Created
April 1, 2012 03:00
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Attempting to grok the λ-calculus through Ruby.
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I = -> x { x } | |
C = -> x { -> y { -> z { x[z][y] } } } | |
T = -> C[I] | |
K = -> x { -> y { x } } | |
U = -> f { f[f] } | |
# I know, this technically isn't the Y combinator, | |
# and it isn't exactly the Z combinator either (like Y, but for applicative order languages). | |
Y = -> g { U[-> f { -> x { g[U[f]][x] } } ] } | |
NOT = -> p -> { -> x { -> y { p[y][x] } } } | |
AND = -> p -> { -> q { p[q][p] } } | |
OR = -> p -> { -> q { p[p][q] } } | |
TRUE = K | |
FALSE = NOT[TRUE] | |
IF = I | |
ZERO = FALSE | |
IS_ZERO = -> n { n[-> x { FALSE }][TRUE] } | |
IS_LEQ = -> m { -> n { IS_ZERO[SUB[m][n] } } | |
IS_EQ = -> m { -> n { AND[IS_LEQ[m][n]][IS_LEQ[n][m]] } } | |
PAIR = -> x { -> y { -> f { f[x][y] } } } | |
FST = -> p { p[TRUE] } | |
SND = -> p { p[FALSE] } | |
NIL = -> PAIR[TRUE][TRUE] | |
IS_NIL = FST | |
HEAD = -> l { FST[SND[l]] } | |
TAIL = -> l { SND[SND[l]] } | |
UNSHIFT = -> l { -> x { PAIR[FALSE][PAIR[x][l]] } } | |
SUCC = -> n { -> f { -> x { f[n[f][x]] } } } | |
SHFTINC = -> p { PAIR[SECOND[p]][SUCC[SECOND[p]]] } | |
PRED = -> n { FST[n[SHFTINC][PAIR[ZERO][ZERO]]] } | |
ADD = -> m { -> n { n[SUCC][m] } } | |
SUB = -> m { -> n { n[PRED][m] } } | |
MUL = -> m { -> n { n[ADD[m]][ZERO] } } | |
POW = -> m { -> n { n[MUL[m]][ONE] } } | |
MOD = | |
Y[-> f { -> m { -> n { | |
IF[IS_LEQ[n][m]][ | |
-> x { # η-expansion to prevent infinite recursion. | |
f[SUB[m][n]][n][x] | |
} | |
][ | |
m | |
] | |
} } }] | |
RANGE = | |
Y[-> f { | |
-> m { -> n { | |
IF[IS_LEQ[m][n]][ | |
-> x { | |
UNSHIFT[f[SUCC[m]][n]][m][x] | |
} | |
][ | |
NIL | |
] | |
} } | |
}] | |
FOLDL = | |
Y[-> f { | |
-> l { -> x { -> g { | |
IF[IS_NIL[l]][ | |
x | |
][ | |
-> y { | |
f[TAIL[l]][g[x][HEAD[l]][g][y] | |
} | |
] | |
} } } | |
}] | |
FOLDR = | |
Y[-> f { | |
-> l { -> x { -> g { | |
IF[IS_NIL[l]][ | |
x | |
][ | |
-> y { | |
g[f[TAIL[l]][x][g]][HEAD[l]][y] | |
} | |
] | |
} } } | |
}] | |
MAP = | |
-> k { -> f { | |
FOLDR[k][NIL][ | |
-> l { -> x { UNSHIFT[l][f[x]] } } | |
] | |
} } | |
SUM = | |
-> l { | |
FOLDL[l][ZERO][ADD] | |
} | |
PRODUCT = | |
-> l { | |
FOLDL[l][ONE][MUL] | |
} | |
REVERSE = | |
-> l { | |
FOLDL[l][NIL][UNSHIFT] | |
} | |
def to_integer(proc) | |
proc[-> n { n + 1 }][0] | |
end | |
def to_boolean(proc) | |
proc[true][false] | |
end | |
def to_array(proc) | |
array = [] | |
until to_boolean(IS_NIL[proc]) | |
head = HEAD[proc] | |
array << head | |
proc = TAIL[proc] | |
end | |
array | |
end |
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What an amazing gist.