Reduce

Updated May 3, 2026· Base Functions

rreducefunctional-programmingbase-rfoldaccumulate

Reduce takes a binary function and a vector or list, then applies the function cumulatively: given [a, b, c] and binary function f, it computes f(f(a, b), c). The result is a single value.

Signature

Reduce(f, x, init, right = FALSE, accumulate = FALSE)

Parameters:

f — a binary function (takes exactly two arguments)
x — a vector or list to reduce
init — optional initial value for the accumulator
right — if TRUE, fold right-to-left instead of left-to-right
accumulate — if TRUE, return all intermediate results instead of just the final one

Basic Usage

Sum and Product

Reduce(`+`, c(1, 2, 3, 4, 5))
# [1] 15

Reduce(`*`, c(1, 2, 3, 4, 5))
# [1] 120

Set Intersection

Reduce(intersect, list(c("a", "b", "c"), c("b", "c", "d"), c("c", "d", "e")))
# [1] "c"

Initial Value

Pass init to set a starting value for the reduction:

Reduce(`+`, c(1, 2, 3), init = 10)
# [1] 16

Reduce(`+`, c(), init = 10)
# [1] 10

Without init, an empty vector causes an error. With init, empty vectors return the initial value safely.

Right Folding

Set right = TRUE to fold from right to left:

Reduce(`-`, c(10, 3, 2))
# [1] 5

Reduce(`-`, c(10, 3, 2), right = TRUE)
# [1] 9

Left fold: ((10 - 3) - 2) = 5 Right fold: 10 - (3 - 2) = 9

Accumulate Mode

Set accumulate = TRUE to return all intermediate results:

Reduce(`+`, c(1, 2, 3, 4, 5), accumulate = TRUE)
# [1]  1  3  6 10 15

Useful when you need running totals or intermediate states:

# Running minimum
Reduce(pmin, c(5, 3, 4, 1, 2), accumulate = TRUE)
# [1] 5 3 3 1 1

Building Complex Objects

Reduce composes operations where later steps depend on earlier results:

# Build a configuration list from partial pieces
configs <- list(
  list(theme = "light"),
  list(font = "Arial"),
  list(size = 14)
)

combined <- Reduce(function(cfg, new) c(cfg, new), configs, init = list())
# [[1]]$theme  [1] "light"
# [[2]]$font  [1] "Arial"
# [[3]]$size  [1] 14

Common Pitfalls

Function Must Be Binary

Reduce passes exactly two arguments at a time:

Reduce(function(x) x^2, c(1, 2, 3))
# Error: evaluation nested too deeply

Wrap unary functions to adapt them:

Reduce(function(a, b) a + b^2, c(1, 2, 3))
# [1] 32

Mistaking Accumulated Value

With accumulate = TRUE, the output length changes:

result <- Reduce(`+`, c(1, 2, 3), accumulate = TRUE)
length(result)
# [1] 3