Infix — Readable Math and Data Processing for Clojure

"Making Clojure more readable for data science, business logic, and mathematical expressions."

Infix is a Clojure library that adds optional infix notation for mathematical expressions, comparisons, boolean logic, and data processing pipelines — while compiling to standard Clojure code.

Key Features

• 🧮 Mathematical Expressions: Write a * b + c / d instead of (+ (* a b) (/ c d))
• 🔄 Data Pipelines: Use -> and ->> as infix operators for readable transformations
• ⚡ Arrow Lambdas: Clean x => x * 2 syntax for anonymous functions
• 🔧 Function Definitions: infix-defn for functions with infix bodies
• 🎯 Early Returns: Guard clause patterns with return statement
• 📞 Function Calls: Familiar fn(args) syntax within expressions
• 🏗️ OOP Interop: Java method chaining with obj -> .method() syntax
• 💯 Zero Runtime Overhead: Everything compiles to standard Clojure forms

Transform readable code like this:

(infix-defn calculate-discount [subtotal tier quantity]
  (let [rate (cond (tier = :premium) 0.15
                   (quantity >= 10) 0.10  
                   :else 0.05)]
    (min (subtotal * rate) 100)))

Into efficient Clojure that runs at full speed.

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✨ Goals

• Keep Clojure semantics — compile to normal Clojure forms.
• Make math and pipelines readable without prefix clutter.
• Allow gradual adoption: you can mix infix and regular Clojure.
• Serve as domain language for data transformations, analytics, pricing, and ETL pipelines.

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⚙️ Installation

Add as a git dependency in deps.edn:

;; deps.edn
io.github.flexiana/infix {:git/url "https://github.com/Flexiana/infix"
                           :git/tag "v1.0.0"
                           :git/sha "SHORT_SHA"}

Or clone and use locally:

git clone https://github.com/Flexiana/infix.git
cd infix
lein install  ;; installs to local Maven repo

Then add to your project:

;; deps.edn
com.flexiana/infix {:local/root "/path/to/infix"}

;; or project.clj after lein install
[com.flexiana/infix "1.0.0"]

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🧠 Core Concepts

1. Infix expressions

Use (infix …) to write math, comparisons, and logic in natural order.

(infix a * b + c / d)
;; => (+ (* a b) (/ c d))

(infix x < y and y <= z)
;; => (and (< x y) (<= y z))

(infix not done or a = b)
;; => (or (not done) (= a b))

Supported operators:

Category	Operators	Precedence
Threading	-> ->> some-> some->>	Lowest (0.05)
Boolean	and or not	Low (0.1-0.8)
Comparison	= not= < <= > >=	Medium (0.5)
Arithmetic	+ - * /	High (1-2)

Grouping with normal parentheses works:

(infix (a * (b + c)) / d)

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2. Threading Macros as Infix Operators

The infix library treats Clojure's threading macros (->, ->>, some->, some->>) as infix operators with the lowest precedence, enabling natural data transformation pipelines.

Understanding Threading Operator Precedence

Threading operators have lowest precedence (0.05), meaning they bind last:

;; This expression:
(infix data -> :key + 5 ->> (map inc))

;; Is parsed as:
(infix (data -> :key + 5) ->> (map inc))

;; Not as:
(infix data -> (:key + 5) ->> (map inc))

This design allows mathematical expressions to be computed before threading:

;; Calculate first, then thread
(infix [1 2 3] ->> count * 2 + 1)
;; => (+ (* (count [1 2 3]) 2) 1) => 7

;; Comparison result gets threaded  
(infix 5 > 3 -> (if true "yes" "no"))
;; => (if (> 5 3) "yes" "no") => "yes"

Thread-First (->) vs Thread-Last (->>)

Thread-First (->): Insert result as first argument

(infix {:a 1 :b 2} -> (assoc :c 3) -> (get :c))
;; => (-> {:a 1 :b 2} (assoc :c 3) (get :c))
;; => (get (assoc {:a 1 :b 2} :c 3) :c) => 3

;; Perfect for data access chains
(infix user -> :profile -> :address -> :city)
;; => (-> user :profile :address :city)

