Examples
(1)
In[1]:=
 | LambdaAST |
Out[1]=
ContainerNode[String,{CallNode[LeafNode[Symbol,λ,],{LeafNode[Symbol,x,],LeafNode[Symbol,x,Source{{1,4},{1,5}}]},Source{{1,4},{1,5}}]},Source{{1,4},{1,5}}]
Nodes carry a span of startLinestartColendLineendCol ( LineColumn). An abstraction is special: its head and its bound-name leaf are synthesized by the builder, not lexed from a token, so they have no source and keep empty metadata . Only the parsed variable occurrence in the body - here the trailing at columns - - carries a span, and the abstraction node inherits that body span (the binder is not included).
"Source"
{{
,
},{
,
}}
CodeParser
λ
<||>
x
4
5
The K combinator nests one abstraction inside another:
\x.\y.x
In[2]:=
| LambdaAST |
Out[2]=
ContainerNode[String,{CallNode[LeafNode[Symbol,λ,],{LeafNode[Symbol,x,],CallNode[LeafNode[Symbol,λ,],{LeafNode[Symbol,y,],LeafNode[Symbol,x,Source{{1,7},{1,8}}]},Source{{1,7},{1,8}}]},Source{{1,7},{1,8}}]},Source{{1,7},{1,8}}]
In[3]:=
| LambdaEval |
Out[3]=
a
Scope
(1)
Properties & Relations
(1)
Possible Issues
(1)
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