Drop backslash from lambda definitions

This commit is contained in:
James Eversole 2025-04-15 10:34:38 -05:00
parent 5024a2be4c
commit f2beb86d8a
16 changed files with 181 additions and 182 deletions

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@ -11,12 +11,11 @@ tricu is the word for "tree" in Lojban: `(x1) is a tree of species/cultivar (x2)
## Features
- Tree Calculus operator: `t`
- Assignments: `x = t t`
- Immutable definitions
- Lambda abstraction syntax: `id = (\a : a)`
- Immutable definitions: `x = t t`
- Lambda abstraction: `id = (a : a)`
- List, Number, and String literals: `[(2) ("Hello")]`
- Function application: `not (not false)`
- Higher order/first-class functions: `map (\a : append a "!") [("Hello")]`
- Higher order/first-class functions: `map (a : append a "!") [("Hello")]`
- Intensionality blurs the distinction between functions and data (see REPL examples)
- Simple module system for code organization
@ -24,15 +23,15 @@ tricu is the word for "tree" in Lojban: `(x1) is a tree of species/cultivar (x2)
```
tricu < -- Anything after `--` on a single line is a comment
tricu < id = (\a : a) -- Lambda abstraction is eliminated to tree calculus terms
tricu < head (map (\i : append i " world!") [("Hello, ")])
tricu < id = (a : a) -- Lambda abstraction is eliminated to tree calculus terms
tricu < head (map (i : append i " world!") [("Hello, ")])
tricu > "Hello, world!"
tricu < id (head (map (\i : append i " world!") [("Hello, ")]))
tricu < id (head (map (i : append i " world!") [("Hello, ")]))
tricu > "Hello, world!"
tricu < -- Intensionality! We can inspect the structure of a function or data.
tricu < triage = (\a b c : t (t a b) c)
tricu < test = triage "Leaf" (\z : "Stem") (\a b : "Fork")
tricu < triage = (a b c : t (t a b) c)
tricu < test = triage "Leaf" (z : "Stem") (a b : "Fork")
tricu < test (t t)
tricu > "Stem"
tricu < -- We can even convert a term back to source code (/demos/toSource.tri)

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@ -11,11 +11,11 @@ demo_true = t t
not_TC? = t (t (t t) (t t t)) (t t (t t t))
-- /demos/toSource.tri contains an explanation of `triage`
demo_triage = \a b c : t (t a b) c
demo_matchBool = (\ot of : demo_triage
demo_triage = a b c : t (t a b) c
demo_matchBool = (ot of : demo_triage
of
(\_ : ot)
(\_ _ : ot)
(_ : ot)
(_ _ : ot)
)
-- Lambda representation of the Boolean `not` function
not_Lambda? = demo_matchBool demo_false demo_true

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@ -18,15 +18,15 @@ main = exampleTwo
-- / / \
-- 4 5 6
label = \node : head node
label = node : head node
left = (\node : if (emptyList? node)
left = (node : if (emptyList? node)
[]
(if (emptyList? (tail node))
[]
(head (tail node))))
right = (\node : if (emptyList? node)
right = (node : if (emptyList? node)
[]
(if (emptyList? (tail node))
[]
@ -34,25 +34,25 @@ right = (\node : if (emptyList? node)
[]
(head (tail (tail node))))))
processLevel = y (\self queue : if (emptyList? queue)
processLevel = y (self queue : if (emptyList? queue)
[]
(pair (map label queue) (self (filter
(\node : not? (emptyList? node))
(node : not? (emptyList? node))
(append (map left queue) (map right queue))))))
levelOrderTraversal_ = \a : processLevel (t a t)
levelOrderTraversal_ = a : processLevel (t a t)
toLineString = y (\self levels : if (emptyList? levels)
toLineString = y (self levels : if (emptyList? levels)
""
(append
(append (map (\x : append x " ") (head levels)) "")
(append (map (x : append x " ") (head levels)) "")
(if (emptyList? (tail levels)) "" (append (t (t 10 t) t) (self (tail levels))))))
levelOrderToString = \s : toLineString (levelOrderTraversal_ s)
levelOrderToString = s : toLineString (levelOrderTraversal_ s)
flatten = foldl (\acc x : append acc x) ""
flatten = foldl (acc x : append acc x) ""
levelOrderTraversal = \s : append (t 10 t) (flatten (levelOrderToString s))
levelOrderTraversal = s : append (t 10 t) (flatten (levelOrderToString s))
exampleOne = levelOrderTraversal [("1")
[("2") [("4") t t] t]

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@ -3,11 +3,11 @@
main = size size
size = (\x :
(y (\self x :
size = (x :
(y (self x :
compose succ
(triage
(\x : x)
(x : x)
self
(\x y : compose (self x) (self y))
(x y : compose (self x) (self y))
x)) x 0))

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@ -18,7 +18,7 @@ main = toSource not?
