> ## Documentation Index > Fetch the complete documentation index at: https://companyname-a7d5b98e-v2-pagination.mintlify.site/llms.txt > Use this file to discover all available pages before exploring further. # Basic values and literals in Fift export const Aside = ({type = "note", title = "", icon = "", iconType = "regular", children}) => { const asideVariants = ["note", "tip", "caution", "danger"]; const asideComponents = { note: { outerStyle: "border-sky-500/20 bg-sky-50/50 dark:border-sky-500/30 dark:bg-sky-500/10", innerStyle: "text-sky-900 dark:text-sky-200", calloutType: "note", icon: }, tip: { outerStyle: "border-emerald-500/20 bg-emerald-50/50 dark:border-emerald-500/30 dark:bg-emerald-500/10", innerStyle: "text-emerald-900 dark:text-emerald-200", calloutType: "tip", icon: }, caution: { outerStyle: "border-amber-500/20 bg-amber-50/50 dark:border-amber-500/30 dark:bg-amber-500/10", innerStyle: "text-amber-900 dark:text-amber-200", calloutType: "warning", icon: }, danger: { outerStyle: "border-red-500/20 bg-red-50/50 dark:border-red-500/30 dark:bg-red-500/10", innerStyle: "text-red-900 dark:text-red-200", calloutType: "danger", icon: } }; let variant = type; let gotInvalidVariant = false; if (!asideVariants.includes(type)) { gotInvalidVariant = true; variant = "danger"; } const iconVariants = ["regular", "solid", "light", "thin", "sharp-solid", "duotone", "brands"]; if (!iconVariants.includes(iconType)) { iconType = "regular"; } return <>
{} {icon === "" ? asideComponents[variant].icon : }
{gotInvalidVariant ?

Invalid type passed!
Received: {type}
Expected one of: {asideVariants.join(", ")}

: <> {title &&

{title}

} {children} }
; }; ## Integers Fift recognizes integers in decimal, binary, and hexadecimal formats. Binary literals are prefixed by `0b`, hexadecimal literals are prefixed by `0x`, and decimal literals do not require a prefix. Examples: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 0b1101 // Binary literal, denoting integer 13 13 // Decimal literal 0xd // Hexadecimal literal, denoting integer 13 ``` An integer literal may be prefixed by a minus sign `-` to change its sign; the minus sign is accepted both before and after the `0x` and `0b` prefixes. Examples: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} -0b1101 // Binary literal, denoting integer -13 0b-1101 // Binary literal, denoting integer -13 -13 // Decimal literal -0xd // Hexadecimal literal, denoting integer -13 0x-d // Hexadecimal literal, denoting integer -13 ``` Integer literals are pushed into the Fift stack in the order of their appearance. For example, executing: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 1 0xa 3 -0b10 ``` produces the stack: ```text theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 1 10 3 -2 // Rightmost number is the top of the stack ``` In other words, `1` is pushed first, followed by `0xa` (i.e., `10`), followed by `3`, and finally `-0b10` (i.e., `-2`), leaving `-0b10` at the top of the stack. Fift has special syntax for decimal and common fractions. If a string consists of two valid integer literals separated by a slash `/`, then Fift interprets it as a fractional literal and represents it by two `Integer`s `p` and `q` in the stack, the numerator `p` and the denominator `q`. For instance, `-17/12` pushes `-17` and `12` into the Fift stack, being thus equivalent to executing `-17 12`; and `-0x11/0b1100` does the same thing. Decimal, binary, and hexadecimal fractions, such as `2.39` or `-0x11.ef`, are also represented by two integers `p` and `q`, where `q` is a suitable power of the base (10, 2, or 16, respectively). For instance, `2.39` is equivalent to `239 100`, and `-0x11.ef` is equivalent to `-0x11ef 0x100`. Such a representation of fractions is useful for defining *"rational arithmetic operations"*. For example, the following code defines two words `R-` and `R*` that carry out rational subtraction and multiplication, respectively. Word `R-` takes the stack `a b c d`, representing the fractions `a/b` and `c/d`, and produces the stack `(a*d-b*c) b*d`, representing the arithmetical subtraction `a/b - c/d = (a*d-b*c) / (b*d)`. Similarly, word `R*` takes the stack `a b c d`, representing the fractions `a/b` and `c/d`, and produces the stack `a*c b*d`, representing the arithmetical multiplication `a/b * c/d = (a*c) / (b*d)`. ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // a b c d ---> (a*d-b*c) b*d { -rot over * 2swap tuck * rot - -rot * } : R- // a b c d ---> a*c b*d { rot * -rot * swap } : R* ``` So that, executing `1.7 2/3 R- 5/2 R*` will produce the stack `155 60`, corresponding to the arithmetical operation `(1.7 - 2/3) * 5/2 = 31/30 * 5/2 = 155/60`. For advanced details on integers, see the [Integers section](/languages/fift/whitepaper#2-8-integer-and-fractional-constants%2C-or-literals) in the Fift whitepaper. ## Strings A string is any sequence of UTF-8 characters enclosed by double quotes `"`. Single line strings can be introduced by the character `"`, which scans the remainder of the line until the next `"` character. Single line strings do not support new line characters. When Fift recognizes a string, it pushes it into the Fift stack as a value of type `String`. For instance, `"Hello, world!"` pushes the corresponding `String` into the stack: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} "Hello, world!" // String "Hello, world!" is at the top of the stack ``` For multi-line strings, Fift has the word `$<<"""` which scans all the next lines until it finds triple quote characters in a new line `"""`, which finalize the multi-line string. For instance, ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} $<<""" Hello, world! This is a multi-line string Another line... """ // The following multi-line string is at the top of the stack: // "Hello, world! // This is a multi-line string // Another line... // " ``` ## Booleans As described in the [Types page](/languages/fift/types), Fift does not have a separate type for booleans. Instead, booleans are emulated using `Integer`s, where `-1` represents truth, and `0` falsehood. Comparison primitives normally return `-1` to indicate success and `0` otherwise. Fift has the constants `true` and `false` to push these special integers into the stack: | Word | Description | | :------ | :-------------------------- | | `true` | pushes `-1` into the stack. | | `false` | pushes `0` into the stack. | Certain operations, like conditional execution of blocks and loops with exit conditions, extend the notion of "true" to any non-zero integer. However, if the intention is to work with bitwise operations over booleans, any non-zero integer must first be transformed into `-1`. Fift has the word `0<>` that transforms any non-zero integer into `-1`, and leaves `0` unchanged. For instance: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 5 0<> // Produces -1 at the top of the stack -2 0<> // Produces -1 at the top of the stack 0 0<> // Produces 0 at the top of the stack ``` ## Null Fift has the two words `null` and `null?` to work with values of type `Null`. The word `null` pushes to the stack the `null` value, while the word `null?` consumes the value at the top of the stack and checks if such value is `null` or not. If the value is `null`, word `null?` pushes `-1` to the stack, `0` otherwise. For instance: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // push null, then check if null. // The stack contains -1 at the top. null null? // push 5, then check if null. // The stack contains 0 at the top. 5 null? ``` ## Boxes A `Box` is a location or container that can be used to store exactly one value of any Fift-supported type. They are usually used to define variables and mutable data structures, like mutable [tuples](#tuples). Fift provides the words `hole` and `box` to create boxes. Word `hole` pushes an empty box to the top of the stack, i.e., an empty box is a box containing the [`null`](#null) value. Word `box` consumes the value `v` at the top of the stack and pushes a box containing `v`. For instance: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} hole // Pushes an empty box 5 box // Pushes a box containing 5 "foo" box // Pushes a box containing "foo" ``` The value currently stored in a `Box` may be fetched by means of word `@` (pronounced "fetch"), and modified by means of word `!` (pronounced "store"). Word `@` consumes the box at the top of the stack and pushes the value contained in the box. Word `!` requires a stack of the form `x p`, where `x` is the value to store and `p` is the box in which `x` is going to be stored. `!` consumes both `x` and `p` and stores `x` in `p`. Word `!