Thread-Last (->>): Insert result as last argument

(infix [1 2 3 4 5] ->> (filter even?) ->> (map #(* % 2)))
;; => (->> [1 2 3 4 5] (filter even?) (map #(* % 2)))
;; => (map #(* % 2) (filter even? [1 2 3 4 5])) => (4 8)

;; Perfect for collection transformations
(infix data ->> (map transform) ->> (filter valid?) ->> (take 10))

Nil-Safe Threading (some->, some->>)

Handle nil values gracefully in pipelines:

;; Returns nil if any step returns nil
(infix {:user {:name "john"}} some-> :user some-> :name some-> .toUpperCase)
;; => "JOHN"

(infix {:user nil} some-> :user some-> :name some-> .toUpperCase)  
;; => nil (stops at :user step)

;; Useful for deep data access
(infix request some-> :params some-> :user-id some-> parse-int)

Mixed Threading Patterns

Combine -> and ->> in the same expression:

;; Access data first, then transform collection
(infix {:data [1 2 3 4 5]} -> :data ->> (filter odd?) ->> (reduce +))
;; => (->> (-> {:data [1 2 3 4 5]} :data) (filter odd?) (reduce +)) => 9

;; Build data structure, then process
(infix (range 10) ->> (map #(* % %)) -> vec -> (nth 3))
;; => (nth (vec (map #(* % %) (range 10))) 3) => 9

Threading with All Other Operators

Threading works seamlessly with arithmetic, comparisons, and boolean logic:

;; Threading with arithmetic (threading happens first due to precedence)
(infix ([1 2 3] ->> count) + 5)
;; => (+ (count [1 2 3]) 5) => 8

;; Threading with comparisons  
(infix ([1 2 3 4 5] ->> count) > 3)
;; => (> (count [1 2 3 4 5]) 3) => true

;; Threading with boolean logic
(infix ([1 2] ->> empty?) or ([3 4] ->> empty?))
;; => (or (empty? [1 2]) (empty? [3 4])) => false

;; Complex business logic with threading
(infix {:transactions txns}
       -> :transactions
       ->> (filter #((:type %) = :debit))
       ->> (map :amount)
       ->> (reduce +)
       -> (> 1000))
;; Check if total debits exceed $1000

Advanced Threading Examples

;; ETL pipeline with multiple threading operators
(infix raw-data
       -> :payload               ; Extract payload
       ->> (map parse-record)    ; Transform each record  
       ->> (filter valid?)       ; Filter valid records
       -> (group-by :category)   ; Group by category
       -> vals                   ; Get category groups
       ->> (map count)           ; Count each group  
       ->> (reduce max))         ; Find largest group

;; Error-safe data processing
(infix user-input
       some-> .trim()            ; Safely trim if not nil
       some-> parse-json         ; Parse JSON if string exists
       some-> :data              ; Extract data if parse succeeded
       some->> (map process)     ; Process items if data is collection
       some->> (take 10))        ; Take first 10 if processing succeeded

Key Insight: Threading operators in infix notation make data transformation pipelines read left-to-right like natural language, while maintaining all the power of Clojure's threading macros.

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3. Operator Precedence Rules

Understanding precedence ensures expressions work as expected:

Precedence Order (High to Low):

1. Arithmetic (* /) - Highest precedence (2)
2. Arithmetic (+ -) - High precedence (1)
3. Comparison (< <= > >= = not=) - Medium precedence (0.5)
4. Boolean (and) - Low precedence (0.2)
5. Boolean (or) - Lower precedence (0.1)
6. Threading (-> ->> some-> some->>) - Lowest precedence (0.05)

Precedence Examples:

;; Arithmetic first, then comparison, then boolean
(infix a + b * c > d and e < f)
;; => (and (> (+ a (* b c)) d) (< e f))

;; Threading happens last
(infix [1 2 3] ->> count + 5 > 10)  
;; => (> (+ (count [1 2 3]) 5) 10)

;; Use parentheses to override precedence
(infix (a + b) * (c + d))
;; => (* (+ a b) (+ c d))

Left-to-Right Evaluation: All operators are left-associative, so they evaluate left-to-right:

(infix a - b - c)      ; => (- (- a b) c)
(infix a -> f -> g)    ; => (-> (-> a f) g)  
(infix a and b and c)  ; => (and (and a b) c)

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4. Arrow Lambdas

Use => syntax for clean, readable anonymous functions:

Single Parameter

(map (infix x => x * x) [1 2 3])
;; => [1 4 9]

(filter (infix x => x > 5) [1 5 10 15])
;; => (10 15)

Multi-Parameter

(reduce (infix (acc x) => acc + x) 0 [1 2 3 4])
;; => 10

((infix (x y) => (x + y) * 2) 3 4)
;; => 14

Complex Expressions

(map (infix x => x * x + 2 * x + 1) [1 2 3])
;; => [4 9 16]  ; (x+1)²

;; Mixed with threading
(map (infix x => x -> str -> clojure.string/upper-case) [1 2 3])
;; => ["1" "2" "3"]

Perfect Disambiguation

Arrow lambdas (=>) are completely separate from threading (->):

;; Arrow lambda
(map (infix x => x * 2) [1 2 3])  ; => [2 4 6]

;; Threading
(infix data -> :key ->> (map inc))

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5. Function Definitions with infix-defn

Define functions with infix expressions in their bodies:

Basic Functions

(infix-defn square [x] x * x)
(square 4)  ; => 16

(infix-defn add-multiply [x y z] x + y * z)
(add-multiply 1 2 5)  ; => 11  (1 + (2 * 5))

Functions with Comparisons and Logic

(infix-defn in-range? [x min-val max-val] 
  x >= min-val and x <= max-val)
(in-range? 5 1 10)  ; => true

(infix-defn greater-than-ten? [x] x > 10)
(greater-than-ten? 15)  ; => true

Functions with Threading Operations

(infix-defn process-users [users]
  users 
  ->> (filter :active?)
  ->> (map :name)
  ->> (take 10)
  ->> sort)

(infix-defn calculate-discount [order]
  (:total order)
  -> (* 0.1)        ; 10% discount
  -> (max 5)        ; minimum $5 discount  
  -> (min 100))     ; maximum $100 discount

Functions with Docstrings

(infix-defn circle-area
  "Calculate the area of a circle given radius"
  [radius]
  3.14159 * radius * radius)

Complex Mathematical Functions

(infix-defn quadratic [a b c x]
  a * x * x + b * x + c)

(quadratic 1 2 3 1)  ; => 6  (1*1*1 + 2*1 + 3)

Early Returns with return

Use the return statement for early exits from functions:

(infix-defn safe-divide [x y]
  (when (= y 0) (return nil))
  (/ x y))

(safe-divide 10 0)   ; => nil
(safe-divide 10 2)   ; => 5

;; Guard clauses pattern
(infix-defn validate-age [age]
  (when (age < 0) (return "Invalid: negative age"))
  (when (age > 150) (return "Invalid: too old")) 
  (when (age < 18) (return "Minor"))
  "Adult")

;; Multiple return points
(infix-defn categorize-number [n]
  (when (n < 0) (return "negative"))
  (when (n = 0) (return "zero"))
  (when (n <= 10) (return "small positive"))
  "large positive")

Note: Early returns work by throwing and catching special exceptions internally, providing clean non-local exit semantics without affecting normal exception handling.

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6. Function Call Syntax

Use familiar fn(args) syntax within infix expressions:

Basic Function Calls

(infix max(3, 5))           ; => 5
(infix min(1, 2))           ; => 1
(infix count("hello"))      ; => 5
(infix Math/sqrt(9))        ; => 3.0

Function Calls with Infix Operators

(infix max(3, 5) + min(1, 2))        ; => 6  (5 + 1)
(infix Math/sqrt(9) * 2)             ; => 6.0
(infix count("hello") > 3)           ; => true

Method Calls

(infix .toUpperCase("hello"))        ; => "HELLO"
(infix .length("hello"))             ; => 5
(infix .substring("hello", 0, 2))    ; => "he"

Function Calls with Threading

(infix "hello" -> .toUpperCase() -> .length())  ; => 5
(infix [1 2 3] ->> (map(#(* % 2))) ->> vec())   ; => [2 4 6]

In Function Definitions

(infix-defn distance [x1 y1 x2 y2]
  (infix Math/sqrt(Math/pow(x2 - x1, 2) + Math/pow(y2 - y1, 2))))

(infix-defn string-processor [s]
  (infix .toUpperCase(.trim(s))))

Note: Function call syntax transforms fn(args) to standard Clojure (fn args) during parsing, maintaining full compatibility while providing familiar syntax.