sourceLeaf = t (head "t")
-- Stem case
sourceStem = (\convert : (\a rest :
sourceStem = (convert : (a rest :
t (head "(") -- Start with a left parenthesis "(".
(t (head "t") -- Add a "t"
(t (head " ") -- Add a space.
@ -26,7 +26,7 @@ sourceStem = (\convert : (\a rest :
(t (head ")") rest)))))) -- Close with ")" and append the rest.
-- Fork case
sourceFork = (\convert : (\a b rest :
sourceFork = (convert : (a b rest :
t (head "(") -- Start with a left parenthesis "(".
(t (head "t") -- Add a "t"
(t (head " ") -- Add a space.
@ -36,7 +36,7 @@ sourceFork = (\convert : (\a b rest :
(t (head ")") rest)))))))) -- Close with ")" and append the rest.
-- Wrapper around triage
toSource_ = y (\self arg :
toSource_ = y (self arg :
triage
sourceLeaf -- `triage` "a" case, Leaf
(sourceStem self) -- `triage` "b" case, Stem
@ -44,7 +44,7 @@ toSource_ = y (\self arg :
arg) -- The term to be inspected
-- toSource takes a single TC term and returns a String
toSource = \v : toSource_ v ""
toSource = v : toSource_ v ""
exampleOne = toSource true -- OUT: "(t t)"
exampleTwo = toSource not? -- OUT: "(t (t (t t) (t t t)) (t t (t t t)))"

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@ -1,74 +1,74 @@
false = t
_ = t
true = t t
id = \a : a
const = \a b : a
id = a : a
const = a b : a
pair = t
if = \cond then else : t (t else (t t then)) t cond
if = cond then else : t (t else (t t then)) t cond
y = ((\mut wait fun : wait mut (\x : fun (wait mut x)))
(\x : x x)
(\a0 a1 a2 : t (t a0) (t t a2) a1))
y = ((mut wait fun : wait mut (x : fun (wait mut x)))
(x : x x)
(a0 a1 a2 : t (t a0) (t t a2) a1))
compose = \f g x : f (g x)
compose = f g x : f (g x)
triage = \leaf stem fork : t (t leaf stem) fork
test = triage "Leaf" (\_ : "Stem") (\_ _ : "Fork")
triage = leaf stem fork : t (t leaf stem) fork
test = triage "Leaf" (_ : "Stem") (_ _ : "Fork")
matchBool = (\ot of : triage
matchBool = (ot of : triage
of
(\_ : ot)
(\_ _ : ot)
(_ : ot)
(_ _ : ot)
)
lAnd = (triage
(\_ : false)
(\_ x : x)
(\_ _ x : x))
(_ : false)
(_ x : x)
(_ _ x : x))
lOr = (triage
(\x : x)
(\_ _ : true)
(\_ _ _ : true))
(x : x)
(_ _ : true)
(_ _ _ : true))
matchPair = \a : triage _ _ a
matchPair = a : triage _ _ a
not? = matchBool false true
and? = matchBool id (\_ : false)
and? = matchBool id (_ : false)
or? = (\x z :
or? = (x z :
matchBool
(matchBool true true z)
(matchBool true false z)
x)
xor? = (\x z :
xor? = (x z :
matchBool
(matchBool false true z)
(matchBool true false z)
x)
equal? = y (\self : triage
equal? = y (self : triage
(triage
true
(\_ : false)
(\_ _ : false))
(\ax :
(_ : false)
(_ _ : false))
(ax :
triage
false
(self ax)
(\_ _ : false))
(\ax ay :
(_ _ : false))
(ax ay :
triage
false
(\_ : false)
(\bx by : lAnd (self ax bx) (self ay by))))
(_ : false)
(bx by : lAnd (self ax bx) (self ay by))))
succ = y (\self :
succ = y (self :
triage
1
t
(triage
(t (t t))
(\_ tail : t t (self tail))
(_ tail : t t (self tail))
t))

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@ -1,68 +1,68 @@
!import "base.tri" !Local
matchList = \a b : triage a _ b
matchList = a b : triage a _ b
emptyList? = matchList true (\_ _ : false)
head = matchList t (\head _ : head)
tail = matchList t (\_ tail : tail)
emptyList? = matchList true (_ _ : false)