` does not push anything into the stack. For instance: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // Create a constant A storing an empty box hole constant A // Fetch the contents of box in A A @ // Pushes null into the stack // Store 5 into the box in A 5 A ! // Fetch the contents of box in A A @ // Pushes 5 into the stack // Store "foo" into the box in A "foo" A ! // Fetch the contents of box in A A @ // Pushes "foo" into the stack ``` As the example suggests, the value stored in a box does not need to be of the same type as the box contents mutate. For advanced details about boxes, see the [named and unnamed variables section](/languages/fift/whitepaper#2-14-named-and-unnamed-variables) in the Fift whitepaper and the variables section in the [words, constants, and variables page](/languages/fift/variables#variables). ## Tuples Tuples are ordered collections of arbitrary values of any type. When a `Tuple` consists of values `[ x1 ... xn ]` (in that order), the number `n` is called the length of the tuple. Tuples of length two are called *pairs*; tuples of length three are *triples*. A tuple with no elements is called the *empty tuple*. To construct tuples of known length, Fift provides the word `tuple`. The word `tuple` requires that the tuple's data be laid out in the stack as follows `x1 x2 ..... xn n`, where `x1`, `x2`, `...`, `xn` are the `n` values in the tuple, and `n` is the length of the tuple, located at the top of the stack. For example, to construct tuple `[ 1 2 5 7 ]` consisting of `4` values, execute `1 2 5 7 4 tuple`, which will push the integers `1`, `2`, `5`, `7` into the stack, then it will push integer `4`, which is the tuple's length, and finally, Fift will execute the word `tuple`, which will consume the numbers `1`, `2`, `5`, `7`, `4` from the stack and push the tuple `[ 1 2 5 7 ]` at the top of the stack. To build pairs and triples it is possible to use the words `pair` and `triple`, respectively. For example, to build pair `[ x1 x2 ]`, execute `x1 x2 pair`, which is equivalent to executing `x1 x2 2 tuple`. To build triple `[ x1 x2 x3 ]`, execute `x1 x2 x3 triple`, which is equivalent to executing `x1 x2 x3 3 tuple`. To append a value `x` at the end of tuple `t`, Fift provides the word `,`. The word `,` requires that `t` and `x` be laid out in the stack as `t x`, where `x` is at the top of the stack. The word then consumes `t` and `x` from the stack, appends `x` to the end of `t` and pushes the resulting tuple to the end of the stack. For example, suppose the stack contains `[ 1 2 ] 3`, where `[ 1 2 ]` is a tuple, and `3` is the element to add located at the top of the stack; executing `,` will consume `[ 1 2 ]` and `3` from the stack and push the tuple `[ 1 2 3]` at the top of the stack. Use word `|` to push the empty tuple at the top of the stack. Using words `|` and `,` in combination, allows the construction of tuples in stages, starting from the empty tuple. For instance, the following produces tuple `[ 2 3 9 ]` at the top of the stack: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} | 2 , 3 , 9 , ``` first `|` pushes the empty tuple at the top of the stack; `2` then pushes `2` at the top of the stack, producing the stack `[ ] 2`, where `[ ]` denotes the empty tuple. Next, word `,` consumes `[ ]` and `2`, and pushes the tuple `[ 2 ]` at the top of the stack. Then, `3` pushes `3` at the top of the stack, producing the stack `[ 2 ] 3`, which then gets consumed by word `,` to produce tuple `[ 2 3 ]` at the top of the stack. Finally, `9` pushes `9` to produce stack `[ 2 3 ] 9`, which then gets consumed by word `,` to produce `[ 2 3 9 ]` at the top of the stack. The components of a `Tuple` are not necessarily of the same type, and the components can also be a `Tuple`. For instance: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 1 2 "one" triple 4 5 "two" triple pair ``` produces the tuple at the top of the stack: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} [ [ 1 2 "one" ] [ 4 5 "two" ] ] ``` which is a tuple with two tuples as components, and each tuple component contains two integers and one string. Once a `Tuple` has been constructed, it is possible to extract any of its components, or completely unpack the `Tuple` into the stack. For this, Fift provides words `[]` and `explode`, respectively. The word `[]` extracts a specific index from a tuple. Word `[]` requires that the stack has the form `t i`, where `t` is the tuple and `i` is the index to extract. When word `[]` executes, it consumes the elements `t i` from the stack and pushes to the top of the stack the `i`-th element in `t`. Indexes start counting from 0, so that if a tuple has `n` components, index `i` must satisfy `0 <= i < n`. For instance, the following defines a 3x3 matrix of integers `Matrix`, and then, accesses entry at row `1` and column `2`: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // The first line defines constant Matrix, // containing the nested tuples: // [ // [ 1 2 3 ] // [ 4 5 6 ] // [ 7 8 9 ] // ] 1 2 