It is required not to use any whitespace between the function name and the opening parenthesis. For example, Math/sqrt(9) is valid, but Math/sqrt (9) is not.

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7. OOP Interop and Method Calls

Seamless Java interop with familiar object-oriented syntax:

Method Chaining with Threading

;; Java-style method chaining using -> operator
(infix "hello" -> .toUpperCase() -> (.substring 0 3))  ; => "HEL"

(infix obj -> (.setName "John") -> (.setSurname "Newman") -> .save())
;; => (-> obj (.setName "John") (.setSurname "Newman") (.save))

;; StringBuilder example
(infix (StringBuilder. "Hello") 
       -> (.append " ") 
       -> (.append "World") 
       -> .toString())  ; => "Hello World"

OOP in Function Definitions

(infix-defn clean-text [text]
  (text -> .trim() -> .toLowerCase()))

(infix-defn build-greeting [name]
  (StringBuilder. "Hello, ") 
  -> (.append name) 
  -> (.append "!") 
  -> .toString()))

(infix-defn string-length-plus [s n]
  ((.length s) + n))

OOP with Infix Operators

;; Method results in mathematical expressions
(infix (.length "hello") + 5)           ; => 10
(infix (.getAge user) > 18)             ; => true/false  
(infix (.isValid obj) and (.isActive obj))  ; => boolean result

Note: The infix library supports Java interop through Clojure's standard method call syntax (.method) combined with threading operators for elegant method chaining.

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🧪 Complete Examples

1. Mathematical Expressions

;; Simple arithmetic with proper precedence
(infix a * b + c / d)
;; => (+ (* a b) (/ c d))

;; Complex mathematical formulas
(infix (x + y) * (z - w))
;; => (* (+ x y) (- z w))

;; Function calls in math expressions
(infix Math/sqrt(a * a + b * b) + c)
;; => (+ (Math/sqrt (+ (* a a) (* b b))) c)

2. Data Processing Pipelines

;; Thread-last for collection transformations
(infix users
       ->> (filter #((:age %) > 18))
       ->> (map :email)  
       ->> (take 10)
       ->> set)
;; => (set (take 10 (map :email (filter #(> (:age %) 18) users))))

;; Thread-first for data access and manipulation
(infix {:data [1 2 3 4 5]} 
       -> :data 
       ->> (filter odd?) 
       ->> (reduce +))
;; => (reduce + (filter odd? (:data {:data [1 2 3 4 5]})))

3. Comprehensive Business Logic

Combining all features in realistic business functions:

;; Complete order processing with all infix features
(infix-defn process-order [order customer-tier]
  ;; Early validation with guard clauses
  (when (not (:items order)) (return {:error "No items"}))
  (when ((:total order) <= 0) (return {:error "Invalid total"}))
  
  ;; Calculate discount using comparisons and math
  (let [base-discount (cond (customer-tier = :premium) 0.15
                           ((:total order) >= 100) 0.10
                           :else 0.05)
        
        ;; Function calls with arithmetic  
        discount-amount (min((:total order) * base-discount, 50))
        
        ;; String processing with method chaining
        customer-name ((:customer-name order) 
                      -> .trim() 
                      -> .toLowerCase())
        
        ;; Complex pipeline with threading
        processed-items ((:items order)
                        ->> (filter #((:price %) > 0))
                        ->> (map #(assoc % :discounted-price 
                                    ((:price %) * (1 - base-discount))))
                        ->> (sort-by :discounted-price)
                        ->> reverse)]
    
    ;; Return comprehensive result
    {:customer customer-name
     :discount-rate base-discount
     :discount-amount discount-amount  
     :final-total ((:total order) - discount-amount)
     :items processed-items
     :valid true}))

;; Usage example
(let [order {:total 120
             :customer-name "  JOHN DOE  "
             :items [{:name "Widget A" :price 50}
                     {:name "Widget B" :price 70}]}
      result (process-order order :premium)]
  (:final-total result))  ; => 102.0 (120 - 18 discount)

4. Advanced Data Analytics

;; Statistical calculations with arrow lambdas
(infix-defn analyze-sales-data [sales]
  (let [;; Filter and transform with threading
        valid-sales (sales 
                    ->> (filter #((:amount %) > 0))
                    ->> (filter #((:date %) != nil)))
        
