Implement Meta Lambda Calculus (MLC)

[kamil-adam]

apply

# apply combinator create one local variable/function/definition
#\x \f f x @ &
@ apply \x \f f x
@ ! apply
@ & apply
@ |> apply

& (lambda) ( \ function 
  do something
)

! (lambda1) \ function1 \ 
! (lambda2) \ function2 \ 

---

Lambdas and Let

someLambda1 (\ param1 someLambda2 (\ param2 someLambda3 (\ param3 param1 param2 param3)))

someLambda1 (\ param1 
  someLambda2 (\ param2 
    someLambda3 (\ param3 
      param1 param2 param3
    )
  )
)

someLambda1 \ param1 \
someLambda2 \ param2 \
someLambda3 \ param3 \
param1 param2 param3 

so maybe:

someLambda1 @ name1
\ param1 body1 @ name1

or:

someLambda1 : name1
\ param1 body1 : name1

Maybe it is too crazy?

---

• @ - define and special word
• # - comment
• : - block
• ; - many instruction in one line

---

• define-macro

• define-combinator

• define-syntax-rule

• define-syntax

• https://justinethier.github.io/husk-scheme//2012/12/10/Understanding-Macros.html

• https://3e8.org/pub/pdf-t1/macros_that_work.pdf

• http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.5184

• http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.5184&rep=rep1&type=pdf

• For this project:

  • Add Meta Lambda Calculus is superset for Lazy K
  • Add guard expression
  • Add case expression
  • Add Symbolic Lambda Calculus is superset for Lazy K
  • Translate MLC to SLC
  • Add let expression

• For other project:

  • Build dynamic typed version
  • Build static typed version
  • Compile SLC to eager version (Brilliant Language)
  • Add do expression (seq expression?).
  • Add match expression.

About expression

• abs (\ symbol) is abstraction.
• if (? symbol).
• guard (| symbol) is or line. It is sugar for if.
  • guard K (|K symbol, guard constants). It Is hack.
  • guard is (|= symbol, guard equals, case).
  • guard in (guard belongs to, case list).
• let (& symbol) is and line. It is sugar for abs. Real sugar. Maybe we need macros?

Example expressions

: function ! param1 ! param2 result

: variable ? condition expression1 expression2

; guard is predicate
| guard1 result1
| guard2 result2
default result
expression

; It is sugar for:
? (guard1 expression) result1
? (guard2 expression) result2
result

; it is possible do define `|` as function
: | ! guard ! body ! tail ! expression ? (guard expression) body (tail expression)
: default ! body ! expression body; It is true

& id1 init1
& id2 init2
expression

; It is sugar for:
! variable1 ! variable2 expression init1 init2

Issue with breaking line

• Can we break lines?
• How we should break lines?
• Special character on end line or brackets?
• Braces?
• Indentation?
• Tabs?

Example break lines

: function \
  \ param1 
  \ param2 
  result

: variable \
  ? condition 
  result1
  result2

: variable \
  | guard1 result1
  | guard2 result2 
  default result
  expression

: variable \
  ? (guard1 expression) result1
  ? (guard2 expression) result2
  result

: variable \
  & id1 init1
  & id2 init2
  result

: variable \
  \ id1
  \ id2
  result
  init1
  init2

a b c; => (a b) c ; => default order
a ` b c; => a (b c) => reverted order
! s v o; => v s o; => object order
o s v; => pipe order
o s v; => stack order

[kamil-adam]

1. Split source by NewLine
2. Parse every line separately
3. If we have error we append next line to actual parsed lines, and we will parse again