3 triple 4 5 6 triple 7 8 9 triple triple constant Matrix Matrix 1 [] 2 [] ``` produces `6` at the top of the stack. Line `Matrix 1 [] 2 []` executes as follows. First, constant `Matrix` pushes the entire matrix at the top of the stack. Next, `1` pushes `1` to the top of the stack, so the the stack now looks like `Matrix 1`. Next, word `[]` consumes `Matrix` and `1` from the stack and pushes `[ 4 5 6 ]` to the top of the stack, i.e., the row at index `1`. Finally, `2` pushes `2` to the stack, and `[]` consumes `[ 4 5 6 ]` and `2`, and pushes `6` to the top of the stack, i.e., the element at index `2`. The notation `Matrix 1 [] 2 []` is very reminiscent of the notation `Matrix[1][2]` usually found in programming languages. The word `explode` extracts all the components of a tuple and pushes them into the stack. Word `explode` requires that the stack has the form `[x1 x2 ... xn]`, i.e., a tuple of `n` elements at the top of the stack. When `explode` executes, it consumes the tuple at the top of the stack and produces the stack `x1 x2 ... xn n`, where the number of elements `n` is at the top of the stack. For instance, the following defines a constant `A` containing the tuple `[ 7 8 9 ]`, and the second line decomposes the tuple: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // The first line defines constant A // containing tuple [ 7 8 9 ] 7 8 9 triple constant A A explode ``` produces `7 8 9 3` in the stack, where `3`, the number at the top of the stack, is the number of elements in the original tuple. `Tuples` are immutable: it is not possible to change a component of a `Tuple`. If the intention is to create something like an array, where the components can be freely updated, a `Tuple` of `Box`es needs to be created. Fift has the word `allot` that creates a tuple of a specified number of [boxes](#boxes). The word `allot` takes the integer `n` at the top of the stack and creates a tuple of `n` empty boxes, i.e., each box contains `null`. Later, it is possible to mutate the boxes using the word `!`. For instance, the following defines a constant `A` containing a tuple of `10` empty boxes. Later, it sets the 0-th box to contain the integer `10`, and 2-th box to contain string `"foo"`. ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // Create a tuple of 10 empty boxes, name it A 10 allot constant A // Set 0-th box to contain 10 10 A 0 [] ! // Set 2-th box to contain "foo" "foo" A 2 [] ! ``` The code `10 A 0 [] !` pushes `10` into the stack. Then `A 0 []` pushes the 0-th box into the stack. Finally, `!` consumes both the box and `10` and updates the contents of the box to `10`. The code `"foo" A 2 [] !` has a similar explanation. For advanced details about tuple, see the [Tuples section](/languages/fift/whitepaper#2-15-tuples-and-arrays) in the Fift whitepaper. ## Lists Lisp-style lists can also be represented in Fift. A list `(1 2 3)` can be represented by nesting 2-tuples `[ 1 [ 2 [ 3 null ] ] ]`, where [`null`](#null) represents the empty list. Fift provides several words to create and deconstruct lists. The word `cons` takes a stack of the form `h l`, where `h` is a value and `l` is a list, i.e., a nested tuple; consumes both `h` and `l`, and produces the tuple `[ h l ]`. For instance, the following code produces the list `(1 2 3)`: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 1 2 3 null cons cons cons ``` First, `1 2 3 null` produces the stack `1 2 3 null`, where `null` is at the top of the stack. Then, the first `cons` produces the stack `1 2 [ 3 null ]`, where tuple `[ 3 null ]` is at the top of the stack. Next, the second `cons` produces the stack `1 [ 2 [ 3 null ] ]`. Finally, the third `cons` produces the stack `[ 1 [ 2 [ 3 null ] ] ]` containing a single tuple at the top, which is the list `(1 2 3)`. It is so common to build fixed-length lists like in the above example, that Fift provides a special word for building a list when the elements are known. The word `list` takes a stack of the form `x1 ... xn n`, where `n` is the number of elements in the list, and consumes `x1`, `...