head = matchList t (head _ : head)
tail = matchList t (_ tail : tail)
append = y (\self : matchList
(\k : k)
(\h r k : pair h (self r k)))
append = y (self : matchList
(k : k)
(h r k : pair h (self r k)))
lExist? = y (\self x : matchList
lExist? = y (self x : matchList
false
(\h z : or? (equal? x h) (self x z)))
(h z : or? (equal? x h) (self x z)))
map_ = y (\self :
map_ = y (self :
matchList
(\_ : t)
(\head tail f : pair (f head) (self tail f)))
map = \f l : map_ l f
(_ : t)
(head tail f : pair (f head) (self tail f)))
map = f l : map_ l f
filter_ = y (\self : matchList
(\_ : t)
(\head tail f : matchBool (t head) id (f head) (self tail f)))
filter = \f l : filter_ l f
filter_ = y (self : matchList
(_ : t)
(head tail f : matchBool (t head) id (f head) (self tail f)))
filter = f l : filter_ l f
foldl_ = y (\self f l x : matchList (\acc : acc) (\head tail acc : self f tail (f acc head)) l x)
foldl = \f x l : foldl_ f l x
foldl_ = y (self f l x : matchList (acc : acc) (head tail acc : self f tail (f acc head)) l x)
foldl = f x l : foldl_ f l x
foldr_ = y (\self x f l : matchList x (\head tail : f (self x f tail) head) l)
foldr = \f x l : foldr_ x f l
foldr_ = y (self x f l : matchList x (head tail : f (self x f tail) head) l)
foldr = f x l : foldr_ x f l
length = y (\self : matchList
length = y (self : matchList
0
(\_ tail : succ (self tail)))
(_ tail : succ (self tail)))
reverse = y (\self : matchList
reverse = y (self : matchList
t
(\head tail : append (self tail) (pair head t)))
(head tail : append (self tail) (pair head t)))
snoc = y (\self x : matchList
snoc = y (self x : matchList
(pair x t)
(\h z : pair h (self x z)))
(h z : pair h (self x z)))
count = y (\self x : matchList
count = y (self x : matchList
0
(\h z : matchBool
(h z : matchBool
(succ (self x z))
(self x z)
(equal? x h)))
last = y (\self : matchList
last = y (self : matchList
t
(\hd tl : matchBool
(hd tl : matchBool
hd
(self tl)
(emptyList? tl)))
all? = y (\self pred : matchList
all? = y (self pred : matchList
true
(\h z : and? (pred h) (self pred z)))
(h z : and? (pred h) (self pred z)))
any? = y (\self pred : matchList
any? = y (self pred : matchList
false
(\h z : or? (pred h) (self pred z)))
(h z : or? (pred h) (self pred z)))
intersect = \xs ys : filter (\x : lExist? x ys) xs
intersect = xs ys : filter (x : lExist? x ys) xs

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@ -1,36 +1,36 @@
!import "list.tri" !Local
match_ = y (\self value patterns :
match_ = y (self value patterns :
triage
t
(\_ : t)
(\pattern rest :
(_ : t)
(pattern rest :
triage
t
(\_ : t)
(\test result :
(_ : t)
(test result :
if (test value)
(result value)
(self value rest))
pattern)
patterns)
match = (\value patterns :
match_ value (map (\sublist :
match = (value patterns :
match_ value (map (sublist :
pair (head sublist) (head (tail sublist)))
patterns))
otherwise = const (t t)
matchExample = (\x : match x
[[(equal? 1) (\_ : "one")]
[(equal? 2) (\_ : "two")]
[(equal? 3) (\_ : "three")]
[(equal? 4) (\_ : "four")]
[(equal? 5) (\_ : "five")]
[(equal? 6) (\_ : "six")]
[(equal? 7) (\_ : "seven")]
[(equal? 8) (\_ : "eight")]
[(equal? 9) (\_ : "nine")]
[(equal? 10) (\_ : "ten")]
[ otherwise (\_ : "I ran out of fingers!")]])
