Translate A = -b c + d/e into Quadruples and Triples | AI Research

Translate $A = -b * (c + d)/e$ into Quadruples and Triples

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Sep 12, 2026

Intermediate Code: Quadruples vs Triples (3-Address Code)

Given the expression $A = -b * (c + d)/e,$ we translate it into intermediate representations:

keyword: An array of instructions of form $(op,arg1,arg2,result)$ .
keyword: An array of instructions of form $(op,arg1,arg2)$ where results are referenced by index.
keyword: IR where each instruction uses at most two operands plus an implicit destination.
keyword: A symbol (e.g., $t1$ ) storing intermediate results.
keyword: Rule that multiplication/division bind tighter than addition/subtraction.

A standard evaluation order that respects precedence is:

Compute the parenthesized sum $(c+d)$ .
Multiply by $b$ and apply the unary minus.
Divide by $e$ .
Assign to $A$ .

The key question is how unary minus is represented:

As a separate keyword: Often implemented as $t := -x$ or as $t := 0 - x$ . Below, we use an explicit unary operation $neg$ (common in textbooks/exercises), but I also show the alternative form using $0$ where needed.

Mermaid view of the data flow:

Construct triples (then map to quadruples)

1
Step 1
Create a temp for $c+d$ (call it $t1$ ).
2
Step 2
Compute $t2 = b * t1$ , then compute the unary negation $t3 = -t2$ .
3
Step 3
Compute $t4 = t3 / e$ .
4
Step 4
Final instruction sets $A = t4$ .

Triples Representation

In triples form, each instruction is stored as: $(op, arg1, arg2)$ and later instructions reference prior results by index. If the triple number is $i$ , its value can be referenced as $[i]$ .

We will build 4 computation triples (then a final assignment as a 5th “triple-like” form).

Let:

Triple 1: $t1 = c + d$
Triple 2: $t2 = b * t1$
Triple 3: $t3 = -t2$ (unary negation)
Triple 4: $t4 = t3 / e$
Triple 5: $A = t4$ (assignment)

Triples list

$(+, c, d)$ ⟹ value is $[1]=c+d$
$(*, b, [1])$ ⟹ $[2]=b*(c+d)$
$(neg, [2], \_)$ ⟹ $[3]=-([2])$
$(/, [3], e)$ ⟹ $[4]= -b*(c+d)/e$
$(=, A, [4])$ ⟹ assign

Note: Some conventions encode unary neg as $(neg,arg,\_)$ with a dummy second field. If your course uses $( - , 0, x)$ instead, see the alternative in the accordion.

Quadruples Representation

In quadruples form, each instruction is: $(op, arg1, arg2, result)$

We explicitly name temporaries as results of each instruction:

$t1, t2, t3, t4$

Quadruples table

#	op	arg1	arg2	result
1	+	c	d	t1
2	*	b	t1	t2
3	neg	t2	—	t3
4	/	t3	e	t4
5	=	A	t4	A

This is equivalent to:

t1 = c+d,\quad t2 = b\cdot t1,\quad t3 = -t2,\quad t4 = t3/e,\quad A=t4.

type="tip" title="Pro Tip: Choose a consistent unary minus convention" content="If your course disallows unary ops, rewrite negation as (−, 0, x). Then every operation becomes binary, making quadruples/triples uniform."

type="warning" title="Warning: Parentheses must be computed first" content="If you generate code that computes $b*c$ before $c+d$ , you violate the precedence implied by $(c+d)$ . Always start with the subexpression inside parentheses."

1: (+, c, d) 2: (*, b, [1]) 3: (neg, [2], _) 4: (/, [3], e) 5: (=, A, [4])

Common variations (to match your course format)

Computation Order Breakdown

How the IR instructions map to subexpressions

Expression Lowering Pipeline

Lower (c + d)

Create a temp: $t1=c+d$ "

Lower b * (c + d)

Create temp: $t2=b*t1$ "

Lower unary minus

Create temp: $t3=-t2$ "

Lower division by e

Create temp: $t4=t3/e$ "

Assign to A

Final: $A=t4$ "

Quadruples/Triples Quick Check

1 / 4

Question · Term

What is the difference between quadruples and triples?

Click to reveal

Answer · Definition

Quadruples store (op,arg1,arg2,result). Triples store (op,arg1,arg2) and reference results by index.

Knowledge Check

Question 1 of 4

Q1Single choice

In quadruple form, which tuple includes the destination/result field explicitly?

(op, arg1, arg2, result)

(op, arg1, arg2)

(result, op, arg1, arg2)

(arg1, arg2, op, result)

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Translate A=−b∗(c+d)/eA = -b * (c + d)/eA=−b∗(c+d)/e into Quadruples and Triples