`, `xn` and `n` from the stack to produce the list `(x1 .... xn)` at the top of the stack. For instance, the following produces the same list as the previous example: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} 1 2 3 3 list ``` To deconstruct a list, use the word `uncons`. The word `uncons` consumes the list at the top of the stack and pushes the list's head followed by the list's tail. For instance, the following code defines a constant `A` containing list `(5 6 7)` and deconstruct the list by calling `uncons` several times: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} // Create the list (5 6 7), name it A 5 6 7 3 list constant A // Deconstruct the list by repeatedly calling uncons A uncons uncons uncons ``` The first `uncons` produces the stack `5 [ 6 [ 7 null ] ]`. The second `uncons` the stack `5 6 [ 7 null ]`. Finally, the third `uncons` produces the stack `5 6 7 null`. Since there is a `null` at the top of the stack, `drop` removes the `null` to produce the stack `5 6 7`. For advanced details about lists, see the [Lists section](/languages/fift/whitepaper#2-16-lists) in the Fift whitepaper. ## Atoms An `Atom` is an entity uniquely identified by its name. `Atom`s can be used to represent identifiers, labels, operation names, tags, and stack markers. Fift offers several words to create and manipulate `Atom`s. The word \`name pushes into the stack the atom identified by `name`. For instance, the following builds the [list](#lists) `(+ 2 (* 3 4))`, which is the Lisp-style representation of arithmetical expression `2 + (3 * 4)`: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} `+ 2 `* 3 4 3 list 3 list ``` First \`+ 2 \`\* 3 4 3 produces the stack `+ 2 * 3 4 3`, where `+` and `*` are atoms, i.e., identifiers. Then, `list` produces the stack `+ 2 (* 3 4)`, where list `(* 3 4)` is at the top of the stack. Next, `3` produces the stack `+ 2 (* 3 4) 3`. Finally, `list` produces the stack `(+ 2 (* 3 4))`, containing the final list at the top of the stack. It is possible to compare atoms using the word `eq?`. The word `eq?` consumes the two top-most elements in a stack of the form `u v` where `u` and `v` are the atoms to compare, and pushes to the stack `-1` if the atoms are equal, `0` otherwise. For instance, ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} `+ `+ eq? // pushes -1 to the stack `+ `- eq? // pushes 0 to the stack ``` For advanced details about atoms, see the [Atoms section](/languages/fift/whitepaper#2-17-atoms) in the Fift whitepaper. ## Slices A `Slice` is a read-only view of a portion of a `Cell`. Fift uses the syntax `b{}` and `x{}` for defining slices. `b{}` pushes a slice into the stack that contains no references and up to 1023 data bits specified in ``, which must be a string consisting only of the characters `0` and `1`. `x{}` pushes a slice into the stack that contains no references and up to 1023 data bits specified in ``. More precisely, each hex digit from `` is transformed into four binary digits in the usual fashion. After that, if the last character of `` is an underscore `_`, then all trailing binary zeroes and the binary digit immediately preceding them are removed from the resulting binary string. An empty `Slice` can be pushed into the stack by `b{}` or `x{}`. For example, `b{00011101}` and `x{1d}` both push the same `Slice` consisting of eight data bits and no references. Similarly, `b{111010}` and `x{EA_}` push the same `Slice` consisting of six data bits. For `x{EA_}` the binary representation of `EA` is `11101010`, but since `EA_` has a final underscore, the trailing zeroes in the binary representation are removed together with the binary digit immediately preceding them, i.e., the final `10`, producing `111010`. To construct a `Slice` with some `Cell` references, Fift provides the word `|_`, which consumes the top-most two elements in a stack of the form `s s'`, where `s` and `s'` are slices. It crates a new slice `s''` obtained from `s` by appending a new reference to a cell containing `s'`; then, pushes `s''` into the stack. For instance, the following code creates a cell containing the slice `b{001}`, and attaches the cell as a reference to the slice `b{101}`: ```fift theme={"theme":{"light":"github-light-default","dark":"dark-plus"},"languages":{"custom":["/resources/grammars/tolk.tmLanguage.json","/resources/grammars/tlb.tmLanguage.json","/resources/grammars/fift.tmLanguage.json","/resources/grammars/tasm.tmLanguage.json","/resources/grammars/func.tmLanguage.json"]}} b{101} b{001} |_ ``` First, `b{101} b{001}` pushes the two slices in that order. Next, `|_` consumes the two slices. Then, `|_` copies `b{101}` into a new slice `s` and creates a cell `c` containing `b{001}`. Finally, `|_` attaches `c` as a reference to `s` and pushes `s` into the stack. For advanced details about slices, see the [Slices section](/languages/fift/whitepaper#5-1-slice-literals) in the Fift whitepaper. For a list of words for manipulating slices and reading their contents, see the list of common slice words page.