matchExample = (x : match x
[[(equal? 1) (_ : "one")]
[(equal? 2) (_ : "two")]
[(equal? 3) (_ : "three")]
[(equal? 4) (_ : "four")]
[(equal? 5) (_ : "five")]
[(equal? 6) (_ : "six")]
[(equal? 7) (_ : "seven")]
[(equal? 8) (_ : "eight")]
[(equal? 9) (_ : "nine")]
[(equal? 10) (_ : "ten")]
[ otherwise (_ : "I ran out of fingers!")]])

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@ -130,7 +130,6 @@ parseFunctionM = do
parseLambdaM :: ParserM TricuAST
parseLambdaM = do
let ident = (\case LIdentifier _ -> True; _ -> False)
_ <- satisfyM (== LBackslash)
params <- some (satisfyM ident)
_ <- satisfyM (== LColon)
scnParserM
@ -145,11 +144,11 @@ parseLambdaExpressionM = choice
parseAtomicLambdaM :: ParserM TricuAST
parseAtomicLambdaM = choice
[ parseVarM
[ try parseLambdaM
, parseVarM
, parseTreeLeafM
, parseLiteralM
, parseListLiteralM
, try parseLambdaM
, between (satisfyM (== LOpenParen)) (satisfyM (== LCloseParen)) parseLambdaExpressionM
]
@ -205,7 +204,8 @@ parseTreeLeafOrParenthesizedM = choice
parseAtomicM :: ParserM TricuAST
parseAtomicM = choice
[ parseVarM
[ try parseLambdaM
, parseVarM
, parseTreeLeafM
, parseListLiteralM
, parseGroupedM

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@ -87,7 +87,7 @@ parser = testGroup "Parser Tests"
Right _ -> assertFailure "Expected failure when trying to assign the value of T"
, testCase "Parse function definitions" $ do
let input = "x = (\\a b c : a)"
let input = "x = (a b c : a)"
expect = SDef "x" [] (SLambda ["a"] (SLambda ["b"] (SLambda ["c"] (SVar "a"))))
parseSingle input @?= expect
@ -107,7 +107,7 @@ parser = testGroup "Parser Tests"
parseSingle input @?= expect
, testCase "Parse function with applications" $ do
let input = "f = (\\x : t x)"
let input = "f = (x : t x)"
expect = SDef "f" [] (SLambda ["x"] (SApp TLeaf (SVar "x")))
parseSingle input @?= expect
@ -149,22 +149,22 @@ parser = testGroup "Parser Tests"
parseSingle input @?= expect
, testCase "Parse nested parentheses in function body" $ do
let input = "f = (\\x : t (t (t t)))"
let input = "f = (x : t (t (t t)))"
expect = SDef "f" [] (SLambda ["x"] (SApp TLeaf (SApp TLeaf (SApp TLeaf TLeaf))))
parseSingle input @?= expect
, testCase "Parse lambda abstractions" $ do
let input = "(\\a : a)"
let input = "(a : a)"
expect = (SLambda ["a"] (SVar "a"))
parseSingle input @?= expect
, testCase "Parse multiple arguments to lambda abstractions" $ do
let input = "x = (\\a b : a)"
let input = "x = (a b : a)"
expect = SDef "x" [] (SLambda ["a"] (SLambda ["b"] (SVar "a")))
parseSingle input @?= expect
, testCase "Grouping T terms with parentheses in function application" $ do
let input = "x = (\\a : a)\nx (t)"
let input = "x = (a : a)\nx (t)"
expect = [SDef "x" [] (SLambda ["a"] (SVar "a")),SApp (SVar "x") TLeaf]
parseTricu input @?= expect
@ -259,7 +259,7 @@ simpleEvaluation = testGroup "Evaluation Tests"
, testCase "Apply identity to Boolean Not" $ do