        ;; Mathematical aggregations with function calls
        total-revenue (valid-sales 
                      ->> (map :amount) 
                      ->> (reduce +))
        
        average-sale (total-revenue / count(valid-sales))
        
        ;; Complex filtering with lambda functions
        high-value-sales (valid-sales 
                         ->> (filter (infix sale => (:amount sale) > average-sale))
                         ->> count)
        
        ;; String manipulation and formatting
        summary-text (StringBuilder("Sales Analysis: ")
                     -> (.append count(valid-sales))
                     -> (.append " sales, $")  
                     -> (.append total-revenue)
                     -> (.append " revenue")
                     -> .toString())]
    
    {:total-sales count(valid-sales)
     :total-revenue total-revenue
     :average-sale average-sale
     :high-value-count high-value-sales
     :high-value-percentage (high-value-sales * 100.0 / count(valid-sales))
     :summary summary-text}))

5. Complex Conditional Logic with All Features

;; Risk assessment combining everything
(infix-defn assess-transaction-risk [transaction user]
  ;; Guard clauses with early returns
  (when (not transaction) (return {:risk :high :reason "Missing transaction"}))
  (when (not user) (return {:risk :high :reason "Missing user"}))
  
  (let [;; Mathematical risk scoring
        amount-risk (cond ((:amount transaction) > 10000) 0.8
                         ((:amount transaction) > 1000) 0.4  
                         :else 0.1)
        
        ;; Time-based calculations with method chaining
        hours-since ((:timestamp transaction)
                    -> .getTime()
                    -> (- (System/currentTimeMillis))
                    -> (/ 3600000))  ; Convert to hours
        
        time-risk (cond (hours-since < 1) 0.6    ; Very recent
                       (hours-since > 24) 0.3    ; Older transaction  
                       :else 0.2)
        
        ;; User history analysis with pipelines
        user-score ((:transaction-history user)
                   ->> (filter #((:status %) = :completed))
                   ->> (map :amount)
                   ->> (filter (infix amt => amt > 0))
                   ->> count
                   -> (max 1)              ; Avoid division by zero
                   -> (min 100)            ; Cap the score
                   -> (/ 100.0))           ; Normalize to 0-1
        
        ;; Geographic risk with string operations
        location-risk (let [country ((:location user) -> .toLowerCase())]
                       (cond (country = "us") 0.1
                             (country = "ca") 0.1  
                             :else 0.3))
        
        ;; Combined risk calculation
        total-risk (amount-risk + time-risk + location-risk - user-score)
        normalized-risk (max(0, min(1, total-risk)))
        
        ;; Risk categorization
        risk-level (cond (normalized-risk >= 0.7) :high
                        (normalized-risk >= 0.4) :medium
                        :else :low)]
    
    {:risk risk-level
     :score normalized-risk
     :factors {:amount amount-risk
               :timing time-risk
               :location location-risk
               :user-history user-score}
     :recommendation (cond (risk-level = :high) "Block transaction"
                          (risk-level = :medium) "Require additional verification"
                          :else "Approve transaction")}))

This example demonstrates:

• Mathematical expressions: amount-risk calculations with proper precedence
• Function calls: count(valid-sales), min(1, total-risk)
• Threading pipelines: -> for data access, ->> for collection processing
• Method chaining: .getTime() and .toLowerCase() on Java objects
• Arrow lambdas: (infix amt => amt > 0) for filtering
• Early returns: Guard clauses with return statements
• Complex comparisons: Multi-condition cond statements with infix operators
• String building: StringBuilder with method chaining

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⚖️ Design Philosophy

1. Opt-in readability: Clojure stays pure; infix is a macro layer.
2. No string parsing: all syntax is real data (lists and symbols).
3. Functional parity: everything compiles to normal Clojure forms.
4. Composable: infix, infix-let, and infix-defn can nest freely.
5. Safe early returns: no hidden mutations or dynamic vars.
6. Gradual expansion: new tokens can be added as tables, not syntax hacks.

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🎯 Current Status: Version 1.0.0

The infix library provides comprehensive infix notation support for Clojure!