let not = "(t (t (t t) (t t t)) t)"
let input = "x = (\\a : a)\nx " ++ not
let input = "x = (a : a)\nx " ++ not
env = evalTricu Map.empty (parseTricu input)
result env @?= Fork (Fork (Stem Leaf) (Fork Leaf Leaf)) Leaf
]
@ -267,84 +267,84 @@ simpleEvaluation = testGroup "Evaluation Tests"
lambdas :: TestTree
lambdas = testGroup "Lambda Evaluation Tests"
[ testCase "Lambda Identity Function" $ do
let input = "id = (\\x : x)\nid t"
let input = "id = (x : x)\nid t"
runTricu input @?= "Leaf"
, testCase "Lambda Constant Function (K combinator)" $ do
let input = "k = (\\x y : x)\nk t (t t)"
let input = "k = (x y : x)\nk t (t t)"
runTricu input @?= "Leaf"
, testCase "Lambda Application with Variable" $ do
let input = "id = (\\x : x)\nval = t t\nid val"
let input = "id = (x : x)\nval = t t\nid val"
runTricu input @?= "Stem Leaf"
, testCase "Lambda Application with Multiple Arguments" $ do
let input = "apply = (\\f x y : f x y)\nk = (\\a b : a)\napply k t (t t)"
let input = "apply = (f x y : f x y)\nk = (a b : a)\napply k t (t t)"
runTricu input @?= "Leaf"
, testCase "Nested Lambda Application" $ do
let input = "apply = (\\f x y : f x y)\nid = (\\x : x)\napply (\\f x : f x) id t"
let input = "apply = (f x y : f x y)\nid = (x : x)\napply (f x : f x) id t"
runTricu input @?= "Leaf"
, testCase "Lambda with a complex body" $ do
let input = "f = (\\x : t (t x))\nf t"
let input = "f = (x : t (t x))\nf t"
runTricu input @?= "Stem (Stem Leaf)"
, testCase "Lambda returning a function" $ do
let input = "f = (\\x : (\\y : x))\ng = f t\ng (t t)"
let input = "f = (x : (y : x))\ng = f t\ng (t t)"
runTricu input @?= "Leaf"
, testCase "Lambda with Shadowing" $ do
let input = "f = (\\x : (\\x : x))\nf t (t t)"
let input = "f = (x : (x : x))\nf t (t t)"
runTricu input @?= "Stem Leaf"
, testCase "Lambda returning another lambda" $ do
let input = "k = (\\x : (\\y : x))\nk_app = k t\nk_app (t t)"
let input = "k = (x : (y : x))\nk_app = k t\nk_app (t t)"
runTricu input @?= "Leaf"
, testCase "Lambda with free variables" $ do
let input = "y = t t\nf = (\\x : y)\nf t"
let input = "y = t t\nf = (x : y)\nf t"
runTricu input @?= "Stem Leaf"
, testCase "SKI Composition" $ do
let input = "s = (\\x y z : x z (y z))\nk = (\\x y : x)\ni = (\\x : x)\ncomp = s k i\ncomp t (t t)"
let input = "s = (x y z : x z (y z))\nk = (x y : x)\ni = (x : x)\ncomp = s k i\ncomp t (t t)"
runTricu input @?= "Stem (Stem Leaf)"
, testCase "Lambda with multiple parameters and application" $ do
let input = "f = (\\a b c : t a b c)\nf t (t t) (t t t)"
let input = "f = (a b c : t a b c)\nf t (t t) (t t t)"
runTricu input @?= "Stem Leaf"
, testCase "Lambda with nested application in the body" $ do
let input = "f = (\\x : t (t (t x)))\nf t"
let input = "f = (x : t (t (t x)))\nf t"
runTricu input @?= "Stem (Stem (Stem Leaf))"
, testCase "Lambda returning a function and applying it" $ do
let input = "f = (\\x : (\\y : t x y))\ng = f t\ng (t t)"
let input = "f = (x : (y : t x y))\ng = f t\ng (t t)"
runTricu input @?= "Fork Leaf (Stem Leaf)"
, testCase "Lambda applying a variable" $ do
let input = "id = (\\x : x)\na = t t\nid a"
let input = "id = (x : x)\na = t t\nid a"
runTricu input @?= "Stem Leaf"
, testCase "Nested lambda abstractions in the same expression" $ do
let input = "f = (\\x : (\\y : x y))\ng = (\\z : z)\nf g t"
let input = "f = (x : (y : x y))\ng = (z : z)\nf g t"
runTricu input @?= "Leaf"
, testCase "Lambda applied to string literal" $ do
let input = "f = (\\x : x)\nf \"hello\""
let input = "f = (x : x)\nf \"hello\""
runTricu input @?= "Fork (Fork Leaf (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) Leaf))))"
, testCase "Lambda applied to integer literal" $ do
let input = "f = (\\x : x)\nf 42"
let input = "f = (x : x)\nf 42"
runTricu input @?= "Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) Leaf)))))"
, testCase "Lambda applied to list literal" $ do
let input = "f = (\\x : x)\nf [t (t t)]"
let input = "f = (x : x)\nf [t (t t)]"
runTricu input @?= "Fork Leaf (Fork (Stem Leaf) Leaf)"
, testCase "Lambda containing list literal" $ do
let input = "(\\a : [(a)]) 1"
let input = "(a : [(a)]) 1"
runTricu input @?= "Fork (Fork (Stem Leaf) Leaf) Leaf"
]
@ -419,7 +419,7 @@ providedLibraries = testGroup "Library Tests"
, testCase "List map" $ do
library <- evaluateFile "./lib/list.tri"
let input = "head (tail (map (\\a : (t t t)) [(t) (t) (t)]))"
let input = "head (tail (map (a : (t t t)) [(t) (t) (t)]))"
env = evalTricu library (parseTricu input)
result env @?= Fork Leaf Leaf

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@ -1,9 +1,9 @@
-- This is a tricu comment!
-- t (t t) (t (t t t))
-- t (t t t) (t t)
-- x = (\a : a)
-- x = (a : a)
main = t (t t) t -- Fork (Stem Leaf) Leaf
-- t t
-- x
-- x = (\a : a)
-- x = (a : a)
-- t

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@ -1 +1 @@
main = (\x : x) t
main = (x : x) t

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@ -1,2 +1,2 @@
x = map (\i : append "Successfully concatenated " i) [("two strings!")]
x = map (i : append "Successfully concatenated " i) [("two strings!")]
main = equal? x [("Successfully concatenated two strings!")]

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@ -1,21 +1,21 @@
compose = \f g x : f (g x)
compose = f g x : f (g x)
succ = y (\self :
succ = y (self :
triage
1
t
(triage
(t (t t))
(\_ tail : t t (self tail))
(_ tail : t t (self tail))
t))
size = (\x :
(y (\self x :
size = (x :
(y (self x :
compose succ
(triage
(\x : x)
(x : x)
self
(\x y : compose (self x) (self y))
(x y : compose (self x) (self y))
x)) x 0))
size size

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@ -1 +1 @@
head (map (\i : append "String " i) [("test!")])
head (map (i : append "String " i) [("test!")])

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@ -1 +1 @@
y = \x : x
y = x : x