✅ Core Features

• Mathematical Expressions: Full arithmetic with proper precedence (+ - * /)
• Comparisons & Logic: All comparison and boolean operators (= < > and or not)
• Threading Integration: Native support for -> ->> some-> some->>
• Arrow Lambdas: Clean x => expr syntax with perfect disambiguation
• Function Definitions: infix-defn with infix expressions in function bodies
• Early Returns: Guard clause patterns with return statement
• Function Call Syntax: Familiar fn(args) notation within expressions
• Java Interop: Method chaining with obj -> .method() syntax
• Zero Overhead: Everything compiles to standard Clojure forms

✅ Production Ready

• Comprehensive test coverage for all features
• Clean, maintainable codebase with proper separation of concerns
• Proper error handling and edge case management
• Full compatibility with existing Clojure code
• Extensible design for future enhancements

🔮 Future Enhancements

• Enhanced error messages with better syntax hints
• Collection operators (in, not-in) for membership testing
• Advanced pattern matching integration
• Performance optimizations for complex expressions

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⚡️ Example Session

user=> (require '[infix.core :refer :all])

user=> (macroexpand-1 '(infix 1 + 2 * 3))
(+ 1 (* 2 3))

user=> (infix 1 + 2 * 3)
7

user=> (infix [1 2 3 4 5] ->> (filter even?) ->> (map #(* % 2)) ->> vec)
[4 8]

user=> (infix {:user {:name "john"}} some-> :user some-> :name some-> .toUpperCase)
"JOHN"

user=> (infix 5 > 3 and 2 < 4)
true

user=> (map (infix x => x * x) [1 2 3 4])
(1 4 9 16)

user=> ((infix (x y) => x + y * 2) 3 4)
11

user=> (infix-defn square [x] x * x)
#'user/square

user=> (square 5)
25

user=> (infix-defn process-data [items] items ->> (filter :active?) ->> count)
#'user/process-data

user=> (process-data [{:active? true} {:active? false} {:active? true}])
2

user=> (infix-defn safe-divide [x y] (when (= y 0) (return nil)) (/ x y))
#'user/safe-divide

user=> (safe-divide 10 0)
nil

user=> (safe-divide 10 2)
5

user=> (infix max(3, 5) + min(1, 2))
6

user=> (infix count("hello") > 3)
true

user=> (infix (.toUpperCase "hello"))
"HELLO"

user=> (infix "hello" -> .toUpperCase() -> (.substring 0 3))
"HEL"

user=> (infix-defn greet-user [name] 
         (name -> .toUpperCase() -> (.concat "!")))
#'user/greet-user

user=> (greet-user "alice")
"ALICE!"

user=> (infix (StringBuilder. "hello") -> (.append " world") -> .toString())
"hello world"

user=> (infix (.length "hello") + 5)
10

user=> (infix-defn string-processor [text]
         (text -> .trim() -> .toLowerCase()))
#'user/string-processor

user=> (string-processor "  HELLO WORLD  ")
"hello world"

user=> ;; Complex example combining all features
user=> (infix-defn analyze-numbers [numbers]
         (when (numbers ->> empty?) (return {:error "No data"}))
         (let [avg (numbers ->> (reduce +) -> (/ count(numbers)))
               above-avg (numbers ->> (filter (infix n => n > avg)) ->> count)]
           {:average avg
            :above-average-count above-avg  
            :percentage (above-avg * 100.0 / count(numbers))}))
#'user/analyze-numbers

user=> (analyze-numbers [1 2 3 4 5])
{:average 3.0, :above-average-count 2, :percentage 40.0}

user=> ;; Threading with arithmetic and comparisons  
user=> (infix [10 20 30] ->> count * 2 + 1 > 5)
true

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🤓 Why

Clojure is beautiful, but for math-heavy or dataflow-heavy code, prefix notation hides intent.
Infix is not a new language — it’s a lens. It lets engineers, analysts, or business rule authors read logic naturally while keeping full Clojure semantics under the hood.

You can use it for:

• BI and ETL transformations
• Pricing and rules engines
• Numeric and ML prototypes
• Teaching Clojure to non-Lispers

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🧩 License

Apache License 2.0

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🪦 Disclaimer

This project commits Lisp heresy.
Use it to make your Clojure more readable — or to horrify your local REPL priest.